IrO2 and IrRuOx(Ir:Ru 60:40 at%),supported by 50 wt%onto titania nanotubes(TNTs)and(3 at%Nb)Nb-doped titania nanotubes(Nb-TNTs),as electrocatalysts for the oxygen evolution reaction(OER),were synthesized and character...IrO2 and IrRuOx(Ir:Ru 60:40 at%),supported by 50 wt%onto titania nanotubes(TNTs)and(3 at%Nb)Nb-doped titania nanotubes(Nb-TNTs),as electrocatalysts for the oxygen evolution reaction(OER),were synthesized and characterized by means of structural,surface analytical and electrochemical techniques.Nb doping of titania significantly increased the surface area of the support from 145(TNTs)to 260 m2g-1(Nb-TNTs),which was significantly higher than those of the Nb-doped titania supports previously reported in the literature.The surface analytical techniques showed good dispersion of the catalysts onto the supports.The X-ray photoelectron spectroscopy analyses showed that Nb was mainly in the form of Nb(IV)species,the suitable form to behave as a donor introducing free electrons to the conduction band of titania.The redox transitions of the cyclic voltammograms,in agreement with the XPS results,were found to be reversible.Despite the supported materials presented bigger crystallite sizes than the unsupported ones,the total number of active sites of the former was also higher due to their better catalyst dispersion.Considering the outer and the total charges of the cyclic voltammograms in the range 0.1–1.4 V,stability and electrode potentials at given current densities,the preferred catalyst was Ir O2 supported on the Nb-TNTs.The electrode potentials corresponding to given current densities were between the smallest ones given in the literature despite the small oxide loading used in this work and its Nb doping,thus making the Nb-TNTs-supported IrO2 catalyst a promising candidate for the OER.The good dispersion of IrO2,high specific surface area of the Nb-doped supports,accessibility of the electroactive centers,increased stability due to Nb doping and electron donor properties of the Nb(IV)oxide species were considered the main reasons for its good performance.展开更多
In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be c...In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).展开更多
The mechanism of obtaining the fractional angular momentum by employing a trapped atom which possesses a permanent magnetic dipole moment in the background of two electric fields is reconsidered by using an alternativ...The mechanism of obtaining the fractional angular momentum by employing a trapped atom which possesses a permanent magnetic dipole moment in the background of two electric fields is reconsidered by using an alternative method. Then, we generalize this model to a noncommutative plane. We show that there are two different mechanisms,which include cooling down the atom to the negligibly small kinetic energy and modulating the density of electric charges to the critical value to get the fractional angular momentum theoretically.展开更多
The associated Legendre polynomials play an important role in the central fields,but in the case of′the non-central field we have to introduce the universal associated Legendre polynomials P^m'l_′(x) when studyi...The associated Legendre polynomials play an important role in the central fields,but in the case of′the non-central field we have to introduce the universal associated Legendre polynomials P^m'l_′(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential.We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor(1-x^2)^(-p-1) as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction.The calculations are obtained systematically using some properties of the generalized hypergeometric series.展开更多
We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight.All qubits are linear superposit...We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight.All qubits are linear superposition,changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit.Classically,these states are just bytes represented in a binary matrix,having code combinations of 1 or 0 at all pixel locations.This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods.展开更多
We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation in...We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.展开更多
Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acc...Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π_(4) and geometric average Π_(4) is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter γ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S_(ABCDI), S_(ABCIDI), S_(ABICIDI) and S_(AIBICIDI) always decrease with the controllable angle θ, while the entropies S_(3-3 non), S_(3-2 non), S_(3-1 non) and S_(3-0 non) first increase with the angle θ and then decrease with it.展开更多
We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magne...We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magnetic fields we applied contain a magnetic and two electric fields.We find that when the atom is cooled down to the limit of the negligibly small kinetic energy,the atom behaves like an anyon because its angular momentum takes fractional values.The fractional part of the angular momentum is determined by both the magnetic and one of the electric fields.Roles electric and magnetic fields played are analyzed.展开更多
Using the single-mode approximation,we study entanglement measures including two independent quantities;i.e.,negativity and von Neumann entropy for a tripartite generalized Greenberger-Horne-Zeilinger(GHZ)state in non...Using the single-mode approximation,we study entanglement measures including two independent quantities;i.e.,negativity and von Neumann entropy for a tripartite generalized Greenberger-Horne-Zeilinger(GHZ)state in noninertial frames.Based on the calculated negativity,we study the whole entanglement measures named as the algebraic average π3-tangle and geometric average Π3-tangle.We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits.The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers.The results show that there will always exist entanglement,even if acceleration r arrives to infinity.The degree of entanglement for all 1-1 tangles are alwa.ys equal to zero,but 1-2 tangles always decrease with the acceleration parameter r.We notice that the von Neumann entropy increases with the number of the accelerated observers and SκΙζΙ(κ,ζ∈(A,B,C)) first increases and then decreases with the acceleration parameter r.This implies that the subsystem ρκΙζΙ is first more disorder and then the disorder will be reduced as the acceleration parameter r increases.Moreover,it is found that the von Neumann entropies SABCI,SABICI and SAIBICI always decrease with the controllable angle θ,while the entropies of the bipartite subsystems S2-2non(two accelerated qubits),S2-1non(one accelerated qubit) and S2-0non(without accelerated qubit) first increase with the angle θ and then decrease with it.展开更多
We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum inform...We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.展开更多
The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are brok...The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.展开更多
We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied.Two cases are considered.First, whe...We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied.Two cases are considered.First, when one qubit has uniform acceleration whilst the other three remain stationary.Second, when two qubits have nonuniform accelerations and the others stay inertial.The 1–1 tangle, 1–3 tangle, and whole entanglement measurements π4 and Π4, are studied and illustrated with graphics through their dependence on the acceleration parameter rd for the first case and rc and rd for the second case.It is found that the negativities(1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter rd or in the second case rc and rd increase, remaining a nonzero entanglement in the majority of the results.This means that the system will be always entangled except for special cases.It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when r > 0.472473.An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.展开更多
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation.Specifically,we have investigated the information entropy for a one-dimensional system with a schematic"...Calculations of the quantum information entropy have been extended to a non-analytically solvable situation.Specifically,we have investigated the information entropy for a one-dimensional system with a schematic"Landau"potential in a numerical way.Particularly,it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy.The calculated results also indicate that the position entropy S_(x)and the momentum entropy S_(p)at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state.In addition,the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.展开更多
Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated...Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated using the operator form of Taylor＇s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e.l＇ ≠ k＇ and m＇≠ n＇ .Their selection rules are a/so given. We also verify the correctness of those integral formulas numerically.展开更多
We first convert the angular Teukolsky equation under the special condition ofτ≠0,s≠0,m=0 into a confluent Heun differential equation(CHDE)by taking different function transformation and variable substitution.And t...We first convert the angular Teukolsky equation under the special condition ofτ≠0,s≠0,m=0 into a confluent Heun differential equation(CHDE)by taking different function transformation and variable substitution.And then according to the characteristics of both CHDE and its analytical solution expressed by a confluent Heun function(CHF),we find two linearly dependent solutions corresponding to the same eigenstate,from which we obtain a precise energy spectrum equation by constructing a Wronskian determinant.After that,we are able to localize the positions of the eigenvalues on the real axis or on the complex plane whenτis a real number,a pure imaginary number,and a complex number,respectively and we notice that the relation between the quantum number l and the spin weight quantum number s satisfies the relation l=∣s∣+n,n=0,1,2….The exact eigenvalues and the corresponding normalized eigenfunctions given by the CHF are obtained with the aid of Maple.The features of the angular probability distribution(APD)and the linearly dependent characteristics of two eigenfunctions corresponding to the same eigenstate are discussed.We find that for a real numberτ,the eigenvalue is a real number and the eigenfunction is a real function,and the eigenfunction system is an orthogonal complete system,and the APD is asymmetric in the northern and southern hemispheres.For a pure imaginary numberτ,the eigenvalue is still a real number and the eigenfunction is a complex function,but the APD is symmetric in the northern and southern hemispheres.Whenτis a complex number,the eigenvalue is a complex number,the eigenfunction is still a complex function,and the APD in the northern and southern hemispheres is also asymmetric.Finally,an approximate expression of complex eigenvalues is obtained when n is greater than∣s∣.展开更多
In this work we analyze the characteristics of quantum entangleinent of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will h...In this work we analyze the characteristics of quantum entangleinent of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity Nas (ρ^TA AB 1) increases with F but decreases with the variable y、while the variation of the negativity Nb1b11(ρ^TB1 B1B11)is opposite to that of the negativity N AB1(ρ^TA AB1). We also study the von Neumann entropies S(ρAB1) and S(ρB1B11)、We find that the S(ρAB1) increases with variable y but S(ρB1B11) is independent of it. However, both S(ρAB1) and S(ρB1B11) first decreases with F and then increases with it. The concurrences C(ρAB1) and C(ρB1B11) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.展开更多
Using the single-mode approximatiou,we first calculate entanglement measures such as negativity(1-3 and 11 tangles)and von Neumann entropy for a tetrapartite W-Class system in noninertial fiarne and then anal^e the wh...Using the single-mode approximatiou,we first calculate entanglement measures such as negativity(1-3 and 11 tangles)and von Neumann entropy for a tetrapartite W-Class system in noninertial fiarne and then anal^e the whole entanglement measures,the residualπ4 and geometricП4 average of tangles.Notice that the difference betweenπ4 andП4 is very small or disappears with the increasing accelerated observers.The entanglement properties are compared among the different cases from oue accelerated observer to four accelerated observers.The results show that there still exists entanglement for the complete system even when accelemtion r tends to infinity.The degree of entanglement is disappeared for the 1-1 tangle case when the acceleration r>0.472473.We reexamine the Unriih effect in noninertiai frames.It is shown that the entanglement system in which only one qubit is accelerated is more robust than those eutangled systems in whicli two or three or four qubits are accelerated.It is also found that the von Neumann entropy S of the total system always increases with the increasing accelerated observers,but the Sκξand Sκζδwith two and three involved noniuertial qubits first increases and then decreases with the acceleration parameter r,but they are equal to constants 1 and 0.811278 respectively for zero involved iioniiiertial qubit.展开更多
Quantum teleportation provides a ＂bodiless＂ way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. I...Quantum teleportation provides a ＂bodiless＂ way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a fourqubit cluster state of the form ｜Ф） 1234 = α｜10000） ＋β｜1010） ＋ γ｜0101） - η｜1111）, as the quantum channel, where the nonzero real numbers α, β, γ, and η satisfy the relation ｜α｜^2 ＋ ｜β｜^2 ＋ ｜γ｜^2 ＋ ｜η｜^2 = 1. With the introduction of an auxiliary qubit with state ｜0}, using a suitable unitary transformation and a positive-operator valued measure （POVM）, the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.展开更多
文摘IrO2 and IrRuOx(Ir:Ru 60:40 at%),supported by 50 wt%onto titania nanotubes(TNTs)and(3 at%Nb)Nb-doped titania nanotubes(Nb-TNTs),as electrocatalysts for the oxygen evolution reaction(OER),were synthesized and characterized by means of structural,surface analytical and electrochemical techniques.Nb doping of titania significantly increased the surface area of the support from 145(TNTs)to 260 m2g-1(Nb-TNTs),which was significantly higher than those of the Nb-doped titania supports previously reported in the literature.The surface analytical techniques showed good dispersion of the catalysts onto the supports.The X-ray photoelectron spectroscopy analyses showed that Nb was mainly in the form of Nb(IV)species,the suitable form to behave as a donor introducing free electrons to the conduction band of titania.The redox transitions of the cyclic voltammograms,in agreement with the XPS results,were found to be reversible.Despite the supported materials presented bigger crystallite sizes than the unsupported ones,the total number of active sites of the former was also higher due to their better catalyst dispersion.Considering the outer and the total charges of the cyclic voltammograms in the range 0.1–1.4 V,stability and electrode potentials at given current densities,the preferred catalyst was Ir O2 supported on the Nb-TNTs.The electrode potentials corresponding to given current densities were between the smallest ones given in the literature despite the small oxide loading used in this work and its Nb doping,thus making the Nb-TNTs-supported IrO2 catalyst a promising candidate for the OER.The good dispersion of IrO2,high specific surface area of the Nb-doped supports,accessibility of the electroactive centers,increased stability due to Nb doping and electron donor properties of the Nb(IV)oxide species were considered the main reasons for its good performance.
基金the support of PID2021-124341OB-C22 and PID2021-124341OB-C21(MCIU/AEI/FEDER,UE)ADITIMAT-CM(S2018/NMT-4411,Regional Government of Madrid and EU Structural Funds)+2 种基金the support of RYC-2017-21843the support of PEJD-2019-POST/IND-16119(Regional Government of Madrid and EU Structural Funds)FEI-EU-20-05(UCM)。
基金Supported by the project under Grant No.20180677-SIP-IPN,COFAA-IPN,Mexicopartially by the CONACYT project under Grant No.288856-CB-2016
文摘In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).
基金Supported by National Natural Science Foundation of China under Grant No.11465006partially supported by 20190234-SIP-IPN and the CONACyT under Grant No.288856-CB-2016
文摘The mechanism of obtaining the fractional angular momentum by employing a trapped atom which possesses a permanent magnetic dipole moment in the background of two electric fields is reconsidered by using an alternative method. Then, we generalize this model to a noncommutative plane. We show that there are two different mechanisms,which include cooling down the atom to the negligibly small kinetic energy and modulating the density of electric charges to the critical value to get the fractional angular momentum theoretically.
基金Supported by the National Natural Science Foundation of China under Grant No.11275165Partially by 20160978-SIP-IPN,Mexico
文摘The associated Legendre polynomials play an important role in the central fields,but in the case of′the non-central field we have to introduce the universal associated Legendre polynomials P^m'l_′(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential.We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor(1-x^2)^(-p-1) as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction.The calculations are obtained systematically using some properties of the generalized hypergeometric series.
基金Supported partially by the project 20150964-SIP-IPN,Mexico
文摘We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight.All qubits are linear superposition,changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit.Classically,these states are just bytes represented in a binary matrix,having code combinations of 1 or 0 at all pixel locations.This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975196)partially by SIP,Instituto Politecnico Nacional(IPN),Mexico(Grant No.20210414)。
文摘We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.
基金partially supported by the 20210414-SIPIPN, Mexico。
文摘Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π_(4) and geometric average Π_(4) is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter γ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S_(ABCDI), S_(ABCIDI), S_(ABICIDI) and S_(AIBICIDI) always decrease with the controllable angle θ, while the entropies S_(3-3 non), S_(3-2 non), S_(3-1 non) and S_(3-0 non) first increase with the angle θ and then decrease with it.
基金the National Natural Science Foundation of China(Grant No.11465006),20200981-SIP-IPN,and the CONACyT(Grant No.288856-CB-2016).
文摘We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magnetic fields we applied contain a magnetic and two electric fields.We find that when the atom is cooled down to the limit of the negligibly small kinetic energy,the atom behaves like an anyon because its angular momentum takes fractional values.The fractional part of the angular momentum is determined by both the magnetic and one of the electric fields.Roles electric and magnetic fields played are analyzed.
基金Supported by the CONACYT of Mexico under Grant No 288856-CB-2016,and the 20190234-SIP-IPN of Mexico
文摘Using the single-mode approximation,we study entanglement measures including two independent quantities;i.e.,negativity and von Neumann entropy for a tripartite generalized Greenberger-Horne-Zeilinger(GHZ)state in noninertial frames.Based on the calculated negativity,we study the whole entanglement measures named as the algebraic average π3-tangle and geometric average Π3-tangle.We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits.The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers.The results show that there will always exist entanglement,even if acceleration r arrives to infinity.The degree of entanglement for all 1-1 tangles are alwa.ys equal to zero,but 1-2 tangles always decrease with the acceleration parameter r.We notice that the von Neumann entropy increases with the number of the accelerated observers and SκΙζΙ(κ,ζ∈(A,B,C)) first increases and then decreases with the acceleration parameter r.This implies that the subsystem ρκΙζΙ is first more disorder and then the disorder will be reduced as the acceleration parameter r increases.Moreover,it is found that the von Neumann entropies SABCI,SABICI and SAIBICI always decrease with the controllable angle θ,while the entropies of the bipartite subsystems S2-2non(two accelerated qubits),S2-1non(one accelerated qubit) and S2-0non(without accelerated qubit) first increase with the angle θ and then decrease with it.
基金Project supported by the Iranian Nanotechnology Initiative Council(INIC)the 20180677-SIP-IPN,Mexicothe CONACYT 288856-CB-2016,Mexico
文摘We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.
基金supported partially by project 20150964SIP-IPN, COFAA-IPN, Mexico
文摘The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.
基金Project partially supported by the CONACYT,Mexico under the Grant No.288856-CB-2016partially by 20190234-SIP-IPN,Mexicopartially by the program XXVIII Verano de la Investigación Científica 2018 supported by the Academia Mexicana de Ciencias
文摘We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied.Two cases are considered.First, when one qubit has uniform acceleration whilst the other three remain stationary.Second, when two qubits have nonuniform accelerations and the others stay inertial.The 1–1 tangle, 1–3 tangle, and whole entanglement measurements π4 and Π4, are studied and illustrated with graphics through their dependence on the acceleration parameter rd for the first case and rc and rd for the second case.It is found that the negativities(1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter rd or in the second case rc and rd increase, remaining a nonzero entanglement in the majority of the results.This means that the system will be always entangled except for special cases.It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when r > 0.472473.An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.
基金Project supported by the National Natural Science Foundation of China(Grant No.11375005)partially by 20150964-SIP-IPN,Mexico
文摘Calculations of the quantum information entropy have been extended to a non-analytically solvable situation.Specifically,we have investigated the information entropy for a one-dimensional system with a schematic"Landau"potential in a numerical way.Particularly,it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy.The calculated results also indicate that the position entropy S_(x)and the momentum entropy S_(p)at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state.In addition,the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.
文摘Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated using the operator form of Taylor＇s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e.l＇ ≠ k＇ and m＇≠ n＇ .Their selection rules are a/so given. We also verify the correctness of those integral formulas numerically.
基金supported by the National Natural Science Foundation of China(Grant No.11975196)partially by 20220355-SIP,IPN。
文摘We first convert the angular Teukolsky equation under the special condition ofτ≠0,s≠0,m=0 into a confluent Heun differential equation(CHDE)by taking different function transformation and variable substitution.And then according to the characteristics of both CHDE and its analytical solution expressed by a confluent Heun function(CHF),we find two linearly dependent solutions corresponding to the same eigenstate,from which we obtain a precise energy spectrum equation by constructing a Wronskian determinant.After that,we are able to localize the positions of the eigenvalues on the real axis or on the complex plane whenτis a real number,a pure imaginary number,and a complex number,respectively and we notice that the relation between the quantum number l and the spin weight quantum number s satisfies the relation l=∣s∣+n,n=0,1,2….The exact eigenvalues and the corresponding normalized eigenfunctions given by the CHF are obtained with the aid of Maple.The features of the angular probability distribution(APD)and the linearly dependent characteristics of two eigenfunctions corresponding to the same eigenstate are discussed.We find that for a real numberτ,the eigenvalue is a real number and the eigenfunction is a real function,and the eigenfunction system is an orthogonal complete system,and the APD is asymmetric in the northern and southern hemispheres.For a pure imaginary numberτ,the eigenvalue is still a real number and the eigenfunction is a complex function,but the APD is symmetric in the northern and southern hemispheres.Whenτis a complex number,the eigenvalue is a complex number,the eigenfunction is still a complex function,and the APD in the northern and southern hemispheres is also asymmetric.Finally,an approximate expression of complex eigenvalues is obtained when n is greater than∣s∣.
文摘In this work we analyze the characteristics of quantum entangleinent of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity Nas (ρ^TA AB 1) increases with F but decreases with the variable y、while the variation of the negativity Nb1b11(ρ^TB1 B1B11)is opposite to that of the negativity N AB1(ρ^TA AB1). We also study the von Neumann entropies S(ρAB1) and S(ρB1B11)、We find that the S(ρAB1) increases with variable y but S(ρB1B11) is independent of it. However, both S(ρAB1) and S(ρB1B11) first decreases with F and then increases with it. The concurrences C(ρAB1) and C(ρB1B11) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.
基金supported by the CONACYT,Mexico under the Grant No.288856-CB-2016 and partially by 20190234-SIP-IPN,Mexico.
文摘Using the single-mode approximatiou,we first calculate entanglement measures such as negativity(1-3 and 11 tangles)and von Neumann entropy for a tetrapartite W-Class system in noninertial fiarne and then anal^e the whole entanglement measures,the residualπ4 and geometricП4 average of tangles.Notice that the difference betweenπ4 andП4 is very small or disappears with the increasing accelerated observers.The entanglement properties are compared among the different cases from oue accelerated observer to four accelerated observers.The results show that there still exists entanglement for the complete system even when accelemtion r tends to infinity.The degree of entanglement is disappeared for the 1-1 tangle case when the acceleration r>0.472473.We reexamine the Unriih effect in noninertiai frames.It is shown that the entanglement system in which only one qubit is accelerated is more robust than those eutangled systems in whicli two or three or four qubits are accelerated.It is also found that the von Neumann entropy S of the total system always increases with the increasing accelerated observers,but the Sκξand Sκζδwith two and three involved noniuertial qubits first increases and then decreases with the acceleration parameter r,but they are equal to constants 1 and 0.811278 respectively for zero involved iioniiiertial qubit.
文摘Quantum teleportation provides a ＂bodiless＂ way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a fourqubit cluster state of the form ｜Ф） 1234 = α｜10000） ＋β｜1010） ＋ γ｜0101） - η｜1111）, as the quantum channel, where the nonzero real numbers α, β, γ, and η satisfy the relation ｜α｜^2 ＋ ｜β｜^2 ＋ ｜γ｜^2 ＋ ｜η｜^2 = 1. With the introduction of an auxiliary qubit with state ｜0}, using a suitable unitary transformation and a positive-operator valued measure （POVM）, the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.
