Quantum fields and poisson processes II: Interaction of boson-boson and boson-fermion fields with a cut-off

Quantum field evolutions are written as expectation values with respect to Poisson processes in two simple models: interaction of two boson fields (with conservation of the number of particles in one field) and interaction of a boson with a fermion field. The introduction of a cut-off ensures that the expectation values are well-defined.     

Ising model in a quasiperiodic transverse field,percolation, and contact processes in quasiperiodic environments

Quantum Ising models in a transverse field are related to continuous-time percolation processes whose oriented percolation versions are contact processes. We study such models in the presence of quasiperiodic disorder and prove localization in the ground state, no percolation, and extinction, respectively, for sufficiently large disorder.     

Solvable Models in the Conventional and Light-Front Field Theory: Recent Progress

We discuss a few new results within the exactly solvable relativistic models studied in both the conventional and the light front field theory. The models include the Rothe–Stamatescu, the Thirring, the Federbush and the Thirring–Wess model. The unifying feature is that the corresponding field equations are solved in a simple and exact form. We work within the hamiltonian framework and pay a careful attention to the correct definition of interacting currents which are built from the known solutions in a point-split regularized manner. Quantum “anomalies” follow immediately. The Hamiltonians of the models are expressed in terms of the correct (dynamically independent) field variables, namely the free Heisenberg fields. Due to the simplicity of the models’ dynamics, one can explicitly determine structure of the physical ground states.     

Charged anisotropic matter with quadratic equation of state

We extend the work of Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) by considering quadratic equation of state for the matter distribution to study the general situation of a compact relativistic body. Presence of electromagnetic field and anisotropy in the pressure are also assumed. Some new classes of static spherically symmetrical models of relativistic stars are obtained. All the results given in Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) and there in can also be recovered as a particular case of our work.     

Measurement-induced disturbance and thermal entanglement in spin models

Quantum correlation in two-qubit spin models is investigated by use of measurement-induced disturbance [S. Luo, Phys. Rev. A, 77 (2008) 022301]. Its dependences on external magnetic field, spin–spin coupling, and Dzyaloshinski–Moriya (DM) interactions are presented in detail. We also compare measurement-induced disturbance and thermal entanglement in spin models and illustrate their different characteristics.     

Yangian superalgebras in conformal field theory

Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory.     

Dynamical theory of an atom with two or three levels interacting with quantized cavity fields

We review the dynamical interaction of an atom with radiation in the framework of models of the Jaynes-Cummings type. The atom is restricted to a few energy levels and the radiation consists of quantized near-resonant loss-free modes. A general formalism is presented that allows a compact discussion of atom and field dynamics without approximations. Quantum wave packet collapse and revival phenomena, coherent trapping states, and some experimental prospects for two-level and three-level atoms are treated in detail, and some related effects are discussed more briefly.     

Investigation of Commuting Hamiltonian in Quantum Markov Network

Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics. We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.     

Twisted N=2 Supersymmetry with Central Charge and Equivariant Cohomology

We present an equivariant extension of the Thom form with respect to a vector field action, in the framework of the Mathai-Quillen formalism. The associated Topological Quantum Field Theories correspond to twisted N=2 supersymmetric theories with a central charge. We analyze in detail two different cases: topological sigma models and non-abelian monopoles on four-manifolds. Received: 2 April 1996 / Accepted: 15 July 1996     

非线性相互作用下三qubit系统中的量子关联

通过对系统施加不同的非线性作用,利用量子关联的几何度量,研究了三个qubit体系中的两体量子关联.不同的非线性相互作用模型都能使系统产生最大值为0.1752的量子关联.z方向的横场对量子关联的优化有控制作用,对于三个模型,通过调节z方向的横场,系统能产生最大值为0.09645的平均量子关联.最佳组合的三个横场,不仅能够大幅度提高量子关联的振荡周期,使得两qubit长时间处于量子关联态,而且还能够提高两qubit的平均量子关联.     

基于量子Fisher信息的量子计量进展

量子计量是超冷原子气体研究中的一个热点领域.超冷原子体系独特的量子性质(量子纠缠)和量子效应有助于大幅度提高待测物理量的测量精度,这已经成为量子精密测量中的共识.量子Fisher信息对该领域的发展起了非常重要的作用.本文首先介绍量子Fisher信息的基本概念和量子计量的主要内容;然后简要回顾这些理论在提高测量精度方面的应用,特别是多粒子量子纠缠态的产生及其判定;再介绍线性和非线性原子干涉仪的相关进展;最后论述量子测量过程中的统计方法的研究进展.     

Evidence for macroscopic quantum tunneling of phase slips in long one-dimensional superconducting Al wires

Quantum phase slips have received much attention due to their relevance to superfluids in reduced dimensions and to models of cosmic string production in the early universe. Their establishment in one-dimensional superconductors has remained controversial. Here we study the nonlinear current-voltage characteristics and linear resistance in long superconducting Al wires with lateral dimensions approximately 5 nm. We find that, in a magnetic field and at temperatures well below the superconducting transition, the observed behaviors can be described by the nonclassical, macroscopic quantum tunneling of phase slips, and are inconsistent with the thermal activation of phase slips.     

Integrable models and stochastic processes

A general way for constructing square lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These models give rise to series of integrable (stochastic) systems. As examples theAn-symmetric chain models and theSU(2)-invariant ladder models are investigated. Presented at the 10th Colloquium on Quantum Groups: “Quantum Groups and Intergrable Systems”, Prague, 21–23 June, 2001 SFB 256; BiBoS; CERFIM(Locarno); Acc. Arch.; USI(Mendriso)     

Quantum Energy-Transport and Drift-Diffusion Models

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an h expansion of these models, h² perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.This revised version was published online in March 2005 with corrections to the title. In the previous version, the author names were missing.     

Principal chiral models with non-constant metric

Field equations for generalized principal chiral models with non-constant metric and their possible Lax formulation are considered. Ansatz for Lax operators is taken linear in currents. Results of a complete investigation of models allowing Lax formulation with linear ansatz for Lax operators on solvable 2- and 3-dimensional groups are given; all such models appear to be almost linear. Also models on simple groupSU(2) with diagonal metric are considered; it turns out that Lax formulation exists in this case for constant metrics only. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. This work was partially supported by grant No. 1929/2001 of Fund for Development of Higher Education.     

双模腔场与一个V型三能级原子共振相互作用的量子统计性质

采用全量子理论和数值计算方法,研究了初始处于相干态的双模腔场与一个V型三能级原子共振相互作用的量子统计性质,讨论了在没有对原子进行态选择性测量、直接对原子进行态选择性测量和应用经典微波场并对原子进行态选择性测量的三种情况下,腔模平均光子数、耦合系数及相互作用时间对亚泊松统计、模间相干性、光子聚束反聚束效应和违背Cauchy-Schwarz不等式的影响。结果表明:对原子进行态选择性测量后,亚泊松统计特性明显地增强、模间反相关性明显地减弱、Cauchy-Schwarz不等式总是被违背;两个腔模平均光子数差比较大时,对原子进行态选择性测量后,a模腔场总是呈现反聚束效应。