多模玻色二次多项式型系统的特性函数和准概率分布函数

运用多模玻色系统广义线性量子变换的普遍理论，对多模玻色二次多项式型系统进行了研究.给出了多模玻色二次多项式型系统的正规、反正规、Wigner特性函数、P表示和Q表示.举例讨论了该系统的压缩性质. 关键词： 多模玻色二次多项式型系统 特性函数 准概率分布函数     

Nonlinear dynamical systems,first integrals,Bose operators,and Lie algebras

A connection between nonlinear autonomous systems of ordinary differential equations, first integrals, Bose operators and Lie algebras is described. An extension to nonlinear partial differential equations is given.     

q-Deformed IWOP Technique and Its Applications

We extend the newly developed technique of integration with an ordered product (IWOP) of operators to q-deformed boson case. The ambiguity arising from defining the normal ordering of q-deformed boson operators, which satisfy aa^↑ - qa^↑a = 1, can be eliminated by following the q-deformed IWOP technique. Some new q-integration formulas and new qboson operator identities are obtained, and the P-representation of q-analogue of the chaotic state of radiation field is derived.     

Kinematical and dynamic interactions do not change properties of two-particle solitons

The system of Frenkel excitons interacting with phonons is treated in the Agranovich-Toshich bosonic representation of Pauli operators up to terms with four Bose operators, comprising both kinematic and dynamic interaction. Equations of motion are formulated for the two-particle soliton wavefunction and it is shown that they are completely identical with those obtained previously with the hamiltonian quadratic in Bose operators.     

New Two-Mode Coherent-Intermediate-Entangled State and Its Squeezing Operator

The coherent-intermediate-entangled state |α,x}>_λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α,x}>_λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α,x}>_λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α,x}>_λ,ν , and the Schmidt decomposition of |α,x}>_λ,ν is investigated.     

The quantum Fokker-Planck equation for certain boson systems

Quantum relations between a class of boson Langevin equations and the associated Fokker-Planck equations are derived. The Fokker-Planck equations for the Wigner distribution Φ_sym related with symmetric ordering of the boson operators, the distribution Φ_A related with antinormal ordering, and the distribution Φ_N related with normal ordering (P-representation) are given.     

Simple inequality for the free energy of disordered systems

It is proved that the free energy of a disordered system described by a quadratic form in Bose or Fermi operators with random coefficients, calculated in the simplest approximation for the associated eigenvalue problem, gives the upper (Bose case) and lower (Fermi case) bounds for the exact free energy.     

Grassmann functional Schrödinger description for Fermions

The Schrödinger picture for the field Dirac theory is derived from a path integral over Grassmann fields and momenta. States and operators are described by wavefunctionals and functional differentiation. Unlike Bose fields, the free Fermi fields are shown to follow only their classical trajectories. An interacting theory is treated; integrating out the fermions gives the non-local effective Bose action.     

Realisations of the representations of para-Fermi algebra in Fock space of Bose operators: part I

Using the matrix realisations of para-Fermi operators we find isomorphic mappings with respect to the Green product of the para-Fermi algebra into second-order polynomials of creation and annihilation para-Bose operators with arbitrary order of parastatistics. In the Fock space ℋ ₂ ¹ of two Bose operators all the irreducible representations of the para-Fermi algebra are realised. The spaces ofn-particle Bose statesn=1,2,..., from which ℋ ₂ ¹ is constructed as a direct sum, can be interpreted as spaces of para-Fermi states of para-statisticsn.     

Light—induced nonlinear effects of dispersion relation of ultracold Bose gas

We have investigated the optical properties of Λ-configuration ultracold dense Bose gas interacting with two laser pulses, which usually result in electromagnetically induced transparency. With the nonrelativistic quantum electrodynamics and taking into account the atomic dipole－dipole interaction and local field effect, we have derived the Maxwell－Bloch equations of the system. The dispersion relation of an ultracold Bose gas has been obtained and the light-induced nonlinear effects have been analysed. The light-induced nonlinear effects are different from the effects induced by two-body collision of Bose－Einstein condensation atoms which have a frequency shift of transparent window.     

Realisations of the representations of para-Fermi algebra-Part III: Fock space of Fermi operators

Following the idea given by Kademova (1969b), Green's isomorphisms of the para-Fermi algebra F _2n ¹ into the space of all bilinear products of para-Fermi type operators are constructed. The induced transformations in Fock space of Fermi operators are considered. The difference between the induced transformations in Fock space of Bose operators and in Fock space of Fermi operators is discussed.     

Dynamical effects in superfluid helium 4

The close structural similarity between the commutation relations of harmonic oscillator operators and the operators for Bose fields is exploited to study the excitation spectrum in superfluid helium 4. By applying ‘broken symmetry’ condition it is shown how the creation of phonon gives rise to superfluid behaviour of liquid He 4. The energy gap needed for roton excitation is derived.     

玻色爱因斯坦凝聚体一维轴向干涉中的非线性现象

利用含时的Ｇｒｏｓｓ－Ｐｉｔａｅｖｓｋｉｉ方程,研究了轴对称的高密度玻色爱因斯坦凝聚体在干涉过程中因原子间相互人用而产生的非线性现象。发现玻色爱因斯坦凝聚体的一维轴向干涉条纹的密度分布是一种驻波状结构。通过原子波之间非线性耦合相互作用,这种结构可以表现为物质波光栅,对其周期的原子波产生衍射现象。     

玻色子多体系统的平均场理论:玻色-爱因斯坦凝聚体(BEC)的冷却与激发

用量子主方程的平均场近似和代数动力学研究玻色-爱因斯坦凝聚体的sympathetic cooling; 用玻色-爱因斯坦凝聚体波函数的运动方程的平均场近似 非线性薛定谔方程研究玻色 爱因斯坦凝聚体的暗孤子和明孤子激发.     

Local Gaussian domination and Bose condensation in lattice boson model

We use infrared bounds method to study the existence of a Bose condensation phase transition in a three-dimensional lattice model of interacting bosons. Upper bound (local Gaussian domination) is presented on the Bogolyubov inner product of creation and annihilation bosonic operators in momentum space. We focus on the situation with a non-negative chemical potential. The presence of a Bose condensation is established for sufficiently small superstable interaction potential. A special case of the model considered is the Bose–Hubbard model.     

Representations of the CAR generated by representations of the CCR. Fock case

We present a method of constructing the Fock representation of the canonical anti-communtation relations in the Fock representation of the canonical commutation relations. An explicit formula for Fermi creation and annihilation operators in terms of Bose ones is given.