The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for ...The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.展开更多
We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncert...We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncertainty principle and Matolcsi-Sz^ics uncertainty principle.展开更多
Jeans mass is regarded as a crucial factor in the study of nebula collapse.Astronomical data shows that Jeans mass is larger in theory than it is in observation.Someone mentioned that Jeans mass can be modified by usi...Jeans mass is regarded as a crucial factor in the study of nebula collapse.Astronomical data shows that Jeans mass is larger in theory than it is in observation.Someone mentioned that Jeans mass can be modified by using the generalized uncertainty principle(GUP).However,different physical backgrounds lead to different forms of GUP expression.In order to make the theoretical values of Jeans mass and its observed values match better,we use three distinct types of GUPs to correct Jeans mass in this paper.We find that the corrected Jeans masses are smaller than the uncorrected ones,where the Pedram corrected Jeans mass is the minimum and is close to the observed value.In addition,we consider the impact of temperature T and the GUP parameters(η,βandγ)for the corrected Jeans mass.展开更多
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-B...The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-Bessel transform.展开更多
In this paper,we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0<p,q≤∞.Furthermore,we establish Renyi entropic...In this paper,we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0<p,q≤∞.Furthermore,we establish Renyi entropic uncertainty principles for subfactor planar algebras.展开更多
In this paper,we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra,which heavily depend on the Clifford algebraic structure.The obtained inequalities furth...In this paper,we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra,which heavily depend on the Clifford algebraic structure.The obtained inequalities further lead to very general uncertainty inequalities on these modules.Some new phenomena arise,due to the non-commutative nature,the Clifford-valued inner products and the Krein geometry.Taking into account applications,special attention is given to the Dirac operator and the Howe dual pair Pin(m)×osp(1|2).Moreover,it is surprisingly to find that the recent highly nontrivial uncertainty relation for triple observables is indeed a direct consequence of our Cauchy–Schwarz inequality.This new observation leads to refined uncertainty relations in terms of the Wigner–Yanase–Dyson skew information for mixed states and other generalizations.These show that the obtained uncertainty inequalities on Clifford modules can be considered as new uncertainty relations for multiple observables.展开更多
We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality.The particle mass M is no ...We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality.The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle,which is interpreted as a regularized self-energy.We extend our results and find corrections to the relativistic particles using the Klein–Gordon,Proca and Dirac equations.An important finding is that we extract a form of the generalized uncertainty principle(GUP)from the corrected energy.This form of the GUP is shown to depend on the nature of particles;namely,for bosons(spin 0 and spin 1)we obtain a quadratic form of the GUP,while for fermions(spin 1/2)we obtain a linear form.The correlation we find between spin and GUP may offer insights for investigating quantum gravity.展开更多
We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the...We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off. And reveal the possible value of the minimum length.展开更多
In recent years,researchers have investigated the evaporation of Schwarzschild black holes using various forms of the generalized uncertainty principle(GUP),metric quantum correction,and noncommutative geometry,respec...In recent years,researchers have investigated the evaporation of Schwarzschild black holes using various forms of the generalized uncertainty principle(GUP),metric quantum correction,and noncommutative geometry,respectively.However,there are differences between the GUP correction and the other two methods in terms of describing the later stages of black hole evaporation.Furthermore,some studies argue that the GUP with a negative parameter cannot effectively correct black hole evaporation,while others contend that the positivity or negativity of the GUP parameters should not affect the correction results.Taking the above into consideration,we reconsider black hole evaporation with the generalized uncertainty principle including a linear term(LGUP),and examine the case of negative parameters.The results indicate that the evaporation behavior of both Schwarzschild black holes and Reissner–Nordstr?m black holes,under LGUP correction,is consistent with the results of metric quantum correction and non-commutative geometry.Additionally,the negative parameter LGUP can also effectively correct for black hole evaporation.展开更多
In this paper,we employ the extended generalized uncertainty principle with linear terms(LEGUP)to investigate the thermodynamics properties of the Schwarzschild and Reissner–Nordstr?m(RN)black holes.Firstly,by constr...In this paper,we employ the extended generalized uncertainty principle with linear terms(LEGUP)to investigate the thermodynamics properties of the Schwarzschild and Reissner–Nordstr?m(RN)black holes.Firstly,by constructing the theoretical framework of LEGUP,the minimal temperature of the Schwarzschild black hole and the modified mass–temperature function for the black hole are calculated.Furthermore,the heat capacity function for the Schwarzschild black hole is obtained.After that,we compare LEGUP black hole thermodynamics with EGUP black hole and with the usual forms.Besides,the modification of black hole entropy is discussed,which involves a heuristic analysis of particles absorbed by the black hole.Finally,we derive the LEGUP-corrected temperature,heat capacity and entropy functions of the RN black hole.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the s...We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.展开更多
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-- Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coetticient ...Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-- Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coetticient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty prlnciple and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.展开更多
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein- Hawking black hole entropy. The different correction leading terms are obtained by the different methods. In this...Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein- Hawking black hole entropy. The different correction leading terms are obtained by the different methods. In this paper, we calculate the correction to SAdS5 black hole thermodynamic quantity due to the generalized uncertainty principle. Furthermore we derive that the black hole entropy obeys Bekenstein Hawking area theorem. The entropy has infinite correction terms. And every term is finite and calculable. The corrected Cardy-Vedinde formula is derived. In our calculation, Bekenstein Hawking area theorem still holds after considering the generalized uncertainty principle. We have not introduced any hypothesis. The calculation is simple. Physics meaning is clear. We note that our results are quite general. It is not only valid for four-dimensional spacetime but also for higher-dimensional SAdS spacetime.展开更多
We use the generalized uncertainty principle to compute the first correction to the Hawking temperature associated to Hawking effect.From this value we obtain a new evaporation time and entropy of any Schwarzschild bl...We use the generalized uncertainty principle to compute the first correction to the Hawking temperature associated to Hawking effect.From this value we obtain a new evaporation time and entropy of any Schwarzschild black hole analyzing their expressions and consequences.展开更多
After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the ...After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.展开更多
In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertain...In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.展开更多
Uncertainty principle plays an important role in multiple fields such as physics,mathem-atics,signal processing,etc.The linear canonical transform(LCT)has been used widely in optics and information processing and so o...Uncertainty principle plays an important role in multiple fields such as physics,mathem-atics,signal processing,etc.The linear canonical transform(LCT)has been used widely in optics and information processing and so on.In this paper,a few novel uncertainty inequalities on Fisher information associated with linear canonical transform are deduced.These newly deduced uncer-tainty relations not only introduce new physical interpretation in signal processing,but also build the relations between the uncertainty lower bounds and the LCT transform parameters a,b,c and d for the first time,which give us the new ideas for the analysis and potential applications.In addi-tion,these new uncertainty inequalities have sharper and tighter bounds which are the generalized versions of the traditional counterparts.Furthermore,some numeric examples are given to demon-strate the efficiency of these newly deduced uncertainty inequalities.展开更多
The real random number generation is a critical problem in computer science.The current generation methods are either too dangerous or too expensive,such as using decays of some radioactive elements.They are also hard...The real random number generation is a critical problem in computer science.The current generation methods are either too dangerous or too expensive,such as using decays of some radioactive elements.They are also hard to control.By the declaration of uncertainty principles in quantum mechanics,real probabilistic events can be substituted by easier and safer processes,such as electron diffraction,photon diffraction and qubits.The key to solve the problem of Schr?dinger’s cat is to identify that the atom stays in different states after and before the decay,and the result of the decay is probabilistic according to the wave packet co llapse hypothesis.Same matter is able to possess different kinds of properties such as wave-particle duality due to that it can stay in various states,and which state will the matter stay is determined by the chosen set of physical quantities(or mechanical quantities).One eigenstate of a set of physical quantities can be a superpos ition of other eigenstates of different sets of physical quantities,and the collapse from a superposition to an eigenstate it contains is really random.Using this randomness,real random number can be generated more easily.展开更多
文摘The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.
文摘We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles： local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark＇s uncertainty principle and Matolcsi-Sz^ics uncertainty principle.
基金the National Natural Science Foundation of China(Grant No.12265007)。
文摘Jeans mass is regarded as a crucial factor in the study of nebula collapse.Astronomical data shows that Jeans mass is larger in theory than it is in observation.Someone mentioned that Jeans mass can be modified by using the generalized uncertainty principle(GUP).However,different physical backgrounds lead to different forms of GUP expression.In order to make the theoretical values of Jeans mass and its observed values match better,we use three distinct types of GUPs to correct Jeans mass in this paper.We find that the corrected Jeans masses are smaller than the uncorrected ones,where the Pedram corrected Jeans mass is the minimum and is close to the observed value.In addition,we consider the impact of temperature T and the GUP parameters(η,βandγ)for the corrected Jeans mass.
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
文摘The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports related to a Bessel type of(LCT)so called canonical Fourier-Bessel transform.
基金supported by Templeton Religion Trust(Grant No.TRT0159)supported by National Natural Science Foundation of China(Grant No.11771413)Templeton Religion Trust(Grant No.TRT0159)。
文摘In this paper,we calculate the norm of the string Fourier transform on subfactor planar algebras and characterize the extremizers of the inequalities for parameters 0<p,q≤∞.Furthermore,we establish Renyi entropic uncertainty principles for subfactor planar algebras.
基金Supported by NSFC(Grant No.12101451)Tianjin Municipal Science and Technology Commission(Grant No.22JCQNJC00470)。
文摘In this paper,we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra,which heavily depend on the Clifford algebraic structure.The obtained inequalities further lead to very general uncertainty inequalities on these modules.Some new phenomena arise,due to the non-commutative nature,the Clifford-valued inner products and the Krein geometry.Taking into account applications,special attention is given to the Dirac operator and the Howe dual pair Pin(m)×osp(1|2).Moreover,it is surprisingly to find that the recent highly nontrivial uncertainty relation for triple observables is indeed a direct consequence of our Cauchy–Schwarz inequality.This new observation leads to refined uncertainty relations in terms of the Wigner–Yanase–Dyson skew information for mixed states and other generalizations.These show that the obtained uncertainty inequalities on Clifford modules can be considered as new uncertainty relations for multiple observables.
文摘We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality.The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle,which is interpreted as a regularized self-energy.We extend our results and find corrections to the relativistic particles using the Klein–Gordon,Proca and Dirac equations.An important finding is that we extract a form of the generalized uncertainty principle(GUP)from the corrected energy.This form of the GUP is shown to depend on the nature of particles;namely,for bosons(spin 0 and spin 1)we obtain a quadratic form of the GUP,while for fermions(spin 1/2)we obtain a linear form.The correlation we find between spin and GUP may offer insights for investigating quantum gravity.
基金Supported by National Natural Science Foundation of China under Grant Nos.11275099,11435006,11405130the Double FirstClass University Construction Project of Northwest University
文摘We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off. And reveal the possible value of the minimum length.
基金supported by the National Natural Science Foundation of China(Grant No.12265007)。
文摘In recent years,researchers have investigated the evaporation of Schwarzschild black holes using various forms of the generalized uncertainty principle(GUP),metric quantum correction,and noncommutative geometry,respectively.However,there are differences between the GUP correction and the other two methods in terms of describing the later stages of black hole evaporation.Furthermore,some studies argue that the GUP with a negative parameter cannot effectively correct black hole evaporation,while others contend that the positivity or negativity of the GUP parameters should not affect the correction results.Taking the above into consideration,we reconsider black hole evaporation with the generalized uncertainty principle including a linear term(LGUP),and examine the case of negative parameters.The results indicate that the evaporation behavior of both Schwarzschild black holes and Reissner–Nordstr?m black holes,under LGUP correction,is consistent with the results of metric quantum correction and non-commutative geometry.Additionally,the negative parameter LGUP can also effectively correct for black hole evaporation.
基金supported by the National Natural Science Foundation of China(Grant No.11565009)。
文摘In this paper,we employ the extended generalized uncertainty principle with linear terms(LEGUP)to investigate the thermodynamics properties of the Schwarzschild and Reissner–Nordstr?m(RN)black holes.Firstly,by constructing the theoretical framework of LEGUP,the minimal temperature of the Schwarzschild black hole and the modified mass–temperature function for the black hole are calculated.Furthermore,the heat capacity function for the Schwarzschild black hole is obtained.After that,we compare LEGUP black hole thermodynamics with EGUP black hole and with the usual forms.Besides,the modification of black hole entropy is discussed,which involves a heuristic analysis of particles absorbed by the black hole.Finally,we derive the LEGUP-corrected temperature,heat capacity and entropy functions of the RN black hole.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
文摘We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.
基金The project supported by the Natural Science Foundation of Shanxi Province under Grant No. 2006011012 tCorresponding author,
文摘Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-- Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coetticient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty prlnciple and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for four-dimensional spacetimes but also for higher-dimensional spacetimes. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.
基金Natural Science Foundation of Shanxi Province of China under Grant No.2006011012the Doctoral Sustentation Fund of Shanxi Datong University
文摘Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein- Hawking black hole entropy. The different correction leading terms are obtained by the different methods. In this paper, we calculate the correction to SAdS5 black hole thermodynamic quantity due to the generalized uncertainty principle. Furthermore we derive that the black hole entropy obeys Bekenstein Hawking area theorem. The entropy has infinite correction terms. And every term is finite and calculable. The corrected Cardy-Vedinde formula is derived. In our calculation, Bekenstein Hawking area theorem still holds after considering the generalized uncertainty principle. We have not introduced any hypothesis. The calculation is simple. Physics meaning is clear. We note that our results are quite general. It is not only valid for four-dimensional spacetime but also for higher-dimensional SAdS spacetime.
基金The author is partially supported by a MINECO/FEDER Grant Number 2017-84383-Pan AGAUR(Generalitat de Catalunya)Grant Number 2017SGR 1276.
文摘We use the generalized uncertainty principle to compute the first correction to the Hawking temperature associated to Hawking effect.From this value we obtain a new evaporation time and entropy of any Schwarzschild black hole analyzing their expressions and consequences.
基金Project supported by the Natural Science Foundation of Shanxi Province, China (Grant No. 2006011012)the Shanxi Datong University Doctoral Sustentation Fund, China
文摘After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60473141)the Natural Science Foundation of Liaoning Province of China (Grant No. 20062191)
文摘In this paper the relations between two spreads, between two group delays, and between one spread and one group delay in fractional Fourier transform （FRFT） domains, are presented and three theorems on the uncertainty principle in FRFT domains are also developed. Theorem 1 gives the bounds of two spreads in two FRFT domains. Theorem 2 shows the uncertainty relation between two group delays in two FRFT domains. Theorem 3 presents the crossed uncertainty relation between one group delay and one spread in two FRFT domains. The novelty of their results lies in connecting the products of different physical measures and giving their physical interpretations. The existing uncertainty principle in the FRFT domain is only a special ease of theorem 1, and the conventional uncertainty principle in time-frequency domains is a special case of their results. Therefore, three theorems develop the relations of two spreads in time-frequency domains into the relations between two spreads, between two group delays, and between one spread and one group delay in FRFT domains.
基金supported by the National Natural Science Foundation of China(Nos.61771020,61471412)Project of Zhijiang Lab(No.2019KD0AC02).
文摘Uncertainty principle plays an important role in multiple fields such as physics,mathem-atics,signal processing,etc.The linear canonical transform(LCT)has been used widely in optics and information processing and so on.In this paper,a few novel uncertainty inequalities on Fisher information associated with linear canonical transform are deduced.These newly deduced uncer-tainty relations not only introduce new physical interpretation in signal processing,but also build the relations between the uncertainty lower bounds and the LCT transform parameters a,b,c and d for the first time,which give us the new ideas for the analysis and potential applications.In addi-tion,these new uncertainty inequalities have sharper and tighter bounds which are the generalized versions of the traditional counterparts.Furthermore,some numeric examples are given to demon-strate the efficiency of these newly deduced uncertainty inequalities.
文摘The real random number generation is a critical problem in computer science.The current generation methods are either too dangerous or too expensive,such as using decays of some radioactive elements.They are also hard to control.By the declaration of uncertainty principles in quantum mechanics,real probabilistic events can be substituted by easier and safer processes,such as electron diffraction,photon diffraction and qubits.The key to solve the problem of Schr?dinger’s cat is to identify that the atom stays in different states after and before the decay,and the result of the decay is probabilistic according to the wave packet co llapse hypothesis.Same matter is able to possess different kinds of properties such as wave-particle duality due to that it can stay in various states,and which state will the matter stay is determined by the chosen set of physical quantities(or mechanical quantities).One eigenstate of a set of physical quantities can be a superpos ition of other eigenstates of different sets of physical quantities,and the collapse from a superposition to an eigenstate it contains is really random.Using this randomness,real random number can be generated more easily.
