Related papers: Comparing classical and quantum probability distri…
In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the semiclassical limit. This system is analyzed using both time-independent perturbation theory (PT)…
A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might…
Quantization in the mini-superspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such…
We suggest a somewhat non-standard view on a set of curious, paradoxical from the standpoint of simple classical physics and everyday experience phenomena. There are the quantisation (discrete set of values) of the observables (e.g.,…
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into…
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical…