数学物理
We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups $Z_3^2$, $Z_2^p\times Z_3^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg-Wyler's…
We consider annihilating random walks on the finite one-dimensional integer torus with deposition of pairs of particles, conditioned on an atypical jump activity. All cumulants of the activity, defined as the number of particle jumps up to…
The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays. Despite its success, its validity in $\mathcal{PT}$-symmetric systems characterized by strong longitudinal…
We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…
The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly…
We study the question of global attraction, in the energy norm, for finite energy solutions to classical particle coupled to a scalar wave field. The attraction could take place to either the set of the stationary solutions in the case of a…
We construct a family of metric-deformed gauge theories based on a recently introduced $q$-Dirac operator $D_q = \gamma^\mu \sqrt{|g^{\mu\mu}|}\partial_\mu$, which arises from a deformed D'Alembertian $\Box_q = |g^{00}|\partial_t^2 - \sum_i…
We report on the effect of the kinetic energy operator ambiguity on the energy spectra of various double heterostructures when the mass of the charge carriers, subjected to a potential, depends on position. The spectra are calculated using…
We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high…
This paper presents a conceptual and efficient geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the $n$-dimensional lattice $\mathbb{Z}^n$. It is shown…
We study the Lorentzian Wetterich Renormalization Group (RG) flow equation for interacting quantum fields on curved backgrounds within the framework of perturbative Algebraic Quantum Field Theory (pAQFT). Specifically, we consider two…
We prove that the three-dimensional incompressible Navier-Stokes equations with the deformation Laplacian on hyperbolic 3-space $\HH^3$ admit a unique global mild solution for sufficiently small initial data in $L^3(\HH^3)$, and that this…
The asymptotic behavior of the integrated density of states (IDS), \(N(E)\), is investigated for random Schr\"{o}dinger operators with a single-site potential \(V\) satisfying \(\mathrm{essinf}\, V = -\infty\). Under the assumption that the…
In this work we studied a generalized Fisher equation in cylindrical coordinate using Lie symmetry method. We have determined for what type of source function the generalized Fisher equation has Lie Symmetries other than time translation…
In arXiv:1711.05958, arXiv:2103.12673, the authors derive one-dimensional Landau-Ginzburg mirrors of Dubrovin-Zhang Frobenius manifolds constructed on regular orbit spaces of an extension of affine Weyl groups. We generalise the method…
The group-theoretic approach is used to construct exact solutions to perfect fluid equations invariant under the Schrodinger group, or the l-conformal Galilei group, or the Lifshitz group. In each respective case, the velocity vector field…
The first part of these lecture notes is devoted to an introduction to the theory of exact WKB analysis for second-order Schr\"odinger-type ordinary differential equations. It reviews the construction of the WKB solution, Borel summability,…
In this work, we study the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, we formulate the…
Parametric instabilities are a known feature of periodically driven dynamic systems; at particular frequencies and amplitudes of the driving modulation, the system's quasi-periodic response undergoes a frequency lock-in, leading to a…
It is known that there are two inequivalent $\mathbb{Z}_2^2$-graded $osp(1|2)$ Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits two central elements, one is non-graded and the other is…