Related papers: Zeta Function Methods and Quantum Fluctuations
In loop quantum cosmology, the values of volume fluctuations and correlations determine whether the dynamics of an evolving state exhibits a bounce. Of particular interest are states that are supported only on either the positive or the…
In this paper we give a pedagogical introduction to the ideas of quantum thermodynamics and work fluctuations, using only basic concepts from quantum and statistical mechanics. After reviewing the concept of work, as usually taught in…
It is suggested that the vacuum expectation of the quantum vacuum energy-momentum is zero, but quantum fluctuations give rise to a space-time curvature equivalent to that of a cosmological constant or dark energy. Calculations within…
The purpose of this article is to give an explicit description, in terms of hypergeometric functions over finite fields, of zeta function of a certain type of smooth hypersurfaces that generalizes Dwork family. The point here is that we…
We have studied the effects of quantum fluctuations on dynamical behavior by using squeezed state approach. Our numerical results of the kicked harmonic oscillator demonstrate qualitatively and quantitatively that quantum fluctuations can…
A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…
Coupling tailored electromagnetic fluctuations to materials provides a resource for controlling correlated quantum matter. By structuring the frequency, spatial, and modal distribution of fluctuations through a new generation of cavity…
After the emergence of quantum mechanics and realising its need for an accurate understanding of physical systems, numerical methods were being used to undergo quantum mechanical treatment. With increasing system correlations and size,…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends previous work of ours to all curves for which a good lift to characteristic zero is known. We develop all the necessary bounds,…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
This note contains a short proof of the functional equation for the zeta function.
The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
We use the $\zeta$-function regularization method to evaluate the finite temperature 1-loop effective potential for $\phi^4$ theory in the Godel spacetime. It is used to study the effects of temperature and curvature coupling on the…
We study the thermodynamics of ultrasmall metallic grains with level spacing $\delta$ comparable or smaller than the pairing correlation energy, at finite temperatures, $T \gsim \delta$. We describe a method which allows to find quantum…
A new minimal coupling method is introduced. A general dissipative quantum system is investigated consistently and systematically. Some coupling functions describing the interaction between the system and the environment are introduced.…
We present some methods and results in the application of algebraic geometry and computer algebra to the study of algebraic vector bundles, foliations and zeta functions. A connection of the methods and results with noncommutative geometry…
We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…
During the inflationary phase of the early universe, quantum fluctuations in the vacuum generate particles as they stretch beyond the Hubble length. These fluctuations are thought to result in the density fluctuations and gravitational…