Related papers: Single point potentials with total resonant tunnel…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
Several families of one-point interactions are derived from the system consisting of two and three $\delta$-potentials which are regularized by piecewise constant functions. In physical terms such an approximating system represents two or…
A three barrier resonant tunneling structure in which the two quantum wells are formed by a dilute magnetic semiconductor material (ZnMnSe) with a giant Zeeman splitting of the conduction band is theoretically investigated. Self-consistent…
Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…
A new mechanism of tunnelling at macroscopic distances is proposed for a wave packet localized in one-dimensional disordered potential with mirror symmetry, V(-x)=V(x). Unlike quantum tunnelling through a regular potential barrier, which…
The fastest tunneling response in double barrier resonant structures is investigated by considering explicit analytic solutions of the time dependent Schr\"{o}dinger equation. For cutoff initial plane waves, we find that the earliest…
We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose condensed atoms. These setups contain at least one black hole sonic horizon from which the analog of Hawking radiation should be…
We introduce a model of a nonlinear double-barrier structure, to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where…
We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the…
We consider the stationary one dimensional Schr\"odinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the…
The poles of the quantum scattering matrix (S-matrix) in the complex momentum plane have been studied extensively. Bound states give rise to S-matrix poles, and other poles correspond to non-normalizable anti-bound, resonance and…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each well, the energy eigenvalues of the low lying excited states…
We introduce a solvable model of a nonlinear double-barrier structure, described by a generalized effective-mass equation with a nonlinear coupling term. This model is interesting in its own right for possible new applications, as well as…
We present a self-consistent calculation, based on the global coherent tunnelling model, and show that structural asymmetry of double barrier resonant tunnelling structures significantly modifies the current-voltage characteristics compared…
We present a microscopical theory and experimental results concerning resistance resonance in two tunneling coupled quantum wells with different mobilities. The shape of the resonance appears to be sensitive to the small angle scattering…
We study strong tunneling (i.e. transmission $h/e^2R_T \gg 1$) in the single-electron box with many transverse modes at zero temperature. We develop a new renormalization group method which includes all charge states and requires no initial…
We study the quantum behaviour of a particle moving in a one-dimensional double well potential. This double well is obtained by gluing together, at the origin, two shifted harmonic oscillator potentials. The Schr\"odinger equation is…
We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…