Related papers: HeatK: A Mathematica Program for Computing Heat Ke…
We consider an approximate solution to the heat equation which consists of the derivatives of heat kernel. Some conditions in the initial value, under which the approximation converges to the solution of the heat equation or diverges when…
We propose an efficient regularization method for functional determinants of radial operators using heat kernel coefficients. Our key finding is a systematic way to identify heat kernel coefficients in the angular momentum space. We…
We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…
Near-field radiative heat transfer is investigated in composite media including nanoparticles. By modeling pair interactions only, the effective thermal conductivity due to near field radiation is calculated based on a thermal nodes model.…
Interesting problems in quantum computation take the form of finding low-energy states of (pseudo)spin systems with engineered Hamiltonians that encode the problem data. Motivated by the practical possibility of producing very…
In this perspective, we discuss thermal imbalance and the associated electron-mediated thermal transport in quantum electronic devices at very low temperatures. We first present the theoretical approaches describing heat transport in…
In the paper the thermal energy transfer for elementary particles is described. The quantum heat transport equation is obtained. It is shown that for thermal excitation of the order of the relaxation time the excited matter response is…
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…
A covariant scattering kernel is a core component in any self-consistent general relativistic radiative transfer formulation in scattering media. An explicit closed-form expression for a covariant Compton scattering kernel with a good…
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…
Quantum thermodynamics aims to explore quantum features to enhance energy conversion beyond classical limits. While significant progress has been made, the understanding of caloric potentials in quantum systems remains incomplete. In this…
We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the…
We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.
We present a diagram technique used to calculate the Seeley-DeWitt coefficients for a covariant Laplace operator. We use the combinatorial properties of the coefficients to construct a matrix formalism and derive a formula for an arbitrary…
The generating function method is applied to the trace of the heat kernel and the one-loop effective action derived from the covariant perturbation theory. The basis of curvature invariants of second order for the heat kernel (Green…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
The Heat Kernel Method is applied to the constituent quark model. We calculate the effect of thermal quark fluctuations on the meson action and the resulting quark condensate and pi pi-scattering amplitude at finite temperature. The quarks…
This work introduces novel numerical algorithms for computational quantum mechanics, grounded in a representation of the Laplace operator -- frequently used to model kinetic energy in quantum systems -- via the heat semigroup. The key…
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular…
In this paper, we study the geometry associated with Schroedinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both…