In the coherent thermal state representation we introduce thermal Wigner operator and find that it is'squeezed' under the thermal transformation. The thermal Wigner operator provides us with a new direct and n...In the coherent thermal state representation we introduce thermal Wigner operator and find that it is'squeezed' under the thermal transformation. The thermal Wigner operator provides us with a new direct and neatapproach for deriving Wigner functions of thermal states.展开更多
By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuu...By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum state are calculated, which generalize the relevant results from ordinary Bose statistics to the parabose case.展开更多
The new soliton solutions for the variable-coefficient Boussinesq system, whose applications are seen influid dynamics, are studied in this paper with symbolic computation. First, the Painleve analysis is used to inve...The new soliton solutions for the variable-coefficient Boussinesq system, whose applications are seen influid dynamics, are studied in this paper with symbolic computation. First, the Painleve analysis is used to investigateits integrability properties. For the identified case we give, the Lax pair of the system is found, and then the Darbouxtransformation is constructed. At last, some new soliton solutions are presented via the Darboux method. Those solutionsmight be of some value in fluid dynamics.展开更多
The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of op...The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.展开更多
We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifest...We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifestly shown. Finally, we discuss their application.展开更多
The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and bio...The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and biology. As decoherence is a fundamental mechanism in some biological process such as photosynthesis and others examples, the gravitational quantum approach may contribute to elucidate if neuron function really emerges from quantum coherence in neuronal microtubules. The Einstein equation correlates the stress-energy tensor Tμv to a specific divergence-free combination Ricci tensor Rμv and the metric. In the semiclassical formulation, we have Gμv = Rμv -1/2gμvR=8πG/C^4〈ψ｜μvψ〉 which describes the quantum field in curved space-time geometry. But for a more precise equation in relation to the stress-energy tensor, we know that in a non-zero temperature, the wave-function is not enough to describe the physical reality. A more precise equation demands a formulation in the density-matrix form but for now there is no Diosi-Penrose model with density-matrix formulation. Such a density-matrix description can be viewed as a probability mixture of different wave-functions. Using some algebra and rules related to the mathematical manipulation of the density-matrix applied to operators, such the stress energy tensor, we found the von Neumann-Einstein equation for the general relativity equation in the density matrix operator form, Gμv = 8πG/C^4Tr[pTμv]. Thus density-matrix operator--instead of just a wave function of pure states--applied to the stress-energy tensor gives the curvature of space time, given by Einstein tensor, Gμv. The quantum fluctuation in the gravitational space-time field might feed back to decohere the quantum density-matrix. As long as decoherence can be viewed as the loss of information from a system to the environment, the density-matrix p is also related to that process and considering the measurement problem, density-matrix /garter is a more complete description of the possible outcome of the measurement. It is possible that some characteristics of the special microtubulin-associated proteins （MAP） that capes the dendritic-somatic microtubulins which could induces longer-lived nuclear spin states prevented from de-polymerization and suitable for long term information encode and memory. Understand the mechanism by which the hyper-phosphorylation in type tau-MAP displacements from microtubulins results in neurofibrillary tangles and cognitive dysfunctions in Alzheimer＇s disease.展开更多
This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plas...This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained.展开更多
In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identiti...In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q-P ordering and P-Q ordering is introduced.The Q-P ordered and P-Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q-P or P-Q ordering much more convenient.展开更多
A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of th...A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.展开更多
We propose an efficient scheme for realizing two-mode squeezing for two cavity modes with an atomic ensemble trapped in the cavity and driven by two classical fields. Through a suitable choice of the driving classical...We propose an efficient scheme for realizing two-mode squeezing for two cavity modes with an atomic ensemble trapped in the cavity and driven by two classical fields. Through a suitable choice of the driving classical fields, the evolution dynamics of the two cavity modes is decoupled with the atomic system and described by a two-mode squeezing operator. We show that a highly squeezed state can be obtained at the output even with a bad cavity. The required experimental techniques are within the scope of what can be obtained in the BEG-cavity setup.展开更多
文摘In the coherent thermal state representation we introduce thermal Wigner operator and find that it is'squeezed' under the thermal transformation. The thermal Wigner operator provides us with a new direct and neatapproach for deriving Wigner functions of thermal states.
文摘By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum state are calculated, which generalize the relevant results from ordinary Bose statistics to the parabose case.
基金Supported by the National Natural Science Foundation of China under Grant No. 60772023the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. BUAA-SKLSDE-09KF-04+1 种基金Beijing University of Aeronautics and Astronautics, by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 200800130006, Chinese Ministry of Education
文摘The new soliton solutions for the variable-coefficient Boussinesq system, whose applications are seen influid dynamics, are studied in this paper with symbolic computation. First, the Painleve analysis is used to investigateits integrability properties. For the identified case we give, the Lax pair of the system is found, and then the Darbouxtransformation is constructed. At last, some new soliton solutions are presented via the Darboux method. Those solutionsmight be of some value in fluid dynamics.
基金support from NYU Shanghai,the National Natural Science Foundation of China(No.21903054)the Hefei National Laboratory for Physical Sciences at the Microscale(No.KF2020008)+1 种基金the Shanghai Sailing Program(No.19YF1435600)the Program for Eastern Young Scholar at Shanghai Institutions of Higher Learning。
文摘The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.
文摘We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifestly shown. Finally, we discuss their application.
文摘The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and biology. As decoherence is a fundamental mechanism in some biological process such as photosynthesis and others examples, the gravitational quantum approach may contribute to elucidate if neuron function really emerges from quantum coherence in neuronal microtubules. The Einstein equation correlates the stress-energy tensor Tμv to a specific divergence-free combination Ricci tensor Rμv and the metric. In the semiclassical formulation, we have Gμv = Rμv -1/2gμvR=8πG/C^4〈ψ｜μvψ〉 which describes the quantum field in curved space-time geometry. But for a more precise equation in relation to the stress-energy tensor, we know that in a non-zero temperature, the wave-function is not enough to describe the physical reality. A more precise equation demands a formulation in the density-matrix form but for now there is no Diosi-Penrose model with density-matrix formulation. Such a density-matrix description can be viewed as a probability mixture of different wave-functions. Using some algebra and rules related to the mathematical manipulation of the density-matrix applied to operators, such the stress energy tensor, we found the von Neumann-Einstein equation for the general relativity equation in the density matrix operator form, Gμv = 8πG/C^4Tr[pTμv]. Thus density-matrix operator--instead of just a wave function of pure states--applied to the stress-energy tensor gives the curvature of space time, given by Einstein tensor, Gμv. The quantum fluctuation in the gravitational space-time field might feed back to decohere the quantum density-matrix. As long as decoherence can be viewed as the loss of information from a system to the environment, the density-matrix p is also related to that process and considering the measurement problem, density-matrix /garter is a more complete description of the possible outcome of the measurement. It is possible that some characteristics of the special microtubulin-associated proteins （MAP） that capes the dendritic-somatic microtubulins which could induces longer-lived nuclear spin states prevented from de-polymerization and suitable for long term information encode and memory. Understand the mechanism by which the hyper-phosphorylation in type tau-MAP displacements from microtubulins results in neurofibrillary tangles and cognitive dysfunctions in Alzheimer＇s disease.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023the Open Fund under Grant No.SKLSDE-2011KF-03+2 种基金Supported project under Grant No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsthe National High Technology Research and Development Program of China(863 Program) under Grant No.2009AA043303the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
文摘This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained.
基金supported by the National Natural Science Foundation of China (Grant No.11175113)
文摘In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q-P ordering and P-Q ordering is introduced.The Q-P ordered and P-Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q-P or P-Q ordering much more convenient.
文摘A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.
基金Supported by the Major State Basic Research Development Program of China under Grant No.2012CB921601
文摘We propose an efficient scheme for realizing two-mode squeezing for two cavity modes with an atomic ensemble trapped in the cavity and driven by two classical fields. Through a suitable choice of the driving classical fields, the evolution dynamics of the two cavity modes is decoupled with the atomic system and described by a two-mode squeezing operator. We show that a highly squeezed state can be obtained at the output even with a bad cavity. The required experimental techniques are within the scope of what can be obtained in the BEG-cavity setup.
