Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M...Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.展开更多
Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp...Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.展开更多
By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As a...By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.展开更多
We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in t...We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.展开更多
A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed;in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommu...A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed;in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommutative phase-space are investigated and the Schrödinger-Pauli equation is found, knowing that the used methods for extracting the full phase-space noncommutative Dirac equation are, the Bopp-shift linear translation method, and the Moyal-Weyl product (*-product).展开更多
The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum f...The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.展开更多
We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizont...We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.展开更多
In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusio...In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.展开更多
In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix paramet...In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix parameter β_(ij)=∈_(ij)~kβ_k,is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS).Imposing some constraints on this particular transformation,we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations,and secondly that the two parameters are equivalent but with opposite sign,up to a dimension factor depending on the physical system under study.This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS.Within our framework,we treat some physical systems on NCQPS:free particle,harmonic oscillator,system of two-charged particles,Hydrogen atom.Among the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,representing the same particle in presence of a magnetic field=q~(-1).For the other examples,additional correction terms depending on β appear in the expression of the energy spectrum.Finally,in the two-particle system case,we emphasize the fact that for two opposite charges noncornmutativity is effectively feeled with opposite sign.展开更多
Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some ...Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.展开更多
We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative addit...We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.展开更多
For the first time we construct the eigenstate ｜τ〉 of noncommutatlve coordinate. It turns out that｜τ〉 is an entangled state in the ordinary space. Remarkably, its Schmidt decomposition has definite expression in...For the first time we construct the eigenstate ｜τ〉 of noncommutatlve coordinate. It turns out that｜τ〉 is an entangled state in the ordinary space. Remarkably, its Schmidt decomposition has definite expression in the coordinate representation and the momentum representation. The 〈τ｜ representation can simplify some calculations for obtaining energy level of two-dimensional oscillator in noncommutative space.展开更多
The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical ar...The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical argument showing that the main manifestation of dark matter in connection with flat galactic rotation curves is also a consequence of noncommutative geometry. The latter case requires an examination of the local effect of noncommutative geometry and the subsequent extension to the global phenomenon of an accelerating Universe.展开更多
While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null...While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.展开更多
We consider a system of N particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine t...We consider a system of N particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding internal energy and heat capacity where different corrections are obtained. In analogy with the magnetic field case, we define an effective magnetization and study its susceptibility in terms of the noncommutative parameter θ.By introducing the chemical potential, we investigate the Bose-Einstein condensation for the present system. Different limiting cases related to the temperature and θ will be analyzed as well as some numerical illustration will be presented.展开更多
The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphat...The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative(NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.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
We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state repres...We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.展开更多
A method for calculating the radiation spectrum of an arbitrary black holes was recently proposed by Ma et al.,[Europhys.Lett.122(2018) 30001] in which a non-thermal spectrum of a black hole can be obtained from its e...A method for calculating the radiation spectrum of an arbitrary black holes was recently proposed by Ma et al.,[Europhys.Lett.122(2018) 30001] in which a non-thermal spectrum of a black hole can be obtained from its entropy using an approach based on canonical typicality.The non-thermal spectrum of a black hole enables a nonzero correlation between the black hole and its radiation, which can ensure that information is conserved during black hole evaporation.In this paper, by using the Kantowski-Sachs metric and Feynman-Hibbs procedure, the entropy of a noncommutative quantum black hole is calculated based on the Wheeler-DeWitt equation.Then, the radiation spectrum of the noncommutative quantum black hole is studied based on canonical typicality method.At last, the correlation between the radiation spectra is calculated.It is shown that the noncommutative effect increases the correlation among radiation and the information remains conserved for noncommutative quantum black holes.展开更多
基金supported by the National Natural Science Foundation of China (11071190)
文摘Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.
文摘Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.
基金Supported by the China Pcetdoctoral Science Foundation by a grant from Henan University(05YBZR014)Supported by the Tianyuan Foundation for Mathematics of National Natural Science Foundation of China(10626016)
文摘By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.
文摘We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.
文摘A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed;in the present work the basic properties of the Dirac hamiltonian in the FW representation in the noncommutative phase-space are investigated and the Schrödinger-Pauli equation is found, knowing that the used methods for extracting the full phase-space noncommutative Dirac equation are, the Bopp-shift linear translation method, and the Moyal-Weyl product (*-product).
基金Supported by the Natural Science Foundation of Sichuan Education Committee under Grant No.08ZA038
文摘The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.
基金The project supported by National Natural Science Foundation of China under Grant No.10626016China Postdoctor Science Foundation of Henan University under Grant No.05YBZR014
文摘We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.
文摘In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.
文摘In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix parameter β_(ij)=∈_(ij)~kβ_k,is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS).Imposing some constraints on this particular transformation,we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations,and secondly that the two parameters are equivalent but with opposite sign,up to a dimension factor depending on the physical system under study.This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS.Within our framework,we treat some physical systems on NCQPS:free particle,harmonic oscillator,system of two-charged particles,Hydrogen atom.Among the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,representing the same particle in presence of a magnetic field=q~(-1).For the other examples,additional correction terms depending on β appear in the expression of the energy spectrum.Finally,in the two-particle system case,we emphasize the fact that for two opposite charges noncornmutativity is effectively feeled with opposite sign.
基金Supported by the National Natural Science Foundation of China under Grant No.11071157Shanghai Leading Academic Discipline Project under Grant No.J50101Beijing Natural Science Foundation under Grant No.1101024 and PHR(IHLB)
文摘Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.
文摘We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.
基金The project supported by Specialized Research Fund for the Doctorial Progress of Higher Education （SRFDP） under Grant No. 2004035819
文摘For the first time we construct the eigenstate ｜τ〉 of noncommutatlve coordinate. It turns out that｜τ〉 is an entangled state in the ordinary space. Remarkably, its Schmidt decomposition has definite expression in the coordinate representation and the momentum representation. The 〈τ｜ representation can simplify some calculations for obtaining energy level of two-dimensional oscillator in noncommutative space.
文摘The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical argument showing that the main manifestation of dark matter in connection with flat galactic rotation curves is also a consequence of noncommutative geometry. The latter case requires an examination of the local effect of noncommutative geometry and the subsequent extension to the global phenomenon of an accelerating Universe.
文摘While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.
基金support provided by the Saudi Center for Theoretical Physics (SCTP)
文摘We consider a system of N particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding internal energy and heat capacity where different corrections are obtained. In analogy with the magnetic field case, we define an effective magnetization and study its susceptibility in terms of the noncommutative parameter θ.By introducing the chemical potential, we investigate the Bose-Einstein condensation for the present system. Different limiting cases related to the temperature and θ will be analyzed as well as some numerical illustration will be presented.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11465006 and 11565009
文摘The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative(NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.
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 Nos 11405060 and 11571119
文摘We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.
基金Supported by the National Natural Science Foundation of China under Grant No.11647060Shaanxi Youth Outstanding Talent Support Planthe Fundamental Research Funds of Xianyang Normal University under Grant Nos.15XSYK034 and XSYGG201802
文摘A method for calculating the radiation spectrum of an arbitrary black holes was recently proposed by Ma et al.,[Europhys.Lett.122(2018) 30001] in which a non-thermal spectrum of a black hole can be obtained from its entropy using an approach based on canonical typicality.The non-thermal spectrum of a black hole enables a nonzero correlation between the black hole and its radiation, which can ensure that information is conserved during black hole evaporation.In this paper, by using the Kantowski-Sachs metric and Feynman-Hibbs procedure, the entropy of a noncommutative quantum black hole is calculated based on the Wheeler-DeWitt equation.Then, the radiation spectrum of the noncommutative quantum black hole is studied based on canonical typicality method.At last, the correlation between the radiation spectra is calculated.It is shown that the noncommutative effect increases the correlation among radiation and the information remains conserved for noncommutative quantum black holes.
