伪自伴量子系统的酉演化与绝热定理

经典量子系统的哈密尔顿是自伴算子.哈密尔顿算符的自伴性不仅确保了系统遵循酉演化,而且也保证了它自身具有实的能量本征值.但是,确实有一些物理系统,其哈密尔顿是非自伴的,但也具有实的能量本征值,这种具有非自伴哈密尔顿的系统就是非自伴量子系统.具有伪自伴哈密尔顿的系统是一类特殊的非自伴量子系统,其哈密尔顿相似于一个自伴算子.本文研究伪自伴量子系统的酉演化与绝热定理.首先,给出了伪自伴算子定义及其等价刻画;其次,对于伪自伴哈密尔顿系统,通过构造新内积,证明了伪自伴哈密尔顿在新内积下是自伴的,并给出了系统在新内积下为酉演化的充分必要条件.最后,建立了伪自伴量子系统的绝热演化定理及与绝热逼近定理.     

Quantum Cable Equations in Terms of Generalized Operators

A quantum cable equation in the sense of generalized operators is introduced. The existence and uniqueness of solutions are established and the continuity and a Markov-like property of the solution are obtained.     

广义算子意义下的量子随机微分方程

本文研究广义算子及其Wick积意义下的最子随机微分方程。主要结果为：建立了解的存在唯一性定理；证明了解的连续性及解对初值的连续依赖性，本文给出了两个例子。     

Interpretation of Quantum Hamiltonian Monodromy in Terms of Lattice Defects

The analogy between monodromy in dynamical (Hamiltonian) systems and defect in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.Mathematics Subject Classifications (2000) 37J05, 70H33, 81Q70.     

一些数学名词的由来

介绍数学领域中一些学科概念,如代数学、几何学、微积分学、拓扑学和概率论等的产生与演变过程。     

BRST-Invariant Algebra of Constraints in Terms of Commutators and Quantum Antibrackets

We establish the general structure of the BRST-invariant algebra of constraints in its commutator and antibracket forms via the formulation of algebra-generating equations in a supplementally extended phase space. New ghost-type variables behave as fields and antifields with respect to quantum antibrackets. The explicit form of the BRST-invariant gauge algebra is given in detail for rank-one theories with a Weyl- and a Wick-ordered ghost sector. We construct a fixed-gauge unitarizing Hamiltonian and show that the formalism is physically equivalent to the standard BRST–BFV approach.     

Evolution Operator for a Quantum Pendulum

We conjecture one remarkable relation for infinite series in the simple Weyl algebra. This relation expresses an evolution operator for a quantum pendulum via its Hamiltonian.     

Markov Approximations of the Evolution of Quantum Systems

Doklady Mathematics - The convergence in probability of a sequence of iterations of independent random quantum dynamical semigroups to a Markov process describing the evolution of an open quantum...     

Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)

Constructing the basic operators of scattering theory on and off the mass shell in terms of spatially bounded stationary wave packets or proper differentials is described. For this, we use a technique based on a certain scheme for discretizing the continuum. Finite-dimensional approximations for the Green's functions and T-matrix, which are first found here, are immediately constructed for any energy using a single simple diagonalization of the Hamiltonian matrix in an L ₂-type complete basis. We show that the developed approach leads to a convenient finite-dimensional representation of the scattering operators in the basis of the wave functions of a harmonic oscillator. The method allows an immediate extension to the problem of three and more bodies.     

Evolution of Holographic Entropy Quantities for Composite Quantum Systems

Theoretical and Mathematical Physics - We consider entanglement entropy quantities for a three-part system, namely, the tripartite information, total correlation, and so-called secrecy monotone. A...     

Time Evolution of Quadratic Quantum Systems: Evolution Operators,Propagators, and Invariants

Theoretical and Mathematical Physics - We use the evolution operator method to describe time-dependent quadratic quantum systems in the framework of nonrelativistic quantum mechanics. For...     

Parametric Resonance in Adiabatic Oscillators

We use the averaging method and Levinson’s fundamental theorem to study phenomenon of parametric resonance in some new equations from the class of adiabatic oscillators.     

The Quantum Faedo-Galerkin Equation: Evolution Operator and Time Discretization

Time dependent quantum systems have become indispensable in science and nanotechnology. Disciplines including chemical physics and electrical engineering have used approximate evolution operators to solve these systems for targeted physical quantities. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains via evolution operators. The work builds upon the use of weak solutions, which includes a framework for the evolution operator based upon dual spaces. We are able to derive the corresponding Faedo-Galerkin equation as well as its time discretization, yielding a fully discrete theory. We obtain corresponding approximation estimates. These estimates make no regularity assumptions on the weak solutions, other than their inherent properties. Of necessity, the estimates are in the dual norm, which is natural for weak solutions. This appears to be a novel aspect of this approach.     

Initial Value Problem for a Nonlinear Evolution System with Singular Integral Differential Terms

The initial value problem for a nonlinear evolution system with singular integral differential terms is studied. Dy means of a priori estimates of the solutions and Lcray-Schauder's fixed point theorem, we demonstrate the existence and uniqueness theorems of the generalized and classical global solutions to the problem.     

Adiabatic switching in abstract scattering theory

The paper discusses the relations between the usual wave operator, the adiabatic switched one and the ABEL wave operator. By means of H = -i d/dx + q(x) examples are constructed where the usual wave operator exists but the adiabatic switched one does not exist, or both exist and they are not equal.