Related papers: Heat kernel and number theory on NC-torus
We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) $AdS_N$ for $N\geq 3$ using the group theoretic techniques employed for $AdS_3$ in arXiv:0911.5085. Our approach…
We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in…
We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using Random Matrix Theory considerations, that both the average phonon heat current and its variance are…
We develop the heat kernel method in the context of finite temperature quantum field theory. We compute the heat kernel expansion in the presence of general gauge and scalar fields which may be non Abelian and non stationary. The Polyakov…
The study of spectral properties of natural geometric elliptic partial differential operators acting on smooth sections of vector bundles over Riemannian manifolds is a central theme in global analysis, differential geometry and…
Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the…
We consider a generic curved non-commutative torus extending the notion of conformally deformed non-commutative torus from \cite{Connes-Tretkoff}. In general, a curved non-commutative torus is no longer represented by a spectral triple, not…
Let $\alpha(x)$ be a measurable function taking values in $ [\alpha_1,\alpha_2]$ for $0<\A_1\le \A_2<2$, and $\kappa(x,z)$ be a positive measurable function that is symmetric in $z$ and bounded between two positive constants. Under a…
By applying the particle-number projection to the finite-temperature BCS theory, the $S$-shaped heat capacity, which has recently been claimed to be a fingerprint of the superfluid-to-normal phase transition in nuclei, is reexamined. It is…
We study the behavior of the heat kernel of the Hodge Laplacian on a contact manifold endowed with a family of Riemannian metrics that blow-up the directions transverse to the contact distribution. We apply this to analyze the behavior of…
A quantitative description of the properties of hot nuclear matter will be needed for the interpretation of the available and forthcoming astrophysical data, providing information on the post merger phase of a neutron star coalescence. We…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating…
We develop the finite temperature theory of p-adic string models. We find that the thermal properties of these non-local field theories can be interpreted either as contributions of standard thermal modes with energies proportional to the…
We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics…
For a large class of field theories there exist portions of parameter space for which the loop expansion predicts increased symmetry breaking at high temperature. Even though this behavior would clearly have far reaching implications for…
We study second-order elliptic partial differential operators acting on sections of vector bundles over a compact manifold with boundary with a non-scalar positive definite leading symbol. Such operators, called non-Laplace type operators,…
In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in H\"older space and the zero-order potential term in generalized Kato's class, and obtain sharp two-sided estimates as well as…
A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…
We derive nonperturbative flow equations within an effective constituent quark model for two quark flavors. Heat-kernel methods are employed for a renormalization group improved effective potential. We study the evolution of the effective…
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…