A density-corrected quantum Boltzmann equation

Binary correlations are a recognized part of the pair density operator, but the influence of binary correlations on the singlet density operator is usually not emphasized. Here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators. Binary correlations are assumed to arise from the collision of twofree particles. Together with the first BBGKY equation and a retention of all terms that are second order in gas density, a generalization of the Boltzmann equation is obtained. This is an equation for thefree particle density operator rather than for the (full) singlet density operator. The form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct (Beth-Uhlenbeck) second virial coefficient, in contrast to a previous quantum Boltzmann equation, which gave only part of the quantum second virial coefficient. Generalizations to include higher-order correlations and collision types are indicated.     

Triple-collision operator for a quantum gas with bound states

The triple-collision operator of dense gas theory is analyzed for a quantum-mechanical gas obeying Boltzmann statistics. The contribution of two-body bound states is extracted by using Faddeev's representation of the three-body resolvent. The result is a binary atom-molecule collision operator which includes the effects of molecular formation and breakup, and inelastic and rearrangement collisions. An additional contribution is a modification of the Boltzmann collision operator due to the binding of one member of the colliding pair to a third particle. The analysis is carried out in the framework of the Green-Kubo formulas so the operators considered are linear and the results are in a form suitable for the evaluation of the transport coefficients.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco-Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Spectral Gap for a Class of Random Billiards

A random billiard is a random dynamical system similar to an ordinary billiard system except that the standard specular reflection law is replaced with a more general stochastic operator specifying the post-collision distribution of velocities for any given pre-collision velocity. We consider such collision operators for certain random billiards that we call billiards with microstructure. Collisions modeled by these operators can still be thought of as elastic and time reversible. The operators are canonically determined by a second (deterministic) billiard system that models “microscopic roughness” on the billiard table boundary. Our main purpose here is to develop some general tools for the analysis of the collision operator of such random billiards. Among the main results, we give geometric conditions for these operators to be Hilbert-Schmidt and relate their spectrum and speed of convergence to stationary Markov chains with geometric features of the microscopic billiard structure. The relationship between spectral gap and the shape of the microstructure is illustrated with several simple examples.     

Auxiliary Field Functional Integral Representation of the Many-Body Evolution Operator

Finding an appropriate functional integral representation of the many-body evolution operator is a crucial task for performing efficient calculations of fermionic systems within the auxiliary field approach. In this paper we derive a new field representation of the imaginary-time evolution operator using the method of Gaussian equivalent representation of Efimov and Ganbold (1991, Physica Status Solidi 168, 165). The goal is to obtain a functional integral representation, in which the main divergences caused by the tadpole Feynman diagrams are efficiently eliminated. These diagrams provide the main contributions to the ground state of the system under consideration, and therefore it is important to take them into account adequately, especially at lower temperatures. In addition, we show that the well-known mean field representation of the imaginary-time evolution operator is only the limiting case of the Gaussian equivalent representation in the small time-step regime.     

Optical Operator Method Studied via Fresnel Operator Decomposition and Coherent State Representation

We find that the mapping from classical optical transformations to the optical operator method can be realized by using the coherent state representation and the technique of integration within an ordered product of operators. The optical Fresnel operator derived in (Commun. Theor. Phys. (Beijing, China) 38 (2002) 147) can unify those frequently used optical operators. Various decompositions of Fresnel operator into the exponential canonical operators are obtained.     

Effective Approach to Constructing n-Mode Wigner Operator in the Entangled State Representation

By extending Fan-Klauder entangled state representation to multipartite case. We construct n-mode Wigner operator in the common eigenvector of the multipartite centre-of-mass coordinate and two mass-weighted relative momenta, and its canonical conjugate state, they are both more complicated entangled state of continuum variables. the technique of integration within an ordered product (IWOP) of operators is essential in our derivation.     

Representation of the coherent state for a beam splitter operator and its applications

A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.     

Kraus representation for the density operator of a qubit

We show that the time evolution of the density operator of a qubit can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.     

Quantum-statistical kinetic equations

Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, we derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors,P _q rule, etc.) to nonequilibrium systems described by a density operator(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived.     

适用于中等耦合等离子体的碰撞算子

完全电离等离子体中，当试探粒子分布函数f_α是关于试探粒子速度v_α的偶函数时，导出了一个新的动力学方程的碰撞算子.该碰撞算子同时包括了大角散射(库仑近碰撞)和小角散射(库仑远碰撞)的二体碰撞的贡献,因此，该碰撞算子同时适用于弱耦合(库仑对数lnΛ≥10)和中等耦合(库仑对数2≤lnΛ≤10)等离子体.而且经过修改的碰撞算子和Rosenbluth势有直接的联系，当试探粒子和场粒子满足条件m_αm_β(如电子-离子碰撞或Lor 关键词： 中等耦合等离子体 小角散射 大角散射 碰撞算子     

求坐标表象中压缩算符显式的3种方法

分别用提取变量积分法、正规乘积内的积分技术及投影算符转换法,得到了坐标表象中压缩算符的显式.     

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived.     

核磁共振波谱的李代数表示与计算方法

本文讨论NMR波谱与李代数表示论之间的联系及NMR波谱解析的李代数方法中的基本问题.若NMR中交换超算符方法中的算符集合生成的李代数为g,本文将讨论g的自然表示和伴随表示,g的典型性质,g的根系结构.提出了解析NMR波谱的三种李代数方法,列举了实例,显示了计算的具体步骤.     

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

We find that the coherent state projection operator representation of symplectic transformation constitutesa loyal group representation of symplectic group. The result of successively applying squeezing operators on numberstate can be easily derived.     

New Formulation of Weyl Quantization Scheme in Coherent State Representation

By virtue of the technique of integration within an ordered product of operators we present a new formulation of the Weyl quantization scheme in the coherent state representation, which not only brings convenience for calculating the Weyl correspondence of normally ordered operators, but also directly leads us to find both the coherent state representation and the Weyl ordering representation of the Wigner operator.     

Some formal aspects of subdynamics

The theory of subdynamics is formulated assuming the existence of a spectral representation of the collision operator. This approach avoids perturbation schemes; however the presentation is formal. It may be used to develop further the theory as well as a starting point for a rigorous mathematical discussion. The construction of the operators introduced in the theory of subdynamics is presented in detail. Some questions related to the transformation theory leading to the so-called “physical representation” are briefly discussed.     

A Difference Hamiltonian Operator and a Hierarchy of Generalized Toda Lattice Equations

A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulations a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy.     

Viscoelasticity of a Fermi liquid

Infinite homogeneous Fermi systems in the degenerate regime are described by the Uehling-Uhlenbeck equation. The eigenvalue problem associated with the linearized collision operator is solved analytically. Initial value problems are studied with the help of the spectral representation of the time evolution operator. The dynamic transport coefficients of the system can then be calculated in the framework of linear response theory. As an example the viscoelastic behaviour of the Fermi liquid is related to the relaxation of a quadrupole deformation in momentum space. In this connection also the coupling of the driving field to 2p-2h excitations will be discussed. The theory is applied to normal liquid³He and to nuclear matter.