Related papers: Bound states without potentials: localization at s…
We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two…
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for…
Quantum entanglement is the quintessential characteristic of quantum mechanics and the basis for quantum information processing. When one of two maximally entangled particles is measured, without measurement the state of another one is…
We numerically study the dual field theory evolution of five-dimensional asymptotically anti-de Sitter solutions of supergravity that develop cosmological singularities. The dual theory is an unstable deformation of the N = 4 gauge theory…
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
We study the localization length of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle.…
Quantum tunnelling, a hallmark phenomenon of quantum mechanics, allows particles to pass through the classically forbidden region. It underpins fundamental processes ranging from nuclear fusion and photosynthesis to the operation of…
The interplay between bulk properties and boundary conditions in one-dimensional quantum systems, gives rise to many intriguing phenomena. These include the emergence of zero energy modes which are of significant interest to a variety of…
We show that a quantum system with nonlocal interaction can have bound states of unusual type (isolated states (IS)). IS is a bound state that do not generate a $S$-matrix pole. IS can have positive as well as negative energy and can be…
As the fundamental quantum mechanical theory predicts, it is believed that electronic states can be bound only to potential wells and not to potential barriers in any dimension and their energies should be below the background potential.…
The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of…
Bound states in the continuum (BICs) are localized modes residing in the radiation continuum. They were first predicted for single-particle states, and became a general feature of many wave systems. In many-body quantum physics, it is still…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…
In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are described by configurations of widely separated constituents with nearly parallel central charges. When the vacuum moduli can be dialed…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…
We unveil the mechanism for the formation of puzzled boundary-localized bound states in a spinless fermionic open lattice with nearest-neighbor interactions. By solving the Bethe-ansatz equation analytically, we uncover asymmetrical string…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
In this paper, we study the exact dynamics of open quantum systems to the case with periodic driving field. It is shown that different from the static adjustment of the system on-site energy that can either generate or destroy the…