Related papers: A continuum limit for the Kronig-Penney model
A quantum system subject to an external perturbation can experience leakage between uncoupled regions of its energy spectrum separated by a gap. To quantify this phenomenon, we present two complementary results. First, we establish…
Boundary conditions in confined geometries and measurement interactions in quantum mechanics share a common structural role: both select a preferred basis by determining which states are compatible with the imposed constraint. This paper…
The spectrum of a bound state of three identical particles with a mass $m$ in a finite cubic box is studied. It is shown that in the unitary limit, the energy shift of a shallow bound state is given by $\Delta E=c (\kappa^2/m)\,(\kappa…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
Following our work [Phys. Rev. Lett. 125, 020401 (2020)], we discuss a semiclassical description of one-dimensional quantum tunneling through multibarrier potentials in terms of complex time. We start by defining a complex-extended…
In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that $V<\Lambda_s^2$, where $\Lambda_s(\phi)$ is the species scale, and the emergent string…
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…
We describe a broad class of bounded non-periodic potentials in one-dimensional stationary quantum mechanics having the same spectral properties as periodic potentials. The spectrum of the corresponding Schroedinger operator consists of a…
A model is proposed for studying the reaction dynamics in complex quantum systems in which the complete mixing of states is hindered by an internal barrier. Such systems are often treated by the transition-state theory, also known in…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha>0$) proposed by Roberts and Massouli\'{e} [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that…
The recent realization of a "Levy glass" (a three-dimensional optical material with a Levy distribution of scattering lengths) has motivated us to analyze its one-dimensional analogue: A linear chain of barriers with independent spacings s…
We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of…
The classical 'time-bandwidth' limit for linear time-invariant (LTI) devices asserts that it is impossible to store broadband waves (large {\Delta}{\omega}'s) for long times (large {\Delta}t's). For standing waves, i.e., vibrations, in…
The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of the…
The theory of 3-layer density stratified ideal fluids is examined with a view towards its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the…
We study the low-temperature low-frequency conductivity sigma of an interacting one dimensional electron system in the presence of a periodic potential. The conductivity is strongly influenced by conservation laws, which, we argue, need be…
Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…
In this Letter, we present a rigorous method to study the stability of periodic lasing systems. In a linear model, the presence of a continuum of modes (with arbitrarily close lasing thresholds) gives the impression that stable single-mode…
We discuss a model in which a quantum particle passes through $\delta$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic properties of wave function phases,…