Related papers: Zeta Function Methods and Quantum Fluctuations
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
Explicit formulas for the zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to fermionic ($\alpha =3$) quantum fields living on a noncommutative, partially toroidal spacetime are derived. Formulas for the most…
Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe…
We prove that the zeta-function $\zeta_\Delta$ of the Laplacian $\Delta$ on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues,…
We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field…
This is a review of some of the interesting properties of the Riemann Zeta Function.
The recent suggestion that late time quantum dynamics may be important for resolving cosmological issues associated with our observed universe requires a consideration of several subtle issues associated with quantum cosmology, as we…
These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects…
Levitodynamics, i.e., the levitation of objects of mesoscopic size has made huge progress in the last decade, giving rise to new experimental opportunities for instance in materials science, but also allowing to address questions of…
In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum…
We present a method for computing the zeta function of a smooth projective variety over a finite field which proceeds by induction on the dimension. We have implemented our approach for some surfaces using the Magma programming language,…
A semiclassical description of quantum systems is applied to probe the dynamics of the cosmological model of an inflationary universe with quadratic inflaton potential, described in a quantum framework of geometrodynamics. The systematic…
The aim of this paper is to show further results following those published in [5], and to relate the Riemann zeta function to the relativistic cosmology.
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
The spectral zeta functions have been found many application in several branches of modern physics, including the quantum field theory, the string theory and the cosmology. In this paper, we shall consider the spectral zeta functions and…
New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…
This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are…
We revisit congruence zeta functions of smooth projective varieties over finite fields in the framework of Scholze's Berkovich motives. Via this formalism and categorical traces, we construct a new zeta function, and show that it agree with…
The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects' electromagnetic response, the necessary calculations in quantum field theory are most naturally…
Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for,…