Related papers: Zeta Function Methods and Quantum Fluctuations
I survey some recent developments in the theory of zeta functions associated to infinite groups and rings, specifically zeta functions enumerating subgroups and subrings of finite index or finite-dimensional complex representations.
This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and…
Spectral functions, such as the zeta functions, are widely used in Quantum Field Theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point…
Some recent (1997-1998) theoretical results concerning the $\zeta$-function regularization procedure used to renormalize, at one-loop, the effective Lagrangian, the field fluctuations and the stress-tensor in curved spacetime are reviewed.
Quantum fluctuations or other moments of a state contribute to energy expectation values and can imply interesting physical effects. In quantum cosmology, they turn out to be important for a discussion of density bounds and instabilities of…
To motivate our discussion, we consider a 1+1 dimensional scalar field interacting with a static Coulomb-type background, so that the spectrum of quantum fluctuations is given by a second-order differential operator on a single coordinate r…
We present a pedagogical exposition of some applications of functional methods in quantum field theory: we use heat-kernel and zeta-function techniques to study the Casimir effect, the pair production in strong electric fields, quantum…
In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
The vacuum fluctuations give rise to a number of phenomena; however, the the Casimir Effect is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral…
Some general properties of local $\zeta$-function procedures to renormalize some quantities in $D$-dimensional (Euclidean) Quantum Field Theory in curved background are rigorously discussed for positive scalar operators $-\Delta + V(x)$ in…
One of the most important goals in quantum thermodynamics is to demonstrate advantages of thermodynamic protocols over their classical counterparts. For that, it is necessary to (i) develop theoretical tools and experimental set-ups to deal…
The paper reviews existing results about the statistical distribution of zeros for the three main types of zeta functions: number-theoretical, geometrical, and dynamical. It provides necessary background and some details about the proofs of…
Of indisputable relevance for non-equilibrium thermodynamics, fluctuations theorems have been generalized to the framework of quantum thermodynamics, with the notion of work playing a key role in such contexts. The typical approach consists…
We introduce and study new versions of polylogarithms and a zeta function on a completion of $\mathbb F_q (x)$ at a finite place. The construction is based on the use of the Carlitz differential equations for $\mathbb F_q$-linear functions.
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
The notion of vacuum fluctuations of the gravitational field plays important role in cosmology. The strong variable gravitational field of the very early Universe amplifies these fluctuations and transforms them into macroscopical…
Boson, fermion, and super oscillators and (statistical) mechanism of cosmological constant; finite approximation of the zeta-function and fermion factorization of the bosonic statistical sum considered.
The relativistic invariant zeta-function approach to computation of the vacuum energy contribution to cosmological constant is discussed. It is shown that this value is determined by the fourth power of the quantized field mass, while the…