An effective bosonic Hamiltonian describing the interaction of a mesoscopic Josephson junction with a quantized radiation field is studied. It is shown that when the field is initially in a coherent state and the junc...An effective bosonic Hamiltonian describing the interaction of a mesoscopic Josephson junction with a quantized radiation field is studied. It is shown that when the field is initially in a coherent state and the junction initially in its lowest energy level state, the state of the coupled field-mesoscopic Josephson junction system can evolve to a squeezed state. A detailed analysis about the quantum fluctuation of the coupled system is given.展开更多
In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from ...In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.展开更多
We present a method of realizing anticontrol chaos in a quantum confined system consisting of N two-levelatoms within a cavity, using a time-delayed optic field. The delay time plays a construction and organization ro...We present a method of realizing anticontrol chaos in a quantum confined system consisting of N two-levelatoms within a cavity, using a time-delayed optic field. The delay time plays a construction and organization role forproducing temporal chaos, while the interaction between atoms and photons creates spatial chaos. The chaos is quitesensitive to small time delayed. The spectral decomposition of the Hamiltonian obtained by using projection methodologyreveals that evolution of the left eigenvectors shows quite complicated chaotic fashions. The method we proposed maybe easily tested in experiment, and provides a general method using a sort of driving optic field to achieve anticontrol ofchaos for quantum systems.展开更多
The energy spectrum of the low-lying states of a system of three charged bosons confined in a twodimensional harmonic trap is investigated as a function of the confinement strength ω0 by means of the exact diagonaliz...The energy spectrum of the low-lying states of a system of three charged bosons confined in a twodimensional harmonic trap is investigated as a function of the confinement strength ω0 by means of the exact diagonalization of the Hamiltonian. The important feature of the low-lying states of three charged bosons in two-dimensional space is obtained via an analysis of the energy spectrum.展开更多
A model has been established for the interaction between a single-mode optical field and a 2-energy-level cold atom with exact analytic solutions given. The processes of momentum and energy exchanges between the optic...A model has been established for the interaction between a single-mode optical field and a 2-energy-level cold atom with exact analytic solutions given. The processes of momentum and energy exchanges between the optical field and the cold atom due to the interaction between them are discussed in detail, and a formula has been given for the variation of momentum and energy exchange volumes with time t in dress state while both the effects of photon recoil and Doppler effect are taken into consideration.展开更多
We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent ...We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.展开更多
Considering full perturbation to infinitesimal generators in the Mei structure equation,a new type of Meiadiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.
Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients ...Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1(whose subtrees are vertices), approaches 0 as the number of branches goes to ∞; in the opposite direction, the coefficient sequence of the bushy trees of height m(m ≥ 2), whose subtrees are all tall trees, approaches ∞ at large speed as the number of branches goes to +∞. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al.(2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli(1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases;(2) the formal energies/formal vector fields are nonconvergent in general case.展开更多
The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. T...The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces： symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti＇s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range II of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of ∏. We show that, a ruled surface on sitting in ∏ has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of , with two boundary pieces of symmetry breaking origin separated by two gapless lines.展开更多
Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time...Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.展开更多
文摘An effective bosonic Hamiltonian describing the interaction of a mesoscopic Josephson junction with a quantized radiation field is studied. It is shown that when the field is initially in a coherent state and the junction initially in its lowest energy level state, the state of the coupled field-mesoscopic Josephson junction system can evolve to a squeezed state. A detailed analysis about the quantum fluctuation of the coupled system is given.
基金Supported by National Nature Science Foundation of China under Grant No. 10701081
文摘In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.
文摘We present a method of realizing anticontrol chaos in a quantum confined system consisting of N two-levelatoms within a cavity, using a time-delayed optic field. The delay time plays a construction and organization role forproducing temporal chaos, while the interaction between atoms and photons creates spatial chaos. The chaos is quitesensitive to small time delayed. The spectral decomposition of the Hamiltonian obtained by using projection methodologyreveals that evolution of the left eigenvectors shows quite complicated chaotic fashions. The method we proposed maybe easily tested in experiment, and provides a general method using a sort of driving optic field to achieve anticontrol ofchaos for quantum systems.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475021
文摘The energy spectrum of the low-lying states of a system of three charged bosons confined in a twodimensional harmonic trap is investigated as a function of the confinement strength ω0 by means of the exact diagonalization of the Hamiltonian. The important feature of the low-lying states of three charged bosons in two-dimensional space is obtained via an analysis of the energy spectrum.
文摘A model has been established for the interaction between a single-mode optical field and a 2-energy-level cold atom with exact analytic solutions given. The processes of momentum and energy exchanges between the optical field and the cold atom due to the interaction between them are discussed in detail, and a formula has been given for the variation of momentum and energy exchange volumes with time t in dress state while both the effects of photon recoil and Doppler effect are taken into consideration.
基金Supported by the Korea Science and Engineering Foundation (KOSEF) Grant Funded by the Korea Government (MOST) under Grant No.F01-2007-000-10075-0
文摘We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.
基金Supported by the Natural Science Foundation of Shandong Province under Grant No.Y2008A33
文摘Considering full perturbation to infinitesimal generators in the Mei structure equation,a new type of Meiadiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.
基金supported by National Natural Science Foundation of China(Grant No.11371357)the Marine Public Welfare Project of China(Grant No.201105032)
文摘Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1(whose subtrees are vertices), approaches 0 as the number of branches goes to ∞; in the opposite direction, the coefficient sequence of the bushy trees of height m(m ≥ 2), whose subtrees are all tall trees, approaches ∞ at large speed as the number of branches goes to +∞. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al.(2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli(1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases;(2) the formal energies/formal vector fields are nonconvergent in general case.
基金supported by the Natural Sciences and Engineering Research Council of Canada,Canadian Institute for Advanced Research,Perimeter Institute for Theoretical PhysicsResearch at Perimeter Institute was supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development&Innovation
文摘The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces： symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti＇s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range II of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of ∏. We show that, a ruled surface on sitting in ∏ has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of , with two boundary pieces of symmetry breaking origin separated by two gapless lines.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271168 and 11671177by the Priority Academic Program Development of Jiangsu Higher Education Institutionsby Innovation Project of the Graduate Students in Jiangsu Normal University
文摘Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.
