This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of...The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.展开更多
We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from ...We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from quantum gravity theories.As an illustration,black hole temperature effects are discussed.It is observed that for specific choices of the moment's kernels,cold black holes may emerge in the theory.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
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
We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because o...We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.展开更多
The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated.We calculate the analytical expresses of corresponding thermodynamic variables,e.g.,the Hawking temperature,entropy of t...The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated.We calculate the analytical expresses of corresponding thermodynamic variables,e.g.,the Hawking temperature,entropy of the black hole.In addition,we derive the heat capacity to analyze the thermal stability of the black hole.We also compute the rate of emission in terms of photons through tunneling.By numerical method,an obvious phase transition behavior is found.Furthermore,according to the general uncertainty principle,we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term.Lastly,we investigate the effects of the magnetic charge g,the dark matter parameter k and the generalized uncertainty principle parameterαon the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.展开更多
The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found ...The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.展开更多
We investigate the information exclusion principle for multiple measurements with assistance of multiple quantum memories that are well bounded by the upper and lower bounds.The lower bound depends on the observables&...We investigate the information exclusion principle for multiple measurements with assistance of multiple quantum memories that are well bounded by the upper and lower bounds.The lower bound depends on the observables'complementarity and the complementarity of uncertainty whilst the upper bound includes the complementarity of the observables,quantum discord,and quantum condition entropy.In quantum measurement processing,there exists a relationship between the complementarity of uncertainty and the complementarity of information.In addition,based on the information exclusion principle the complementarity of uncertainty and the shareability of quantum discord can exist as an essential factor to enhance the bounds of each other in the presence of quantum memory.展开更多
We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and ...We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.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 preparation, characterization, and test of the first wall materials designed to be used in the fusion reactor have remained challenging problems in the material science. This work uses the firstprinciples method a...The preparation, characterization, and test of the first wall materials designed to be used in the fusion reactor have remained challenging problems in the material science. This work uses the firstprinciples method as implemented in the CASTEP package to study the influ ences of the doped titanium carbide on the structural sta bility of the WTiC material. The calculated total energy and enthalpy have been used as criteria to judge the structural models built with consideration of symmetry. Our simulation indicates that the doped TiC tends to form its own domain up to the investigated nanoscale, which implies a possible phase separation. This result reveals the intrinsic reason for the composite nature of the WTiC material and provides an explanation for the experimen tally observed phase separation at the nanoscale. Our approach also sheds a light on explaining the enhancing effects of doped components on the durability, reliability, corrosion resistance, etc., in many special steels.展开更多
基金supported by National Science Foundation of China (10571044)
文摘This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
文摘The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.
文摘We prove the existence of an analogy between spatial long-range interactions,which are of the convolution-type introduced in non-relativistic quantum mechanics,and the generalized uncertainty principle predicted from quantum gravity theories.As an illustration,black hole temperature effects are discussed.It is observed that for specific choices of the moment's kernels,cold black holes may emerge in the theory.
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.
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.
文摘We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.
基金supported by the National Natural Science Foundation of China(Grant No.U1731107)。
文摘The thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter is investigated.We calculate the analytical expresses of corresponding thermodynamic variables,e.g.,the Hawking temperature,entropy of the black hole.In addition,we derive the heat capacity to analyze the thermal stability of the black hole.We also compute the rate of emission in terms of photons through tunneling.By numerical method,an obvious phase transition behavior is found.Furthermore,according to the general uncertainty principle,we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term.Lastly,we investigate the effects of the magnetic charge g,the dark matter parameter k and the generalized uncertainty principle parameterαon the thermodynamics of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle.
基金the National Natural Science Foundation of China(Grant No.11565009)。
文摘The Dirac–Weyl equation characterized quasi-particles in the T3 lattice are studied under external magnetic field using the generalized uncertainty principle(GUP). The energy spectrum of the quasi-particles is found by the Nikiforov–Uvarov method. Based on the energy spectrum obtained, the thermodynamic properties are given, and the influence of the GUP on the statistical properties of systems is discussed. The results show that the energy and thermodynamic functions of massless Dirac–Weyl fermions in the T3 lattice depend on the variation of the GUP parameter.
基金the National Natural Science Foundation of China(Grant Nos.12271394,11775040,12011530014)the Natural Science Foundation of Shanxi Province+3 种基金China(Grant Nos.201801D221032 and 201801D121016)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2019L0178)the Key Research and Development Program of Shanxi Province(Grant No.202102010101004)the China Scholarship Council。
文摘We investigate the information exclusion principle for multiple measurements with assistance of multiple quantum memories that are well bounded by the upper and lower bounds.The lower bound depends on the observables'complementarity and the complementarity of uncertainty whilst the upper bound includes the complementarity of the observables,quantum discord,and quantum condition entropy.In quantum measurement processing,there exists a relationship between the complementarity of uncertainty and the complementarity of information.In addition,based on the information exclusion principle the complementarity of uncertainty and the shareability of quantum discord can exist as an essential factor to enhance the bounds of each other in the presence of quantum memory.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No.LY14A030001)。
文摘We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.
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.
基金finantially supported by the Science Foundation for International Cooperation of Sichuan Province (2014HH0016)the Fundamental Research Funds for the Central Universities (SWJTU2014: A0920502051113-10000)National Magnetic Confinement Fusion Science Program (2011GB112001)
文摘The preparation, characterization, and test of the first wall materials designed to be used in the fusion reactor have remained challenging problems in the material science. This work uses the firstprinciples method as implemented in the CASTEP package to study the influ ences of the doped titanium carbide on the structural sta bility of the WTiC material. The calculated total energy and enthalpy have been used as criteria to judge the structural models built with consideration of symmetry. Our simulation indicates that the doped TiC tends to form its own domain up to the investigated nanoscale, which implies a possible phase separation. This result reveals the intrinsic reason for the composite nature of the WTiC material and provides an explanation for the experimen tally observed phase separation at the nanoscale. Our approach also sheds a light on explaining the enhancing effects of doped components on the durability, reliability, corrosion resistance, etc., in many special steels.
