Mathematical Physics
We study the entanglement entropy (EE) of ground states of a Hamiltonian defined on a domain with a boundary. Surprisingly, boundary conditions can change the spectrum and the nature of the spectrum drastically but not the leading behaviour…
As fusion energy moves from theoretical feasibility toward commercialization, design of new reactor concepts, autonomous tokamak control, and high-performance scenario optimization are becoming increasingly important. Traditionally, such…
This work studies the asymptotic stability of solutions to the good Boussinesq equation in dispersive wave region when the reflection coefficients associated with the initial data belong to weighted Sobolev space. The Dbar-steepest descent…
Renormalization provides a framework for relating microscopic models of physical systems to effective descriptions at larger length scales. This procedure is studied for the boundary states of non-chiral two-dimensional topologically…
The theory of quantum filtering (of quantum continuous measurements) was developed by V.P. Belavkin about 40 years ago. Since then it attracted attention of numerous investigators including mathematicians, theoretical and experimental…
We study eigenfunctions of quantum star graphs in the large edge number limit through the edge-mass distributions associated with their semiclassical measures. For generic edge lengths, we show that these distributions can realize every…
A limiting case is worked out in which the causal action principle for causal fermion systems describing Minkowski space gives rise to the linear Fock space dynamics of perturbative quantum field theory including non-abelian gauge fields…
In this paper, we consider Hamiltonians for aperiodic crystals of the form \begin{align*} H_\varepsilon:=T(-i\nabla_x+{\mathbf A}(x,\varepsilon x))+V(x,\varepsilon x),\qquad x\in {\mathbb R}^d \end{align*} where $T$ represents either a…
We study the quantum Wasserstein distances introduced by De Palma and Trevisan associated with quadratic cost operators generated by families of self-adjoint observables. We first show that an arbitrary positive semidefinite cost operator…
A group-theoretic interpretation of the periodic system of elements is given within the framework of the weight diagram of the Lie algebra $\mathfrak{so}(4,4)$ of the fourth rank, where the four quantum numbers $n$, $l$, $m$, $s$ correspond…
We give an exact solution of the ferromagnetic Ising model on a random regular graph ensemble via analytic combinatorics. Expressing the partition function as the generating function of labeled edge-bicolored graphs, we obtain the free…
We give mathematically self-contained formulations, in the complex-time (kime) representation, of three open problems from the foundations of classical mechanics: (I) the extension of the classical entropic uncertainty principle to…
The Baker--Campbell--Hausdorff (BCH) formula plays a critical role in many branches of mathematics and physics. It expresses the logarithm of the product of exponentials of non-commuting operators as an infinite series of nested commutators…
We develop a geometric reduction mechanism generated by particular integrals. A family of functions whose time derivatives close linearly on the same family defines an invariant zero-level submanifold. In the Hamiltonian case, if this…
We study invariant measures for soliton systems described by Mealy automata. Motivated by recently introduced soliton models associated with 2-letter, 3-state Mealy automata, we formulate the time evolution induced by Mealy automata on…
We study a class of 3-wave kinetic equations arising in wave turbulence theory, with regularized kernels. For radial, nonnegative initial data, we construct an exact global-in-time strong solution which remains nonnegative and is analytic…
We examine the kinematic foundations of relativity by considering two inertial frames, $S$ and $S'$, in a standard configuration, where $S'$ moves along the common spatial $x$-axis at a constant velocity $v$. By relaxing Einstein's second…
We study the Kohmoto model, a family of discrete Schr\"odinger operators with Sturmian potentials depending on a frequency and a coupling constant. We prove that, for all non-vanishing coupling constants, all spectral bands admit a…
Rapidly scaling autonomous science is limited not only by algorithms, compute or data volume, but by which physical records a platform exposes before action. We formulate physically accessible decision-making (PADM) and a measurement-access…
For a class of polaron-type models, we establish a lower bound on the energy-momentum relation in terms of the vacuum overlap and the spectral gap of the total momentum zero Hamiltonian. We show convergence of the rescaled mean square…