Related papers: HeatK: A Mathematica Program for Computing Heat Ke…
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…
In this paper, we introduce heat kernel coupling (HKC) as a method of constructing multimodal spectral geometry on weighted graphs of different size without vertex-wise bijective correspondence. We show that Laplacian averaging can be…
A procedure to find optimal regimes for quantum thermal engines (QTMs) is described and demonstrated. The QTMs are modelled as the periodically-driven non-equilibrium steady states of open quantum systems, whose dynamics is approximated in…
We continue the development of the effective covariant methods for calculating the heat kernel and the one-loop effective action in quantum field theory and quantum gravity. The status of the low-energy approximation in quantum gauge…
Heating under periodic driving is a generic nonequilibrium phenomenon, and it is a challenging problem in nonequilibrium statistical physics to derive a quantitatively accurate heating rate. In this work, we provide a simple formula on the…
Understanding the relationship between the structure of light-harvesting systems and their excitation energy transfer properties is of fundamental importance in many applications including the development of next generation photovoltaics.…
The near-field interaction between two neighboring particles is known to produce enhanced radiative heat transfer. We advance in the understanding of this phenomenon by including the full electromagnetic particle response, heat exchange…
We consider the non-local energy-momentum tensor of quantum scalar and spinor fields in $2 w$-dimensional curved spaces. Working to lowest order in the curvature we show that, while the non-local terms proportional to $\Box {\cal R}$, $\Box…
Selecting optimal kernels for regression in physical systems remains a challenge, often relying on trial-and-error with standard functions. In this work, we establish a mathematical correspondence between support vector machine kernels and…
We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as $L^{1}$, $L^{2}$, and Hilbert spaces, associated to a locally compact Hausdorff space $\mathfrak{X}$ with Borel $\sigma$-algebra $\mathcal{B}$,…
Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full…
I give a short guide into applications of the heat kernel technique to string/brane physics with an emphasis on the emerging boundary value problems.
Computing the trajectories of particles in generic beamlines is an important ingredient of experimental particle physics, in particular regarding near-beam detectors. A new tool, Hector, has been built for such calculations, using the…
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…
We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel…
The article by Anton E. M. van de Ven, Class. Quantum Grav. \textbf{15} (1998), is one of the fundamental references for higher-order heat kernel coefficients in curved backgrounds and with non-abelian gauge connections. In this manuscript,…
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties…
We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.
We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic…