de Broglie-Bohm formulation of quantum mechanics, quantum chaos and breaking of time-reversal invariance

A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically, proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’     

Maximally causal quantum mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics     

On the incompatibility of standard quantum mechanics and conventional de Broglie-Bohm theory

It is shown that conventional de Broglie-Bohm quantum theory is incompatible with the standard quantum theory of a system unless the former is ergodic.     

Modified De Broglie-Bohm Approach to Quantum Mechanics

A modified de Broglie-Bohm (dBB) approach to quantum mechanics is presented. In this new deterministic theory, which uses complex methods in an intermediate step, the problem of zero velocity for bound states encountered in the dBB formulation does not appear. Also, this approach is equivalent to standard quantum mechanics when averages of observables like position, momentum and energy are taken.     

Extension of the de Broglie-Bohm theory to the Ginzburg-Landau equation

The de Broglie-Bohm approach permits to assign well defined trajectories to particles that obey the Schroedinger equation. We extend this approach to electron pairs in a superconductor. In the stationary regime this extension is completely natural; in the general case additional postulates are required. This approach gives enlightening views for the absence of Hall effect in the stationary regime and for the formation of permanent currents.     

How to Avoid Peres' “incompatible results of quantum measurements”

It is demonstrated how, in terms of hidden variables, the claimed incompatibility of results of quantum measurements, obtained in a recent work by A. Peres, may be avoided. The new property which restores the compatibility of quantum measurement results is called the nonreproducibility of individual subquantum states.Research director N.F.W.O. (Belgium).     

An interpretation within philosophy of the relationship between classical mechanics and quantum mechanics

A mapping of a finite directed graph onto a curve in space-time is considered. The mapping induces the dynamics of a free particle moving along the curve. The distinction between the Lagrangian and the Hamiltonian formulation of particle mechanics is expressed in terms of the distinction between referring to a particle in space and time and referring to the points in space which the particle occupies, respectively. These elements are combined to yield an interpretation of Feynman's path integral formulation of quantum mechanics. Describing a bound state of a system as a particle is discussed.     

Erratum to: Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment

正The article Realistic interpretation of quantum mechanics and encounter-delayed-choice experiment,written by Gui Lu Long,Wei Qin,Zhe Yang,and Jun-Lin Li,was originally published online without open access.After publication in volume 61,issue 3:030311 the author decided to opt for Open Choice and to make the article an open access publication.Therefore,the copyright of the article has been changed to c?The Author(s)2017 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Completeness of observables and particle trajectories in quantum mechanics

The complete set of observables (bilinear Hermitian forms) is determined for the Schrödinger equation and their connection with the curvature and torsion of the curves, where conservation laws are fulfilled, is established. It is shown that these curves for a free particle, in the general case, are spiral lines with the radius and step length defined by the observables at the initial point (both parameters are proportional to the de Broglie wavelength). A spiral line turns to a straight line under some conditions. The trajectory variations are considered in the problem with a potential step and a rectangular barrier. It is shown that spiral lines can be transformed into straight lines and vice versa. All observables, which are changed along the potential barrier, can be restored under some constraints on the potential. The Hermitian transformations at the potential step are connected with the Lorentz transformations. A qualitative explanation of the double-slit experiment for extremely low intensity of the particles' source in the absence of the interference conditions is suggested.     

对"Aspect实验与量子力学解释"一文的折磨

简述了Ｂｏｈｍ思想实验和Ｂｅｌｌ不等式中存在的问题，指出Ａｓｐｅｃｔ实验同Ｂｏｈｒ与Ｅｉｎｓｔｅｉｎ之间的“巨人之争”完全无关。     

Principles of maximally classical and maximally realistic quantum mechanics

Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than N+1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative definition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie-Bohm realistic theory gives highly nonclassical trajectories.     

Kinetic effects in recombination of optical excitations in disordered quantum heterostructures: Theory and experiment

An overview of recent experimental and theoretical results on stationary and time-dependent photoluminescence spectra in disordered semiconductor heterostructures is presented. In particular, temperature-dependent peak position and linewidth of the luminescence spectra, as well as the luminescence intensity are considered along with the time evolution of the luminescence intensity after pulsed excitation. Emphasis is given on the comparison between experimental and theoretical results aiming at a characterization of disorder in the underlying structures.