Related papers: Quantum tunneling of a singular potential
For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions), the corresponding…
Time evolution of tunneling phenomena in medium is studied using a standard model of environment interaction. A semiclassical formula valid at low, but finite temperatures is derived in the form of integral transform for the reduced Wigner…
The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave…
An expanding closed universe filled with radiation can either recollapse or tunnel to the regime of unbounded expansion, if the cosmological constant is nonzero. We re-examine the question of particle creation during tunneling, with the…
Two spatial regions $B$ and $R$ are hyperentangled if the generalized entropy satisfies $S_{\text{gen}}^{B\cup R}<S_{\text{gen}}^R$. If in addition all future (or all past) directed inward null shape deformations of $B$ decrease…
Tunneling is a fascinating aspect of quantum mechanics that renders the local minima of a potential meta-stable, with important consequences for particle physics, for the early hot stage of the universe, and more speculatively, for the…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…
We consider a minisuperspace model for a closed universe with small and positive cosmological constant, filled with a massive scalar field conformally coupled to gravity. In the quantum version of this model, the universe may undergo a…
Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map…
Quantum particles can penetrate potential barriers by tunneling (1). If that barrier is rotating, the tunneling process is modified (2,3). This is typical for electrons in atoms, molecules or solids exposed to strong circularly polarized…
One-dimensional scattering by a Coulomb potential V(x)=lambda/|x| is studied for both repulsive (c>0) and attractive (c<0) cases. Two methods of regularizing the singularity at x=0 are used, yielding the same conclusion, namely, that the…
We study the decay of general initial states out of a metastable potential well in quantum mechanics. We provide a closed-form expression for the probability current that tunnels through the barrier in terms of the resonant states into…
Inspired by a recent paper$^*$ by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic field. In the simultaneous limit of strong magnetic field…
The common interpretation of the Hawking radiation as quantum tunneling has some ambiguity such as coordinate-dependence of tunneling rate and non-invariance of the action under canonical transformations. It is shown that the tunneling…
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…
Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a…
We review our recent studies on the Kondo effect in the tunneling phenomena through quantum dot systems. Numerical methods to calculate reliable tunneling conductance are developed. In the first place, a case in which electrons of odd…
Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first…
Quantum tunneling is mostly discussed in the Euclidean path integral formalism using instantons. On the other hand, it is difficult to understand quantum tunneling based on the real-time path integral due to its oscillatory nature, which…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…