Related papers: A regular version of Smilansky model
We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time.…
The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or…
A theory of Sobolev inequalities in arbitrary open sets of Euclidean space is established. Boundary regularity of domains is replaced with information on boundary traces of trial functions and of their derivatives up to some explicit…
We explore a general framework how to treat coupled-channel systems in the presence of overlapping left and right-hand cuts as well as anomalous thresholds. Such systems are studied in terms of a generalized potential, where we exploit the…
We present an abstract result on removing regularization for singular potentials which are not semibounded from below. The relation between ``right'' regularizations and ``right'' self-adjoint extensions of the perturbed Schr\"odinger…
Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such…
We introduce a new framework that yields spectral bounds on norms of functions of transition maps for finite, homogeneous Markov chains. The techniques employed work for bounded semigroups, in particular for classical as well as for quantum…
The breaking of supersymmetry due to singular potentials in supersymmetric quantum mechanics is critically analyzed. It is shown that, when properly regularized, these potentials respect supersymmetry, even when the regularization parameter…
Phase-equivalent transformation of local interaction is generalized to the multi-channel case. Generally, the transformation does not change the number of the bound states in the system and their energies. However, with a special choice of…
The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero…
The quantum-to-classical transition hinges on the nature of wavefunction collapse, which remains a central controversy in foundational physics. Objective collapse theories aim to modify quantum mechanics by introducing a physical,…
Spontaneous symmetry breaking (SSB) occurs when modes of asymmetric profile appear in a symmetric, double-well potential, due to the nonlinearity of the potential exceeding a critical value. In this study, we examine SSB in a periodic…
We study the one-dimensional discrete quasi-periodic Schrodinger equation. We introduce the notion of variations of potential and use it to define "typical" potential. We show that for typical C^3 potential, if the coupling constant is…
Intensity minima and maxima of speckle patterns obtained behind a diffuser are experimentally interchanged by applying a spiral phase delay of charge $\pm 1$ to the impinging coherent beam. This transform arises from the intuitive…
We consider a version of special relativity assuming that the metric in inertial frames is conformally pseudoeuclidean and depends on some scalar field with zero vacuum average. Applying this modified special relativity to the theory of…
It is well known that derivatives of solutions to elliptic boundary value problems may become unbounded near the corner of a domain with a conical singularity, even if the data are smooth. When the corner domain is approximated by more…
Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An…
Superscattering, induced by degenerate resonances, breaks the fundamental single-channel limit of scattering cross section of subwavelength structures; in principle, an arbitrarily large total cross section can be achieved via…
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…
We study the semi-classical trace formula at a critical energy level for a Schr\"odinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result,…