Physics
We construct the causal fermion system for globally hyperbolic spacetimes starting in the framework of algebraic quantum field theory. The fermionic projector is identified with the one-particle density operator of a quasi-free Hadamard…
We study the Dirac equation in the Reissner-Nordstr\"om geometry in horizon-penetrating coordinates up to the Cauchy horizon. A mass decomposition theorem is proved, which gives a covariant representation of the spacetime inner product that…
This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented…
Several scholars have accorded the Tychonic System a prominent place, considering it a credible alternative to the Ptolemaic and Copernican systems. In recent years, there have even been some enthusiastic contributions in support of Brahe,…
The notion of rigour relevant to the practice of physics is an endogenous one. Theoretical physics has its own internal norms about mathematical practice and notions of legitimate derivations or formal objects. These norms are often…
We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct…
We study a determinantal Coulomb gas in the complex plane associated with the external potential $$ Q(z)=\frac{1}{1-\tau^2}\big(|z|^2-\tau \text{Re } z^2\big)-2c\log|z-a|, $$ where $\tau\in[0,1)$, $c\ge0$, and $a\ge0$. In the regimes where…
It is well known that band inversion across a straight interface in a periodic medium gives rise to interface modes that are localized near the interface and propagate along it inside the bulk spectral gap. This phenomenon constitutes the…
We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of…
Timelike Liouville field theory is a candidate model for positive curvature two-dimensional quantum gravity, but a mathematically controlled Lorentzian formulation has remained elusive. In this paper we construct the theory on the cylinder…
In the Bohr model of the hydrogen atom, the energy levels are a negative constant divided by the square of the level number. It is well known that special pairs of transitions exist that have the same energy difference, and a systematic…
We consider a certain first-order linear system of ordinary differential equations, and we analyze the direct and inverse scattering problems for that linear system. The linear system involves two potentials in the Schwartz class, and those…
Using direct methods of the calculus of variations we establish the existence of an infinite class of spherically-symmetric solutions to the multi-field Schr\"odinger-Poisson system. This is achieved by proving that the energy functional…
We present MARUT, a scalable multi-GPU computational fluid dynamics (CFD) framework designed for high-fidelity simulations of compressible flows spanning subsonic to hypersonic regimes, including chemically reacting nonequilibrium flows…
In this paper, we focus on the two-component (2+1)-dimensional Fokas-Lenells equation, which models the propagation of ultrashort optical pulses in nonlinear media with multi-mode interactions and multi-dimensional effects. Firstly, we…
The string hypothesis of Bethe roots is a cornerstone in the thermodynamic analysis of quantum integrable systems, since it connects root configurations with physical quantities such as the ground-state energy, surface energy and excitation…
This paper presents a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is…
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter's groups and the associated word problem, we turn to the…
The GW plus Bethe-Salpeter equation (GW-BSE) formalism is a well-established approach for calculating excitation energies and optical spectra of molecules, nanostructures, and crystalline materials. We implement GW-BSE in the CP2K code and…
The classical definitions of the Incipient Infinite Cluster (IIC) of percolation consist in conditioning the origin on being connected to radius $n$ and letting $n$ go to infinity. We provide a short proof of that convergence in the planar…