Related papers: HeatK: A Mathematica Program for Computing Heat Ke…
We derive estimates of the derivatives of the heat kernel on noncompact symmetric spaces and on locally symmetric spaces. Applying these estimates we study the $L^{p}$-boundedness of Littlewood-Paley-Stein operators and the Laplacian of the…
The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in…
Our knowledge about the "cold" Universe often relies on molecular spectra. A general property of such spectra is that the energy level populations are rarely at local thermodynamic equilibrium. Solving the radiative transfer thus requires…
We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field…
In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
Transport coefficients are obtained by incorporating a gauge principle into thermo field dynamics of inhomogeneous systems. In contrast to previous derivations, neither imaginary time arguments nor perturbation theory in powers of a…
We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin-Niyogi, which produces low dimensional representations of the data, based…
In this paper we derive an explicit formula for the heat kernel of the asymmetric quantum Rabi model (AQRM), a symmetry breaking generalization of the quantum Rabi model (QRM). The method described here is an extension of the recently…
In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we…
We introduce thermometers to define the local temperature of an electronic system driven out-of-equilibrium by local AC fields. We also define the effective temperature in terms of a local fluctuation-dissipation-relation. We show that…
We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle)…
A heat engine is a machine which uses the temperature difference between a hot and a cold reservoir to extract work. Here both reservoirs are quantum systems and a heat engine is described by a unitary transformation which decreases the…
In this note, we compute the Hadamard coefficients of (algebraically) integrable Schrodinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens' principle, and our result completes, in a…
We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study…
Recent developments in nanoscale experimental techniques made it possible to utilize single molecule junctions as devices for electronics and energy transfer with quantum coherence playing an important role in their thermoelectric…
We present a new covariant method of construction of the (position space) propagators in the $N$-dimensional (Euclidean) anti-de Sitter background for any gravitational theory with the Lagrangian that is an analytic expression in the…
Quantum chemistry calculations such as the prediction of molecular properties and modeling of chemical reactions are a few of the critical areas where near-term quantum computers can showcase quantum advantage. We present a method to…
We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a…
We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the…