Classical Mechanics Is not the ħ, → 0 Limit of Quantum Mechanics

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have a common part but there exist tomograms of classical states which are not admissible in quantum mechanics and, vice versa, there exist tomograms of quantum states which are not admissible in classical mechanics. The role of different transformations of reference frames in the phase space of classical and quantum systems (scaling and rotation) determining the admissibility of tomograms as well as the role of quantum uncertainty relations are elucidated. The union of all admissible tomograms of both quantum and classical states is discussed in the context of interaction of quantum and classical systems. Negative probabilities in classical and quantum mechanics corresponding to tomograms of classical and quantum states are compared with properties of nonpositive and nonnegative density operators, respectively. The role of the semigroup of scaling transforms of the Planck's constant is discussed.     

Wave Function in Classical Statistical Mechanics

The possibility to formulate classical statistical mechanics in terms of the complex wave function and density matrix obeying the evolution equation is discussed. It is shown that the modulus squared of the introduced wave function of the classical particle has the same physical meaning as the modulus squared of the wave function of the quantum particle. The tomographic probabilities are studied for both classical and quantum states. Integrals of motion and their relation to the propagators are discussed.     

Probability and logical structure of statistical theories

A characterization of statistical theories is given which incorporates both classical and quantum mechanics. It is shown that each statistical theory induces an associated logic and joint probability structure, and simple conditions are given for the structure to be of a classical or quantum type. This provides an alternative for the quantum logic approach to axiomatic quantum mechanics. The Bell inequalities may be derived for those statistical theories that have a classical structure and satisfy a locality condition weaker than factorizability. The relation of these inequalities to the issue of hidden variable theories for quantum mechanics is discussed and clarified.     

Anomalous isotropic luminescence from anthracene sandwich dimers

A classical statistical probability amplitude is introduced whose square modulus is the distribution function. This enables the analogy between classical statistical mechanics and quantum mechanics to be completed. The analogy is developed until quantum statistical derivations can be used in classical statistical mechanics. Two master equations are found: the classical equivalent of the Pauli Master Equation, and a generally valid master equation. Well-known classical equations are deduced from these in a special representation. Interference terms are found and discussed.     

A novel quantum block encryption algorithm based on quantum computation

Based on quantum computation, a novel quantum block cryptographic algorithm that can be used to encrypt classical messages is proposed. The security of this algorithm is analyzed from several aspects. It is shown that the quantum block cryptographic algorithm, in which the key can be reused after undergoing a check procedure, can prevent quantum attack strategy as well as classical attack strategy. The problem of key management is discussed and the circuits for encryption and decryption are suggested.     

磁三明治结构巨磁阻的量子解析理论

运用量子统计的格林函数方法研究磁三明治结构中的巨磁阻效应，推出一个既适用于厚膜又适用于薄膜的电导统一公式，讨论经典理论与量子理论间的联系和过渡． 关键词：     

On the role of coherent states in quantum foundations

Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that useful connections arise among them. The topics discussed are: (1) a truly natural formulation of phase space path integrals; (2) how this analysis implies that the usual classical formalism is “simply a subset” of the quantum formalism, and thus demonstrates a universal coexistence of both the classical and quantum formalisms; and (3) how these two insights lead to a complete analytic solution of a formerly insoluble family of nonlinear quantum field theory models.     

Classification of the quantum two-dimensional superintegrable systems with quadratic integrals and the Stäckel transforms

The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient -?² plus a quantum deformation of order ?⁴ and ?⁶. The systems inside the classes are transformed using Stäckel transforms in the quantum case as in the classical case. The general form of the Stäckel transform between superintegrable systems is discussed.     

The effect of measurement on the quantum features of a chaotic system

We investigate the quantum dynamics of a periodically kicked nonlinear spin system which exhibits regular and chaotic dynamics in the classical regime. The quantum behaviour is characterised by the evolving eigenvalue distributions for the angular momentum components and the features, including recurrences in the quantum means and the presence of quantum tunneling, are discussed. We employ the evolution operator eigenvalue distribution to prove that coherent quantum tunneling occurs between the fixed points in the regular regions of phase space. Continual quantum measurement is included in the model: the classical dynamics are unchanged but a destruction of coherences occurs in the quantum system. Recurrences in the means are destroyed and quantum tunneling is suppressed by measurement, a manifestation of the quantum Zeno effect.     

Classical and quantum chaos in atom optics

The interaction of an atom with an electro-magnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electro-magnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.     

Constitution of objects in classical mechanics and in quantum mechanics

The constitution of objects is discussed in classical mechanics and in quantum mechanics. The requirement of objectivity and the Galilei invariance of classical and quantum mechanics leads to the postulate of covariance which must be fulfilled by observable quantities. Objects are then considered as carriers of these covariant observables and turn out to be representations of the Galilei group. Individual systems can be defined in classical mechanics by their trajectories in phase space. However, in quantum mechanics the characterization of individuals can only be achieved approximately by means of unsharp observables.     

Coulomb Systems at Low Density: A Review

Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system, Debye–Hückel screening, is compared and contrasted with the quantum case, where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye–Hückel screening is discussed.     

计算的量子飞跃

利用量子力学的迭加和纠缠等特性进行的量子计算是计算技术的巨大飞跃。它能够比经典计算远为有效地解决一些问题。例如最为著名的Ｓｈｏｒ的算法原则上能够以多项式的时间因子化大的合数,从而使得经典计算机难以计算的这一问题得以解决。文章介绍了至今所发现的主要量子算法的基本原理和步骤,并且概述了量子计算的优越性、现状和发展前景,同时讨论了量子计算在物理学上的应用和意义。     

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.     

On geometro-stochastic theory of measurement and quantum geometry

The reasons for the fundamental incompatibility of quantum mechanics with classical relativistic geometries are reviewed, whereupon the basic principles of a theory of measurement leading to quantum geometries are stated and discussed. The ensuing conceptualization of quantum processes is formulated as an integral part of an all-pervasive concept of quantum reality in which systems as well as apparatuses are treated as quantum objects. The basic ideas of the resulting geometro-stochastic theory of quantum measurement are explained.     

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.     

量子算法与量子计算实验

从量子体系的基本特性出发 ,介绍了量子计算的基本概念和物理背景 ,系统阐述了几种主要的量子算法以及量子计算在实验方面的发展现状。对比经典计算机 ,讨论了量子计算机的优越性、实现量子计算的困难和以期克服的途径。     

量子Berry相因子与相位教学

回顾了经典物理和量子力学中的相位问题,着重讨论了量子几何Berry相位及在量子力学中如何进行量子相位教学的问题.     

量子算法与量子计算实验

从量子体系的基本特性出发,介绍了量子计算的基本概念和物理背景,系统阐述了几种主要的最子算法以及量子计算在实验方面的发展现状。 对比经典计算机,讨论了量子计算机的优越性、实现量子计算的困难和以期克服的途径。