Related papers: Quantum implications of non-extensive statistics
In this work, a scattering process of quantum particles through a potential barrier is considered. The statistical complexity and the Fisher-Shannon information are calculated for this problem. The behaviour of these entropy-information…
In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation.…
We consider the wave equation with uncertain initial data and medium, when the wavelength $\varepsilon$ of the solution is short compared to the distance traveled by the wave. We are interested in the statistics for quantities of interest…
We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
The semiclassical formula for the quantum propagator in the coherent state representation $<\mathbf{z}'' | e^{-i\hat{H}T/\hbar} | \mathbf{z}'>$ is not free from the problem of caustics. These are singular points along the complex classical…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…
We use the free evolution propagator to determine the quantum probability representation (i.e., the general expression of the tomogram) of any one-dimensional system described by a density state. The evolution operator for the considered…
We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson…
We derived the expression of the normalized $q$-expectation value based on the density operator to the order $1-q$ with the physical temperature in the Tsallis nonextensive statistics of entropic parameter $q$. With the derived expression…
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent,…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator for the spinor field is then constructed. We discuss the role of time-dependent…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic…
We study the properties of the survival probability of an unstable quantum state described by a Lee Hamiltonian. This theoretical approach resembles closely Quantum Field Theory (QFT): one can introduce in a rather simple framework the…