Structure Of Quantum Phase Space Research Articles

Fermi accelerator: A new insight from quantum theory of motion

Quantum localization is observed in the Fermi accelerator model with monochromatic fluctuation using the Ehrenfest description of quantum dynamics as well as through the quantum theory of motion (QTM). The effects of variations in time period and amplitude of an oscillating wall for a particle in a box, on energy and quantum phase space structures are analyzed. The effects of fluctuation decay with an increase in distance from the fluctuating wall. It is also observed that small amplitude as well as high frequency fluctuation provides enhanced quantum localization. The “quantum phase space structure” in the Ehrenfest description is constructed by following time-dependent Fourier grid Hamiltonian method while that for the grid points are formed from their trajectories obtained from QTM. © 2015 Wiley Periodicals, Inc.

Geometry and Structure of Quantum Phase Space

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an important role in foundations of quantum mechanics and quantum information. In this work we discuss a geometric framework for mixed quantum states represented by density matrices, where the quantum phase space of density matrices is equipped with a symplectic structure, an almost complex structure, and a compatible Riemannian metric. This compatible triple allow us to investigate arbitrary quantum systems. We will also discuss some applications of the geometric framework.

Weak values and modular variables from a quantum phase-space perspective

We address two major conceptual developments introduced by Aharonov and collaborators through a \textit{quantum phase space} approach: the concept of \textit{modular variables} devised to explain the phenomena of quantum dynamical non-locality and the \textit{two-state formalism} for Quantum Mechanics which is a retrocausal time-symmetric interpretation of quantum physics which led to the discovery of \textit{weak values.} We propose that a quantum phase space structure underlies these profound physical insights in a unifying manner. For this, we briefly review the Weyl-Wigner and the coherent state formalisms as well as the inherent symplectic structures of quantum projective spaces in order to gain a deeper understanding of the weak value concept. We also review Schwinger's finite quantum kinematics so that we may apply this discrete formalism to understand Aharonov's modular variable concept in a different manner that has been proposed before in the literature. We discuss why we believe that this\ is indeed the correct kinematic framework for the modular variable concept and how this may shine some light on the physical distinction between quantum dynamical non-locality and the kinematic non-locality, generally associated with entangled quantum systems.

AN INVESTIGATION OF A NONLOCAL ENTANGLEMENT OF TWO UNCOUPLED ATOMS EMBEDDED IN A COHERENT CAVITY FIELD AND THE ASSOCIATED PHASE SPACE DISTRIBUTION: ONE QUANTUM NONLINEAR PROCESS

Entanglement properties of two uncoupled atoms embedded in a coherent field distribution through one quantum transition process are studied. A case of non-linear Hamiltonian of the problem is considered through which the effect of non-linear media is illustrated. Moreover, the effect of the frequency difference between the inter-atomic transition and the electromagnetic field is also analyzed. We show that, adjusting the considered parameters of the non-linear media and frequency difference leads to a strong control of the degree of entanglement where excellent periodicity of evolution with significant amplitudes maxima of entanglement can be obtained that is very important in predicting the behavior of transmitted information through the application of various information processing schemes. We present a detailed and comparative study of atom–atom entanglement for two cases corresponding to different injections of the two atoms one by one into the cavity field. In addition, we present an answer to the question: How is the quantum phase space structure for a composite system related to the entanglement characteristics of the corresponding quantum system? We demonstrate how can the entanglement in nonlinear tripartite systems be strongly associated with a delocalization in the phase space distribution.

Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves

The notion of quantum vector fields and quantum tensors is investigated and applied for explicit calculation of the Weyl star-product over Poisson manifolds, as well as, of the Wick star-product and the reproducing measure over (pseudo) Kählerian manifolds. Quantum phase space structure over Poisson manifolds is discussed and used for the derivation of explicit formulas for irreducible representations of the star-product algebra. The quantum restriction of the star-product onto irreducible leaves is described. Some interesting geometrical constructions (for instance, a series of higher order differential invariants over Kählerian manifolds) are obtained as corollaries of quantum calculations.

On the structure of quantum phase space

The space of labels characterizing the elements of Schwinger’s basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character.

Flux analysis, the correspondence principle, and the structure of quantum phase space.

The hydrodynamic analogy for quantum mechanics is developed in a quantum phase-space representation. The key technical step in this development is the formulation of a phase-space flux (or current) density expression. Lagrangian fluid trajectories in phase space are explicitly found as solutions to a set of first-order ordinary differential equations which are formulated without making semiclassical approximation to the quantum dynamics. These fluid trajectories may be used to construct sharp structures in quantum phase space in the same way that one uses classical trajectories in classical mechanics. While these sharp structures do not themselves represent states, their properties ``control'' the dynamics of states in a manner familiar from the theory of first-order flows. The formalism reduces to Liouville dynamics in the classical limit, \ensuremath{\Elzxh}\ensuremath{\rightarrow}0. In addition to several analytic applications to the pure- and mixed-state dynamics, the approach is numerically implemented for tunneling dynamics in a double-well problem. A new picture for quantum tunneling emerges where the tunneling transport occurs when density spirals outward from one well along real-valued fluid trajectories and then into the other well. The tunneling is found to occur through localized portals, or ``flux gates'' in the phase space. We advocate the phase-space hydrodynamic model as a general tool to understand classical quantum correspondence.

Comparison of classical and quantum phase space structure of nonrigid molecules, LiCN

We examine the classical and quantum phase space structure of the nonrigid molecule LiCN. The quantum phase space density for many vibrational eigenstates exhibits marked localization in classically chaotic regions of phase space.