Classical and quantum theories of the polarization bremsstrahlung in the local electron density model

Classical and quantum theories of polarization bremsstrahlung in a statistical (Thomas-Fermi) potential of complex atoms and ions are developed. The basic assumptions of the theories correspond to the approximations employed earlier in classical and quantum calculations of ordinary bremsstrahlung in a static potential. This makes it possible to study on a unified basis the contribution of both channels in the radiation taking account of their interference. The classical model makes it possible to obtain simple universal formulas for the spectral characteristics of the radiation. The theory is applied to electrons with moderate energies, which are characteristic for plasma applications, specifically, radiation from electrons on the argon-like ion KII at frequencies close to its ionization potential. The computational results show the importance of taking account of the polarization channel of the radiation for plasma with heavy ions.     

超短强激光脉冲与H2＋相互作用研究：经典与量子计算的比较

用经典动力学和量子力学方法分别研究了Ｈ２＋在超短强激光场中的电离、离解和残存行为，得到了相似的结果：即在超短强激光脉冲作用下，Ｈ２＋的电离占优，但有限的量子计算低估了Ｈ２＋的离解几率；而经典处理则没有显示Ｈ２＋在超强场中的稳定化。另外，经典计算表明当核间距Ｒ伸展到一定范围时，Ｈ２＋的电离率最大。这符合量子计算中发现的电荷谐振增强电离（ＣＲＥＩ）现象。     

Quantum phase transitions in the sub-Ohmic spin-boson model: failure of the quantum-classical mapping

The effective theories for many quantum phase transitions can be mapped onto those of classical transitions. Here we show that the naive mapping fails for the sub-Ohmic spin-boson model which describes a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional, variantomega(s). Using an epsilon expansion we prove that this model has a quantum transition controlled by an interacting fixed point at small s, and support this by numerical calculations. In contrast, the corresponding classical long-range Ising model is known to display mean-field transition behavior for 0 < s < 1/2, controlled by a noninteracting fixed point. The failure of the quantum-classical mapping is argued to arise from the long-ranged interaction in imaginary time in the quantum model.     

圆环弹子球量子谱的衍射效应

采用开轨道的量子谱函数,对二维圆环弹子球体系进行了量子谱分析,根据内环半径（f=R_in/R_out）的不同取值,分别计算了相应的量子谱函数的傅里叶变换谱.结果表明,量子峰的位置和粒子运动的经典轨道长度符合得很好,半经典的闭合轨道理论给予了很好的解释;但是随着内环半径的减小,尤其在内环的线度和de Broglie波长可比拟时,量子峰的性质发生了本质性的变化,其特征类似于光学中的衍射图样,这正是由于内环的衍射效应所引起的,非常符合具有波动性的Fresnel-Kirchhoff衍射定理.本文的计算为研究量子台球体系的动力学性质和微腔输运问题提供了理论基础,同时也为研究晶体衍射、光谱分析等提供了一种新的理论方法. 关键词： 圆环弹子球 量子谱函数 傅里叶变换 衍射效应     

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and threfore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with a number of examples.Copyright © 1994 by the author.FFaithful reproduction of this article by any means is permitted for non-commercial purposes.     

On the general covariance and strong equivalence principles in quantum general relativity

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity.     

Quantum simulations of classical annealing processes

We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order 1/sqrt delta steps to find an optimal solution with bounded error probability, where delta is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order 1/delta steps required by the latter.     

Annular Controlled Teleportation

Extending the idea of bidirectional controlled teleportation, we propose a general framework to investigate the annular controlled teleportation (ACT). Under the control of the supervisor, each party transfers her single-qubit state to nearby one with the help of pre-shared entanglement and local unitary operations as well as classical communications. As the examples, we give two specific ACT protocols by using a seven-qubit cluster state and a nine-qubit entangled state as the quantum channel respectively to prove that this framework is possible.

     

Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems

We consider ground states in relatively bounded quantum perturbations of classical lattice models. We prove general results about such perturbations (existence of the spectral gap, exponential decay of truncated correlations, analyticity of the ground state), and also prove that in particular the AKLT model belongs to this class if viewed on a large enough length scale. This immediately implies a general perturbation theory about this model. On leave from Institute for Information Transmission Problems, Moscow The author is an Irish Research Council for Science, Engineering and Technology Postdoctoral Fellow     

Femtosecond pump-probe fluorescence signals from classical trajectories: comparison with wave-packet calculations

A classical approach to simulate femtosecond pump-probe experiments is presented and compared to the quantum mechanical treatment. We restrict the study to gas-phase systems using the I₂ molecule as a numerical example. Thus, no relaxation processes are included. This allows for a direct comparison between purely quantum mechanical results and those obtained from classical trajectory calculations. The classical theory is derived from the phase-space representation of quantum mechanics. Various approximate quantum mechanical treatments are compared to their classical counterparts. Thereby it is demonstrated that the representation of the radial density as prepared in the pump-process is most crucial to obtain reliable signals within the classical approach. Received 28 March 2001     

Distinguishability of particles in glass-forming systems

The distinguishability of particles has important implications for calculating the partition function in statistical mechanics. While there are standard formulations for systems of identical particles that are either fully distinguishable or fully indistinguishable, many realistic systems do not fall into either of these limiting cases. In particular, the glass transition involves a continuous transition from an ergodic liquid system of indistinguishable particles to a nonergodic glassy system where the particles become distinguishable. While the question of partial distinguishability of microstates has been treated previously in quantum information theory, this issue has not yet been addressed for a system of classical particles. In this paper, we present a general theoretical formalism for quantifying particle distinguishability in classical systems. This formalism is based on a classical definition of relative entropy, such as applied in quantum information theory. Example calculations for a simple glass-forming system demonstrate the continuous onset of distinguishability as temperature is lowered. We also examine the loss of distinguishability in the limit of long observation time, coinciding with the restoration of ergodicity. We discuss some of the general implications of our work, including the direct connection to topological constraint theory of glass. We also discuss qualitative features of distinguishability as they relate to the Second and Third Laws of thermodynamics.     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

Efficiency of the energy transfer in lanthanide-organic chelates; spectral overlap integral

The present work is devoted to the evaluation of the efficiency of the sensitized luminescence of the lanthanide complexes. In particular the dependence of the quantum yield of the luminescence on the physical factors that determine the spectral overlap integral is analyzed in detail. The calculations are based on the model of the evaluation of the spectral overlap integral proposed by Malta. It is shown that the theoretical trend in the change of the quantum yield reproduces the general properties of the experimental behavior observed in particular for Tb³⁺ complexes.     

The quantum spectra analysis of the circular billiards in wells

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.     

Maxwell electromagnetic theory,Planck's radiation law,and Bose—Einstein statistics

We give an example in which it is possible to understand quantum statistics using classical concepts. This is done by studying the interaction of chargedmatter oscillators with the thermal and zeropoint electromagnetic fields characteristic of quantum electrodynamics and classical stochastic electrodynamics. Planck's formula for the spectral distribution and the elements of energy hw are interpreted without resorting to discontinuities. We also show the aspects in which our model calculation complement other derivations of blackbody radiation spectrum without quantum assumptions.     

半圆和四分之一圆二维弹子球的量子谱分析

采用近来提出的量子谱函数,我们把闭合轨道理论应用到半圆和四分之一圆弹子球系统,这种量子谱函数的傅利叶变换包含了连接任意两点的许多经典轨道的信息.计算表明量子谱的傅立叶变换和经典轨道的长度符合的很好.从这两个体系可以看出半经典理论为经典和量子力学提供了很好的桥梁作用.     

Spectral duality in integrable systems from AGT conjecture

We describe relationships between integrable systems with N degrees of freedom arising from the Alday-Gaiotto-Tachikawa conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl _N Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the Alday-Gaiotto-Tachikawa relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrödinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2 × 2 and N × N representations of the Toda chain and the famous Adams-Harnad-Hurtubise duality.     

Classical breathers and quantum coherent states in discrete NLS systems

We present a comparison of quantum and “semiclassical” trajectories of coherent states that correspond to classical breather solutions of finite discrete nonlinear Schrödinger (DNLS) lattices. The main goal is to explain earlier numerical observations of recurrent return to the vicinity of initial coherent states corresponding to stable breathers that are also spatially localized. This effect can be considered as a quantum manifestation of classical spatial localization. We show that these phenomena are encoded in a simple expression for the distance between the quantum and semiclassical states that involves the basic frequencies of the classical and quantum systems, as well as the breather amplitude and quantum spectral decomposition of the system. A corollary is that recurrence phenomena are robust under perturbation of the initial conditions for stable breathers.     

Quantum corrections to the conductivity and periodic orbits: Integrable systems

We extend the recently developed semiclassical theory for the conductivity to periodic semiconductor structures whose classical dynamics is integrable. We find that the conductivity of integrable systems exhibits quantum oscillations as function of magnetic field and Fermi energy which are closely related to both the Shubnikov-de Haas oscillations and the oscillations observed in the conductivity of antidot lattices. A general expression for the quantum oscillations is derived which is analogous to the Berry-Tabor formula for the spectral density of integrable systems.