Related papers: The Polyakov loop and the heat kernel expansion at…
The effects of the Polyakov loop and of a regularization procedure that allows the presence of high momentum quark states at finite temperature is investigated within the Polyakov-loop extended Nambu--Jona-Lasinio model. The characteristic…
We present a time-dependent formulation of coupled cluster theory. This theory allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal…
An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements…
We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an…
At low temperatures we expect that all QCD observables are defined in terms of hadrons. This includes the partition function as well as the Polyakov loop in all representations. We analyze the physics underlying a microscopic derivation of…
In this article it will be introduced a new theorem, can be considered a generalization of Hellmann-Feynman theorem[1]. The latter used in conjunction with the quantization of the free energy[2] of a quantum system allows to derive…
At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are…
We demonstrate that quantum mechanics entails a fundamental lower bound on the thermalization time $\tau$ of any system. At finite temperature, we show that $\tau$ is bounded by half the Planckian dissipation time, $\tau \geq \tau_{\rm…
This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, 1) placing what was studied in [1] for thermal quantum fields in the context of early universe cosmology, and 2) extending the…
Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature…
We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation…
We study semigroups generated by two-dimensional relativistic Hamiltonians with magnetic field. In particular, for compactly supported radial magnetic field we show how the long time behaviour of the associated heat kernel depends on the…
We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\mathbb{R}^d$. They are…
The spherically symmetric layer of matter is considered within the frameworks of general relativity. We perform generalization of the already known theory for the case of nonconstant surface entropy and finite temperature. We also propose…
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…
We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the…
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic…
We study the Borel summability of the small time expansion of the heat kernel for the Schr\"odinger operator in several dimensions. On the torus, we prove a Poisson formula.
We study the one-loop Polyakov-loop effective potential in pure gluonic matter under constant acceleration. We perform the computation in both the Euclidean Rindler spacetime and the optical spacetime, which are related via a conformal…