Quantum spectra and classical periodic orbit in the cubic billiard

Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

Quantum Correlations Reduce Classical Correlations with Ancillary Systems

We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy. More precisely, we show that correlations in a bipartite state are classical if and only it each party ot the state can be perfectly correlated with other ancillary systems. In particular, this means that if there are quantum correlations between two parties, then the classical （as well as quantum） correlating capabilities of the two parties with other systems have to be strictly reduced.     

Wavelet-Transform Spectrum for Quantum Optical States

In the context of quantum mechanics we employ the technique of integration within an ordered product of operators to recast the classical wavelet transform to a squeezing-displacing transform between the mother wavelet vector and the state vector to be transformed. In this way we propose the wavelet-transform spectrum for quantum optical states. For some typical states we obtain numerical results which imply that the spectrum can be used to recognize a variety of quantum optical states, and the inverse wavelet transform has the possibility to play a role in quantum state engineering.     

Optically induced phase transition of excitons in coupled quantum dots

The weak classical light excitations in many semiconductor quantum dots have been chosen as important solid- state quantum systems for processing quantum information and implementing quantum computing. For strong classical light we predict theoretically a novel phase transition as a function of magnitude of this classical light from the deformed to the normal phases in resonance ease, and the essential features of criticality such as the scaling behaviour, critical exponent and universality are also present in this paper.     

Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics

In this paper,we present a general approach to the construction of conservation laws for generalized classical dynamical systems.Firstly,we give the definition of integrating factors and ,secondly,we study in detail the necessary conditions for the existence of conserved quantities.Then we establish the conservation theorem and its inverse for the hamilton‘s canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics.Finally,we give an example to illustrate the application of the results.     

A Comparative Study of Quantum and Classical Deletion

Here in this letter, we study the difference between quantum and classical deletion. We point out that the linear mapping deletion operation used in the impossibility proof for quantum systems applies also to classical system. The general classical deletion operation is a combined operation of measurement and transformation, i.e., first read the state and then transfer the state to the standard blank state. Though both quantum information and classical information can be deleted in an open system, quantum information cannot be recovered while classical information can be recovered.     

Multi—Player and Multi—Choice Quantum Game

We investigate a multi-player and multi-choice quantum game.We start from a two-player and two-choice game,and the result is better than its classical version.Then we extend this to N-player and N-choice cases.In the quantum domain,we provide a strategy with which players can always avoid the worst outcome.Also,by changing the value of the parameter of the initial state,the probabilities for players to obtain the best pay-off will be much higher than in its classical version.     

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on compficated graphs. Using this method, we calculate the probability of Continuous-time classical and quantum random walks on many of finite direct product Cayley graphs （complete cycle, complete Kn, charter and n-cube）. Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.     

Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments

The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory.We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment.Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla.Particularly,via preparing the state of the system to the highest excited state with hight fidelity,the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously.We explain these results using the definition of state fidelity.Furthermore,we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control.Therefore,our results may be of importance in the context of quantum information technologies.     

Deformation Quantization for Systems with Fermions

Deformation quantization, which achieves the passage from classical mechanics to quantum mechanics by the replacement of the pointwise multiplication of functions on phase space by the star product, is a powerful tool for treating systems involving bosonic degrees of freedom, both in quantum mechanics and in quantum field theory. In the present paper we show how these methods may be naturally extended to systems involving fermions. In particular we show how supersymmetric quantum mechanics can be formulated in this approach and consider examples involving both non-relativistic and relativistic systems.     

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.     

Questions and answers

The aim of this paper is twofold. First, we shall derive the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions from the classical Maxwell-Boltzmann (MB) distribution by introducing into the classical system the consequences of quantum mechanical indistinguishability in a direct and simple manner. Next, we go through a brief introduction to feedback systems and see how the FD and BE systems may be viewed as classical systems with appropriate feedback. We shall see that the resemblance to feedback systems is more than formal and that a feedback mechanism does exist in systems obeying quantum statistical mechanics.     

Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

We study time dependent correlation functions of ideal classical and quantum gases using methods of equilibrium statistical mechanics. The basis for this is the path integral formalism of quantum mechanical systems. By this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several non-trivial results for quantum systems have been obtained earlier by this analogy. Here we will focus upon particle dynamics. First ideal gases are considered. Then interactions, that are assumed weak and of long range, are added, and methods of classical statistical mechanics are applied to obtain the leading contribution. Comparison is performed with known results of kinetic theory. These results demonstrate how methods developed for systems in thermal equilibrium also is applicable outside equilibrium. Thus, more generally, we have reason to expect that these methods will be accurate and useful for other situations of interacting many-body systems consisting of quantized particles too. To indicate so we sketch the computation of the induced Casimir force between parallel plates filled with ions for the situation where the ions are quantized, but the interaction remains electrostatic. Further in this respect we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules. To our knowledge these two latter applications go beyond earlier results.     

AN ALTERNATIVE ONE-PARTICLE QUANTUM THEORY WITH A NEW EXPECTATION VALUE POSTULATE

Our recent treatment of some single-particle systems implies that if the expectation value postulate in usual quantum theory is changed in some proposed way, we can also have a self-consistent and reasonable one-particle quantum theory. In this paper, the framework of the theory barmonized with a newly proposed self-energy quantum electrodynamics is given. Our theory is compatible with Einstein's completeness. It in statistical ensemble reproduces the results given by the usual theory and in classical limit reduces to the classical mechanics for the single-particle systems.     

Quantum Physics and Classical Physics—In the Light of Quantum Logic

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Solèr condition and Piron's result one obtains the classical Hilbert spaces. However, this approach is not fully convincing. There is no plausible justification of Solèr's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics.     

Interaction between classical and quantum systems and the measurement of quantum observables

Quantum mechanics presumes classical measuring instruments with which they interact. The problem of measurement interaction between classical and quantum systems is posed and solved. The restriction to compatible measurements comes about naturally as the condition for the integrity of the classical system. A technical device is the perspective on classical mechanics as quantum mechanics with essentially hidden dynamical variables. Work supported in part by U.S. Atomic Energy Commission, ERDA.     

On the Classical Limit of Quantum Mechanics

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ε. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.