Related papers: Discrete time heat kernel and UV modified propagat…
We generalize the Endo formula originally developed for the computation of the heat kernel asymptotic expansion for non-minimal operators in commutative gauge theories to the noncommutative case. In this way, the first three non-zero heat…
Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their…
The aim of this article is to calculate (to first order in $\hbar$) the renormalized effective action of a self interacting massive scalar field propagating in the space-time due to a cylindrically symmetric, rotating body. The vacuum…
Asymptotic expansions of heat kernels and heat traces of Schr\"odinger operators on non-compact spaces are rarely explored, and even for cases as simple as $\mathbb{C}^n$ with (quasi-homogeneous) polynomials potentials, it's already very…
We apply the Davies method to give a quick proof for upper estimate of the heat kernel for the non-local Dirichlet form on the ultra-metric space. The key observation is that the heat kernel of the truncated Dirichlet form vanishes when two…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
Accurate modeling of ultrasound wave propagation is essential for high-fidelity simulation and imaging in ultrasonic testing. A primary challenge lies in characterizing the excitation source, particularly for transducers with large…
Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding…
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…
Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis…
A transducer of single photons between microwave and optical frequencies can be used to realize quantum communication over optical fiber links between distant superconducting quantum computers. A promising scalable approach to constructing…
A method for diffracting the weak probe beam into unidirectional and higher-order directions is proposed via a novel Rydberg electromagnetically induced grating, providing a new way for the implementations of quantum devices with cold…
We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.
This paper is devoted to the computation of discrete propagators in two-dimensional crystals and their application to a number of time dependent problems. The methods to compute such kernels are provided by a tight-binding representation of…
We design a class of spatially inhomogeneous heat spreaders in the context of steady-state thermal conduction leading to spatially uniform thermal fields across a large convective surface. Each spreader has a funnel-shaped design, either in…
We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.
The heat-kernel expansion and $\zeta$-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
In this paper we will present very recent results obtained in the ambit of quantum electrodynamics in curved spacetime. We utilize a newly developed non-perturbative heat kernel asymptotic expansion on homogeneous Abelian bundles over…
We discuss a variety of developments in the study of large time behavior of the positive minimal heat kernel of a time independent (not necessarily symmetric) second-order parabolic operator defined on a domain M in $R^d$, or more…