Related papers: Tunneling resonances in systems without a classica…
Let $\Omega \subset \mathbb R^3$ be a waveguide which is obtained by translating a cross-section in a constant direction along an unbounded spatial curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in $\Omega$. Under the…
We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted…
We show that nonlinear resonances in a classically mixed phase space allow to define generic, strongly entangled multi-partite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e. in the…
It is shown that a Dirac particle of mass $m$ and arbitrarily small momentum will tunnel without reflection through a potential barrier $V=U_c(x)$ of finite range provided that the potential well $V=-U_c(x)$ supports a bound state of energy…
The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as both the thickness of the layers and the distance…
We derive a semiclassical quantization for a spin, study it for not too small a spin quantum number (S>5), and compute the 2S+1 eigenvalues of a Hamiltonian exhibiting resonant tunnelling as the magnetic field parallel to the anisotropy…
We study the resonant tunneling properties of an electron through a few types of binary periodic and aperiodic multibarrier systems. Within the framework of the effective-mass approximation, we calculate the transmission coefficients to…
The addition of tunnel barriers to open chaotic systems, as well as representing more general physical systems, leads to much richer semiclassical dynamics. In particular, we present here a complete semiclassical treatment for these…
Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not…
The fundamental problem of how tunneling in thermal medium is completed is addressed, and a new time scale of order 1/friction for its termination, which is usually much shorter than the Hubble time, is pointed out. Enhanced non-linear…
In this paper, we investigate tunneling of conduction band electrons in a system of an asymmetric double quantum dot which interacts with an environment. First, we consider the case in which the system only interacts with the environment…
We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with…
We consider resonant tunneling between disorder localized states in a potential energy displaying perfect correlations over large distances. The phenomenon described here may be of relevance to models exhibiting many-body localization.…
The two-dimensional magnetic Laplacian is considered. We calculate the leading term of the splitting between the first two eigenvalues of the operator in the semiclassical limit under the assumption that the magnetic field does not vanish…
Resonant tunneling through identical potential barriers is a textbook problem in quantum mechanics. Its solution yields total transparency (100% tunneling) at discrete energies. This dramatic phenomenon results from coherent interference…
We propose an electronic double quantum wire system that contains a pair of edge blocking potential and a coupling element in the middle barrier between two ballistic quantum wires. A window and a resonator coupling control between the…
We theoretically studied the quasiparticle transport in a 2D electron gas biased in the quantum Hall regime and in the presence of a lateral potential barrier. The lateral junction hosts the specific magnetic field dependent quasiparticle…
We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
We investigate the tunneling process between two symmetric stable islands of a forced pendulum Hamiltonian in the weak chaos regime. We show that when the tunneling doublet is quantized over a classical non-linear resonance the tunneling…