数学物理
In this work, we introduce a classification scheme for topological phases of matter based on the topology of the space of pure states of a model $C^*$-algebra. Under it, topological phases are described by homotopy classes of sections of…
Wave scattering by localized constraints in microstructured solids is strongly influenced by the interplay of material length scales, dispersion and geometry. This work investigates plane-strain scattering of time-harmonic P and SV waves by…
We consider a Bose gas on the three-dimensional torus in the Gross--Pitaevskii regime and explain how to remove the assumptions of radiality and compact support on the interaction potential in the proof of Bose--Einstein condensation and…
We consider the vortex model on the plane, focusing on the case of vortices with the same sign and, for simplicity, assuming all vortices possess equal circulation. In particular we are interested at the time average of the vorticity…
The resonant nature of scattering in a waveguide with two barriers is proven in the case of a sufficiently arbitrary deformation of the region between the barriers. The problem is considered as an interior boundary value problem with…
In this paper, we introduce quantum Stokes matrices for a noncommutative version of meromorphic linear systems of ordinary differential equations with a pole of order $p+1$. We prove that these quantum Stokes matrices satisfy natural…
We develop a macroscopic thermodynamic theory of nematic liquid crystals starting from a kinetic theory of ordered fluids with a collision operator of Bhatnagar-Gross-Krook (BGK) type. The kinetic description incorporates mean-field…
Following the approach of B.~Enriquez~\cite{E} we exhibit the analytical properties of the products of the currents in the Yangian doubles restricted to the category of the highest weight representations. We will demonstrate that the Serre…
We review the collaboration that led to the first rigorous proof of the stability of the hydrogen molecule within quantum mechanics and discuss several related issues concerning few-charge systems. Particular emphasis is placed on the role…
We consider classical 2d lattice models with face interactions defined in terms of a fusion category. The symmetries of such models typically include an algebra of topological operators sitting on a closed path in the lattice. In the case…
We study boundary conditions in GiMmsy's covariant and instantaneous formulations of classical field theories and show that the instantaneous state space in the presence of a constant Dirichlet boundary condition is a tangent bundle to the…
We review the notion of homotopy of quantum master actions in geometric Batalin-Vilkovisky formalism. Then we construct new examples of such homotopies, coming from renormalization group flow and non-infinitesimal changes of gauge fixing.…
For any conformal net, not necessarily rational, we construct the associated Cardy-type conformal field theory on the Minkowski spacetimes $(\mathbb R/2\pi\mathbb Z)\times\mathbb R$ for closed strings and $[0,\pi]\times\mathbb R$ for open…
We study a system formed by $M$ particles moving in 3 dimensions and interacting with two heat reservoirs, each with $N\gg M$ particles. The system and the reservoirs interact via random collisions and thus evolve via a Kac-type master…
We study a quasi-exactly solvable singular sextic oscillator and its algebraic spectrum. For a distinguished range of parameters, we prove that the discriminant of the characteristic polynomial of the matrix determining the algebraic…
In this paper, we study interacting bosons at zero temperature in a random and higher-dimensional continuum model introduced by Kac and Luttinger. For weak interactions we prove that there is condensation in the lowest eigenstate of the…
We prove a sufficient condition for the absolute convergence of Mayer cluster expansions of log-partition and correlation functions applicable to lattice gases with possibly complex-valued multi-body interactions. Not only are several…
Virtual sensing -- recovering full-field structural response from sparse sensor measurements -- is a fundamental challenge in structural health monitoring. This study formulates virtual sensing as a PDE-constrained optimization (PDE-CO)…
In this paper, we considered a heterogeneous Cattaneo-Vernotte equation with an exponential type of diffusion coefficient under the fundamental initial and boundary conditions stating that the solution vanishes at $+/-$ infinity. Owing to…
We provide a systematic and rigorous geometric framework that relates three structures naturally associated to BPS central charges in $\mathcal{N}=2$ supersymmetric gauge theories: the split attractor flow (SAF) of $|Z|$, the Hessian flow…