Mathematical Physics
We consider a basis of square integrable functions on a rectangle, contained in $R^2$, constructed with Legendre polynomials, suitable, for instance, for the analogical description of images on the plane or in other fields of application of…
We study a lattice Nambu-Jona-Lasinio model with SU(2) and SU(3) flavor symmetries of staggered fermions in the Kogut-Susskind Hamiltonian formalism. This type of four-fermion interactions has been widely used for describing low-energy…
We introduce a notion of a \emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings. On a high level, our result shows that…
A minor change in the Barcelos-Wotzasek (BW) symplectic algorithm for constrained systems is proposed. The change addresses some criticism that formalism has received, placing it on the same footing as Dirac's algorithm.
We propose a general approach for deriving transparent boundary conditions for the stationary Schroedinger equation with arbitrary potential. It is proven that the transparent boundary conditions can be written in terms of the…
We investigate the stability of weak symmetry-protected topological phases (SPTs) in the presence of short-range interactions, focusing on the tenfold way classification. Using Atiyah's Real $\mathit{KR}$-theory and Anderson-dualized…
In recent years, a lot of effort has been put in describing the hydrodynamic behavior of integrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the…
We study the Schr\"{o}dinger operator describing a two-dimensional quantum particle moving in presence of $ N \geqslant 1 $ Aharonov-Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an…
We consider a charged quantum particle immersed in an axial magnetic field, comprising a local Aharonov-Bohm singularity and a regular perturbation. Quadratic form techniques are used to characterize different self-adjoint realizations of…
We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $\mathbb{R}^3$. An explicit general solution is given in terms of classical integral operators,…
Embedding formula allows to recycle solution of a family boundary value problems by expressing all the solutions in terms of a small number of solutions. Such formulas have been previously derived in the context of diffraction by applying a…
Continuous fields (or bundles) of $C^*$-algebras form an important ingredient for describing emergent phenomena, such as phase transitions and spontaneous symmetry breaking. In this work, we consider the continuous $C^*$-bundle generated by…
Given a supermanifold equipped with an odd distribution of maximal dimension and constant symbol, we construct the formal moduli problem of deformations of the distribution. This moduli problem is described by a local super dg Lie algebra…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
We present a metriplectic formulation of the radiative transfer equation with polarization and varying refractive index and show that this formulation automatically satisfies the first two laws of thermodynamics. In particular, the derived…
We consider two Hamiltonians that are close to each other, $H_1 \approx H_2 $, and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle \psi_0, \mathrm{e}^{\mathrm{i} t H_2} \mathrm{e}^{-\mathrm{i} t H_1}…
We study the stability of the mesoscopic fluctuations of certain orthogonal polynomial ensembles on the real line utilizing the recurrence relation of the associated orthogonal polynomials. We prove that under a sparse enough decaying…
This paper examines the existence of centered co-circular central configurations in the general power-law potential n-body problem. We prove the nonexistence of such configurations when the system consists of n-3 equal masses and three…
This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits and clarifies their role; in particular, mixed-bracket Heisenberg-Lie algebras are introduced. These algebras belong to a…
Cylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them…