Related papers: On the Frechet Root Kernel of Certain Wave Equatio…
In this paper, we study an infinite system of Fredholm series of polynomials in $\lambda$, formed, in the classical way, for a continuous Hilbert-Schmidt kernel on $\mathbb{R}\times\mathbb{R}$ of the form…
Schroedinger's equation gave early quantum theory a visual language that looked like physics again: a wave evolving by a linear differential equation. This essay argues that the same success also seeded a recurring impulse to keep quantum…
In spite of their importance for understanding phonon transport phenomena in thin films and polycrystalline solids, the effects of boundary roughness scattering on phonon specularity and coherence are poorly understood because there is no…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…
We study the kernel and cokernel of the Frobenius map on the $p$-typical Witt vectors of a commutative ring, not necessarily of characteristic $p$. We give some equivalent conditions to surjectivity of the Frobenus map on both finite and…
We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
We present a quaternion wavefunction formulation that reduces the incompressible Euler equations to a single nonlinear Schr\"odinger-type equation with a holomorphic constraint, revealing hidden geometric structure connecting quantum and…
This paper addresses the first principles description of coherent phonons in systems subjected to optical excitations and/or doping. We reformulate the first-principles Ehrenfest equation (fpEE) [Phys. Rev. X {\bf 13}, 031026 (2023)] in…
We analyze a numerical method for computing Fredholm determinants of trace class and Hilbert Schmidt integral operators defined in terms of matrix-valued kernels on the entire real line. With this method, the Fredholm determinant is…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
In this work we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We…
Starting with the many-body Schr\"odinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were…
In the early 1930's, Erwin Schroedinger, motivated by his quest for a more classical formulation of quantum mechanics, posed a large deviation problem for a cloud of independent Brownian particles. He showed that the solution to the problem…
For a transition $F_e=0\leftrightarrow F_g=1$ driven by a linearly polarized light and probed by a circularly light, quantum coherence effects are investigated. Due to the coherence between the drive Rabi frequency and Zeeman splitting,…
Operator learning is a recent development in the simulation of Partial Differential Equations (PDEs) by means of neural networks. The idea behind this approach is to learn the behavior of an operator, such that the resulting neural network…