数学物理

We investigate the Dirichlet Laplacian in two spatial waveguides coupled through an elliptic window. The elliptic geometry breaks rotational symmetry and introduces anisotropy through the semi-axes of the aperture, which modifies the…

In their 1972 study of approach to equilibrium, Lanford and Robinson showed that gauge-invariant quasi-free states of lattice fermions maximize entropy among all translation-invariant states with a fixed two-point function, and suggested…

Identifying the nodes that must be directly controlled to steer a network along a desired trajectory remains an open problem for digraphs, and even more so for hypergraphs. In this manuscript, we investigate network systems coupled via…

We develop a geometric framework for the exact integration of Hamiltonian systems based on triangular closure relations among a finite family of functions. Unlike Liouville-Arnold integrability and its noncommutative generalizations, the…

Square roots of complexified (complex) quaternions, namely, the Hamilton quaternion, coquaternion, nectorine, and conectorine are investigated. The isomorphisms between the complex quaternions and 3-dimensional multivectors of Clifford…

We study Stark Hamiltonians with a $\delta$-interaction supported on a compact hypersurface in $\mathbb R^d$. Let $\Sigma$ be a compact Lipschitz hypersurface and let $\alpha\in L^\infty(\Sigma;\mathbb R)$. We define the operator…

In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double $\mathcal D(\mathcal G)$ of a finite 2-group $\mathcal G$ as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten…

We show that the equations of motion of the rigid body about centre of mass in the Newtonian field with a quadratic potential are special reductions of period-one closure of the Darboux dressing chain for the Schr\"odinger operators with…

We consider the kinetic transport equation that arise in the Boltzmann-Grad limit of the two-dimensional periodic Lorentz Gas. This equation has been obtained by extending the phase space of positions and velocities through the introduction…

We consider the Euclidean vacuum for linearized gravity on the global de Sitter space, obtained from the Euclidean Green's function on the 4-sphere. We use the notion of Calder\'on projectors to recover a quantum state for the Lorentzian…

We analyze the entropy production of Quantum Reset Models (QRMs) corresponding to quantum dynamical semigroups driven by Lindbladians motivated by a probabilistic description of dissipation in an external environment. We investigate the…

We consider a class of hyperplane arrangements $\mathcal A$ in ${\mathbb C}^n$ that generalise the locus configurations of \cite{CFV}. To such an arrangement we associate a second order partial differential operator of Calogero-Moser type,…

We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous…

We consider a quantum gas consisting of $N$ hard spheres with radius $\frak{a} > 0$, obeying bosonic statistics and moving in the box $\Lambda = [0;L]^3$ with periodic boundary conditions. We are interested in the ground state energy per…

In random matrices with independent and continuous matrix entries, the degeneracy probability of the eigenvalues is known to be zero. In this paper, random matrices including discontinuous matrix entries are analyzed in order to observe how…

Zero-helicity vortices, such as Hill's vortex and field-reversed configurations (FRCs), have long been assumed to be toroidal in topology. This paper proves this assumption false: under arbitrarily small odd-parity (with respect to the…

We study the critical droplet for a close-to-equilibrium Widom-Rowlinson model of interacting particles, represented by disks of radius $1$, in the two-dimensional plane at low temperature. The critical droplet is the set of macroscopic…

We prove that the grand canonical Gibbs state of an interacting two-dimensional quantum Bose gas confined by a trapping potential converges to the complex Euclidean field theory with local quartic self-interaction, when the density of the…

An anisotropic elastic material is referred to as exotic when, under specific loadings, its mechanical response exhibits a higher degree of symmetry than that prescribed by its intrinsic material symmetry. Such materials, which may be…

In this paper, we study systems of nonlinear partial differential equations which describe surfaces of constant curvature. From the flatness condition of connection 1-forms, we present a classification of systems of Camassa-Holm-type…