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…

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…

Magnetic reconnection is a ubiquitous plasma phenomenon that plays a critical role in particle heating and energization. During reconnection, the topology of magnetic field rearranges, depositing energy into the surrounding plasma through…

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 investigate the February 19, 2025, re-entry of a Falcon 9 upper stage using optical observations from 43 meteor cameras across central Europe together with radar detections of re-entry plasma obtained with the 32.55 MHz SIMONe Germany…

Some optical measurements require relative timing of intensity variations with accuracy much finer than the camera frame period. One motivating example is dynamic aurora, where different prompt emissions are expected to originate from…

In a low Reynolds number fluid environment that microswimmers encounter, back-and-forth motion cannot lead to net displacement. In mammalian sperm, the mechanical wave propagating along their single flagellum breaks the cancellation between…

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…

Virological measurements are often treated as reports of virion structure, mechanics, dielectric response, infectivity, or titer. In practice, an experiment observes a protocol-conditioned projection of a richer latent virion--environment…

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…

Why does the mammalian vascular tree maintain a conserved branching exponent $\alpha^* \approx 2.72$ across a $10^7$-fold range in body mass, despite a fundamental shift from viscous to wave-dominated transport? We prove this universality…

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…

Murray's cubic branching law ($\alpha=3$) predicts a universal diameter scaling exponent for all hierarchical transport networks, yet arterial trees yield $\alpha \sim 2.7-2.9$. We show that this discrepancy has a structural origin:…

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…

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…