Related papers: Nonlinearity in Quantum Theory and Closed Timelike…
This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear…
In the operatorial formulation of quantum statistics, the time evolution of density matrices is governed by von Neumann's equation. Within the phase space formulation of quantum mechanics it translates into Moyal's equation, and a formal…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
Recently, there has been much interest in the evolution of quantum particles on closed time-like curves (CTCs). However, such models typically assume point-like particles with only two degrees of freedom - a very questionable assumption…
The dynamics of a three-state quantum walk with amplitude-dependent phase shifts is investigated. We consider two representative inputs whose linear evolution is known to display either full dispersion of the wave packet or intrinsic…
We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation.…
A non-Markovianity measure for quantum channels is introduced based on causality measure - a monotone of causal (temporal) correlations - arising out of the pseudo-density matrix (PDM) formalism which treats quantum correlations in space…
We discuss the notion of quantum mechanical coherence in its connection with time evolution and stationarity. The transition from coherence to decoherence is examined in terms of an equation for the time dependence of the density matrix. It…
The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical…
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in…
Many solutions of Einstein's field equations contain closed timelike curves (CTC). Some of these solutions refer to ordinary materials in situations which might occur in the laboratory, or in astrophysics. It is argued that, in default of a…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Time dependent dynamics of the chaotic quantum-mechanical system has been studied. Irreversibility of the dynamics is shown. It is shown, that being in the initial moment in pure quantum-mechanical state, system makes irreversible…
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive…
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
A theory of quantum dynamics based on a discrete structure underlying the space time manifold is developed for single particles. It is shown that at the micro domain the interaction of particles with the underlying discrete structure…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…