Related papers: Quantum magnetic billiards: boundary conditions an…
Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic…
We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting,…
Duality transformation, which relates a high-temperature phase to a low-temperature one, is used exactly to determine the critical point for several models (2D Ising, Potts, Ashkin-Teller, 8-vertex), as the self dual condition. By changing…
We study boundary conditions in N=4 super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a ``pole'' at the boundary. The…
We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an…
The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…
We report here the status of different gauge conditions in the canonical formulation of quantum electrodynamics on light-front surfaces. We start with the massive vector fields as pedagogical models where all basic concepts and possible…
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We…
We consider magnetic friction between two square lattices of the ferromagnetic Ising model of finite thickness. We analyze the dependence on the boundary conditions and the sample thickness. Monte Carlo results indicate that the setup…
The presence of a strong magnetic background can modify the nature and the dynamics of the chiral phase transition at finite temperature. We compute the modified effective potential in the linear sigma model with quarks to one loop in the…
We study the quantization of many-body systems in two dimensions in rotating coordinate frames using a gauge invariant formulation of the dynamics. We consider reference frames defined by linear and quadratic gauge conditions. In both cases…
We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…
In this paper, bound states energies and corresponding wave functions of H-shaped quantum wires are calculated numerically in the presence of external magnetic and electric fields and within the Landau gauge. With a suitable definition of…
Discrepancies between theory and recent qBounce data have prompted renewed scrutiny of how boundary conditions are implemented for ultracold neutrons bouncing above a mirror in Earth's gravity. We apply the theory of self-adjoint extensions…
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential…
Motion in bounded domains represents a paradigm in several settings: from billiard dynamics, to random walks in a finite lattice, with applications to relevant physical, ecological and biological problems. A remarkable universal property,…
The framework of shifted boundary conditions has proven to be a very powerful tool for the non-perturbative investigation of thermal quantum field theories. For instance, it has been successfully considered for the determination of the…
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential…
Quantum phase transitions between the magnetically ordered and disordered states are studied for the two-dimensional antiferromagnetic quantum spin systems with ladder, plaquette, and mixed-spin structures. Starting with properly chosen…
Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of spacetime. The intimate connection…