Related papers: HeatK: A Mathematica Program for Computing Heat Ke…
Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients.
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
We define some of the programming and system-level challenges facing the application of quantum processing to high-performance computing. Alongside barriers to physical integration, prominent differences in the execution of quantum and…
We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in $\mathbb{R}^d$. They are…
Quantum computing raises the possibility of solving a variety of problems in physics that are presently intractable. A number of such problems involves the physics of systems in or near thermal equilibrium. There are two main ways to…
In the pursuit of numerically identifying the ground state of quantum many-body systems, approximate quantum wavefunction ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum…
Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\aa)}$ be the…
In recent years, much attention has been paid to the development of techniques which transfer trapped particles to very low temperatures. Here we focus our attention on a heating mechanism which contributes to the finite temperature limit…
Accurate radiative transfer coefficients (emissivities, absorptivities, and rotativities) are needed for modeling radiation from relativistically hot, magnetized plasmas such as those found in Event Horizon Telescope sources. Here we…
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…
We give a detailed presentation of the theory and numerical implementation of an expression for the adiabatic energy flux in extended systems, derived from density-functional theory. This expression can be used to estimate the heat…
We derive all heat kernel coefficients for Laplacians acting on scalars, vectors, and tensors on fully symmetric spaces, in any dimension. Final expressions are easy to evaluate and implement, and confirmed independently using spectral sums…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of…
We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction…
Radiative processes, where a photon/neutrino is emitted as a result of a collision or decay of a particle, play a central role in atomic, nuclear and particle physics. Their rate is determined by certain off-diagonal matrix elements with…
We study heat semigroups generated by self-adjoint Laplace operators on metric graphs characterized by the property that the local scattering matrices associated with each vertex of the graph are independent from the spectral parameter. For…
Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal…
A new web-server called The Molecule Calculator (MolCalc) is presented. The entry page is a molecular editor (JSmol) for interactive molecule building. The resulting structure can then be used to estimate molecular properties such as heats…
We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for…