Related papers: Pseudodynamical evolution and path integral in qua…
We study the time evolution of a state of a relativistic quantum field theory restricted to a spatial subregion $\Omega$. More precisely, we use the Feynman-Vernon influence functional formalism to describe the dynamics of the field theory…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
Process of formation of the universe with its further expansion in the first evolution stage is investigated in the framework of Friedmann-Robertson-Walker metrics on the basis of quantum model, where a new type of matter is introduced,…
We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary…
We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the…
We consider a quantum system dynamics caused by successive selective and non-selective measurements of the probe coupled to the system. For the finite measurement rate $\tau^{-1}$ and the system-probe interaction strength $\gamma$ we derive…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
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 use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the…
We explore a general feature of the interaction mediated by the gravitational fields of spatially superposed masses. For this purpose, based on quantum information theory, we characterize the evolution of two particles each in a…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
This article in Urdu presents an introduction to extension of an established branch of mathematics called game theory towards the quantum domain. We describe concepts of quantum games and evolutionary stability and go through some of the…
In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Several Liouville--Arnold-type theorems and a \( q…
We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the na\"ive continuum limit but which, nevertheless, induce non-trivial effects due to quantum…