Related papers: An abstract framework for interior-boundary condit…
Interacting field theories for systems with a free surface frequently exhibit distinct universality classes of boundary critical behaviors depending on gross surface properties. The boundary condition satisfied by the continuum field theory…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's…
We consider the Laplacian eigenvalues for smooth planar domains with strongly attractive Robin conditions imposed on a part of the boundary and Neumann condition on the remaining boundary. The asymptotics of individual eigenvalues is…
A description of many constituent (particle) systems with fuzzy initial conditions is proposed with the help of the field language. In this language correlation functions are defined and equations for them are derived in the free Fock…
Determining how boundary terms behave in a quantum field theory (QFT) is crucial for understanding the dynamics of the theory. Nevertheless, boundary terms are often neglected using classical-type arguments which are no longer justified in…
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These…
We introduce a new type of boundary conditions, {\it smooth boundary conditions}, for numerical studies of quantum lattice systems. In a number of circumstances, these boundary conditions have substantially smaller finite-size effects than…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
We survey the relationships of rank one self-adjoint and unitary perturbations as well as finite rank unitary perturbations with various branches of analysis and mathematical physics. We include the case of non-inner characteristic operator…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
We classify the possible boundary conditions in JT gravity and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization…
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found…
Some boundedness properties of function spaces (considered as topological groups) are studied.
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface, the network can be rendered…
We investigate an integrable boundary quench, in which one integrable boundary condition is suddenly switched to another. We develop a general framework for analyzing the resulting real-time dynamics based on form factors of bulk and…
We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal…
We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of…