Mathematical Physics
This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…
Quantum $L_\infty$ algebras are higher loop generalizations of cyclic $L_\infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and…
Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this…
We determine the full persistence probability distribution for a non-Markovian stochastic process, motivated by first-passage questions arising in interacting spin systems and allied systems. We show that this distribution is governed by a…
The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios…
In this paper, we study the properties of averaged fundamental solutions of a special type for Laplace operators in the Euclidean space of an arbitrary dimension. We consider a class of kernels suitable for probabilistic averaging, and…
We prove an exact finite-volume symmetry formula for two-point functions in the periodic $N$-state superintegrable chiral Potts spin chain. We show that, for every chain length $L$ and every simultaneous eigenvector of the Hamiltonian and…
We consider a Dirichlet waveguide in $\mathbb{R}^n$ ($n = 2,3$) with an attached cavity. We show that if the cavity admits a small gap, then the original embedded eigenvalues turn into resonances. The main question we address is how the…
We utilize the concentration of measure phenomenon to study the large $N$ limit of the $O(N)$ principal chiral model. The partition function in this limit is demonstrated to be that of a free massive theory.
We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass and rigidity interface parameters are modulated in time.…
We introduce a homothetic extension of classical Weyl integrable geometry by generalizing the usual linear gauge transformations to affine homothetic transformations centered at a distinguished harmonic, scale-invariant form $\alpha_d$.…
Slowly varying nonuniform strains of non-magnetic wave propagating media with honeycomb symmetry induce an effective- or pseudo-magnetic field, a phenomenon observed first in graphene, and later in photonic crystals and other physical…
In this paper, we apply techniques of geometric quantization to study the response of the integer and fractional quantum Hall effects to toroidal geometry deformation. The main method is that of using complex time Hamiltonian evolution to…
We study shape resonances of two-dimensional magnetic Stark Hamiltonians in the semiclassical limit. The magnetic field is assumed to be constant and the scalar potential is a perturbation of a linear potential. Under the assumption that…
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equations. Conservation laws and a Hamiltonian structure for the…
We study stationary scattering for Schr\"odinger operators in $\mathbb R^3$ with finitely many concentric $\delta$--shell interactions of constant real strengths. Starting from the self--adjoint realization and the boundary resolvent…
In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
The article presents a method of cluster expansions for groups of operators associated with the von Neumann equations for states and the Heisenberg equations for observables, aiming to construct generating operators for nonperturbative…