The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classica...The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as wellas the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.展开更多
We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wign...We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p）σ1τσ1τ （p｜ and （p）λ,ν,λ,ν,（x｜ respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states＇ wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram.展开更多
Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendr...Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.展开更多
We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling between latt...We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappears between lattices l and l ＋ 1, and that l and l - 1. Correspondingly, the magnetic soliton appears.展开更多
In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usual...In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.展开更多
By making the analogy between the operator Hamiltonians of a mesoscopic ring carrying the persistent current and a Josephson junction we have introduced a phase operator and entangled state representation to establish...By making the analogy between the operator Hamiltonians of a mesoscopic ring carrying the persistent current and a Josephson junction we have introduced a phase operator and entangled state representation to establish a theoretical formalism for the ring system.展开更多
We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that tho...We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new intermediate coordinate-momentum representation for a two-particle system is proposed and applied to some two-body dynamic problems.展开更多
The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the c...The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωry, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.展开更多
By extending the usual Wigner operator to the s−parameterized one,we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P.This can...By extending the usual Wigner operator to the s−parameterized one,we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P.This can be exposed by comparing the normally ordered form ofΩs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics.Three different expressions ofΩs and the quantization scheme with use of it are presented.展开更多
Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate represe...Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.展开更多
In this letter, the superfluid-Mott-insulator phase transition of two-species cold bosonic atoms in an optical lattices is studied. The Hamiltonian of this model is diagonalized by means of Bogliubov transformations a...In this letter, the superfluid-Mott-insulator phase transition of two-species cold bosonic atoms in an optical lattices is studied. The Hamiltonian of this model is diagonalized by means of Bogliubov transformations and by the inversion symmetry of the optical lattice, the energy spectrum of this system is obtained. From She energy gap of the excitation spectrum, the quantum phase transition condition is obtained and it is determined by the competition between the interatomic repulsions and the tunnel coupling. It is found that there exists an ordinary fluid phase when taking the zero wave-vector limit.展开更多
Based on the bipartite entangled state representation and using the technique of integration within an ordered product （IWOP） of operators we construct the corresponding operator Fredholm equations and then derive t...Based on the bipartite entangled state representation and using the technique of integration within an ordered product （IWOP） of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials.展开更多
By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose margina...By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.展开更多
By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the intersp...By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.19774069and the Natural Science Foundation of Shandong Province of China under Grant No.Y98A03006.
文摘The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as wellas the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056 and the Specialized Research Fund for the Doctorial Progress of Higher Education under Grant No. 20040358019
文摘We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p）σ1τσ1τ （p｜ and （p）λ,ν,λ,ν,（x｜ respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states＇ wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram.
文摘Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.
基金The project partly supported by National Natural Science Foundation of China under Grant No.10574060the Natural Science Foundation of Beijing under Grant No.1072010.
文摘We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappears between lattices l and l ＋ 1, and that l and l - 1. Correspondingly, the magnetic soliton appears.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060
文摘In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060 and the Ph,D Tutoring Foundation of Educational Ministry of China
文摘By making the analogy between the operator Hamiltonians of a mesoscopic ring carrying the persistent current and a Josephson junction we have introduced a phase operator and entangled state representation to establish a theoretical formalism for the ring system.
基金supported by the Natural Science Foundation of Heze Universityof Shandong Province of China under Grant Nos.XY07WL01 and XY08WL03the University Experimental Technology Foundation of Shandong Province under Grant No.S04W138+1 种基金the Natural Science Foundation of Shandong Province under Grant No.Y2008A16the National Natural Science Foundation of China under Grant No.10574060
文摘We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new intermediate coordinate-momentum representation for a two-particle system is proposed and applied to some two-body dynamic problems.
文摘The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωry, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.
基金Supported by the National Natural Science Foundation of China under Grant No.10574060the Natural Science Foundation of Shandong Province under Grant No.ZR2010AQ027the Shandong Provincial Higher Educational Science and Technology Program under Grant Nos.J09LA07 and J10LA15.
文摘By extending the usual Wigner operator to the s−parameterized one,we find that in the process of the generalized Weyl quantization the s parameter plays the role of correlation between two quadratures Q and P.This can be exposed by comparing the normally ordered form ofΩs with the standard form of the Gaussian bivariate normal distribution of random variables in statistics.Three different expressions ofΩs and the quantization scheme with use of it are presented.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and the National Natural Science Foundation of China under Grant No. 10574060
文摘Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.
基金＊The project partly supported by National Natural Science Foundation of China under Grant No. 10574060 and the Natural Science Foundation of Shandong Province of China under Grant No. Y2003A02
文摘In this letter, the superfluid-Mott-insulator phase transition of two-species cold bosonic atoms in an optical lattices is studied. The Hamiltonian of this model is diagonalized by means of Bogliubov transformations and by the inversion symmetry of the optical lattice, the energy spectrum of this system is obtained. From She energy gap of the excitation spectrum, the quantum phase transition condition is obtained and it is determined by the competition between the interatomic repulsions and the tunnel coupling. It is found that there exists an ordinary fluid phase when taking the zero wave-vector limit.
基金The project supported by the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No. 20040358019 and National Natural Science Foundation of China under Grant No. 10475056
文摘Based on the bipartite entangled state representation and using the technique of integration within an ordered product （IWOP） of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475056 and 10574060
文摘By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060 and Natural Science Foundation of Beijing under Grant No. 1072010
文摘By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.
