Mathematical Physics
We study the non-equilibrium steady state of a weakly anharmonic chain of $N$ oscillators driven at its boundary by Langevin thermostats at unequal temperatures. Under a perturbative weak-anharmonicity condition, we prove a full-gradient…
The causal action principle for causal fermion systems is analyzed for a minimizing measure whose support is assumed to have the structure of a smooth manifold $\tilde{M}$. The concept of osculating vacua is introduced. It is shown that the…
We formulate quantisation of gauge field theories on globally hyperbolic Lorentzian manifolds with marked hypersurfaces within the framework of perturbative algebraic quantum field theory (pAQFT) enriched by the Batalin, Fradkin, Vilkovisky…
We investigate a radially symmetric initial-boundary value problem whose separation of variables leads to a regular self-adjoint Sturm-Liouville problem with explicitly determined coefficients and a positive weight function. The resulting…
We study energy transport in a finite one-dimensional unpinned harmonic chain with stochastic nearest-neighbor momentum exchanges and Langevin heat baths at its endpoints. Such systems are known to exhibit superdiffusive transport driven by…
History-dependent entropic formulations require a precise meaning for channelwise terminal variation and a spatial power split that remains valid for weak diffusion fields. This paper establishes both structures and places them in a single…
In this paper, we show that for Schr\"odinger operators with weakly correlated ground states, the Hohenberg-Kohn theorem holds within the maximal class of form-bounded external potentials if and only if the single-particle density is…
We introduce a Tricomi-type generalized fractional calculus in the Sonine kernel framework. The key result is that the Tricomi branch is a Stieltjes function in the admissible parameter range, so its reciprocal is a complete Bernstein…
It is shown that the asymptotics of the Ursell trapping modes on a sloping beach of small slope angle alpha coincide with the inverse Fourier transform of standard WKB exponentials, i.e., the Maslov canonical operator, as alpha tends to 0.
Every human brain folds differently, and such natural variation confounds the search for imaging biomarkers of neurodevelopmental disorders. Physics-based simulation can help determine the causal mechanisms that underpin this variability.…
We revisit the classical expansion of the planetary Hamiltonian for small eccentricities and mutual inclinations of the orbits, presenting a derivation based entirely on vector formalism. We demonstrate that the secular part of the…
In this paper, we establish an optimal global rigidity estimate for the eigenvalues of the Laguerre unitary ensemble. Using the central limit theorem, we first construct a random measure via the eigenvalue counting function and then prove…
The type D ASEP is an asymmetric two--species interacting particle system on $\Z$, in which two separately conserved species hop, bind into a composite ``bound pair'', and split. The model, along with its reversible measures and orthogonal…
We study early-warning signals of climate tipping in the metastable stochastic Ghil--Sellers energy balance model. Rather than relying on a single scalar indicator, we analyze the transition through three complementary lenses: reduced…
Jordan pairs and hermitian Jordan triples were discovered by mathematicians studying Jordan algebras, which describe the possible algebras of observables in quantum mechanics. We point out a striking correspondence between the doubly…
We prove the existence of a nematic phase in a model of $l\times w$ hard rectangles on the square lattice with two allowed orientations and a large aspect ratio $k:=l/w$. The proof is based on a two-scale cluster expansion method developed…
Probability distributions are central to information theory, statistical inference, and modern probabilistic learning. Maximum entropy selects a probability state under prescribed constraints, but it does not specify how that state is…
We prove the existence of full dimensional KAM tori for infinite dimensional mechanical systems exhibiting long range interactions, under a Diophantine condition of Bourgain type [Bourgain2005JFA], in which the radius of the invariant tori…
We settle five conjectures concerning PBW bases and centralisers for the $q$-Onsager algebra. We first prove that the Baseilhac--Kolb root vectors give a PBW basis in every linear order whenever $q$ is not a root of unity, removing the…
We review and extend the results on the group analysis of a class of generalized Kawahara equations with time-dependent coefficients. First, we provide an overview of the existing literature on Lie symmetries and Lie-invariant solutions of…