相关论文: Quantum Tunneling and Caustics under Inverse Squar…

It was recently shown that tunneling wavefunction proposal is consistent with loop quantum geometry corrections including both holonomy and inverse scale factor corrections in the gravitational part of a spatially closed isotropic model…

In this paper we show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential. We demonstrate this by relating both of these systems to…

Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula:…

This paper is devoted to the study of quantum dissipation in cluster decay phenomena in the frame of the Lindblad approach to quantum open systems. The tunneling of a metastable state across a piecewise quadratic potential is envisaged for…

Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…

Applying a technique developed recently [1,2] for an harmonic oscillator coupled to a bath of harmonic oscillators, we present an exact solution for the tunneling problem in an Ohmic dissipative system with inverted harmonic potential. The…

We explore the features of non-relativistic quantum tunneling in space fractional quantum mechanics through a family of Cantor potentials. We consider two types of potentials: general Cantor and general Smith-Volterra-Cantor potential. The…

An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…

The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its…

We compute tunneling in a quantum field theory in 1+1 dimensions for a field potential $U(\Phi)$ of the asymmetric double well type. The system is localized initially in the ``false vacuum''. We consider the case of a {\em compact space}…

We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…

Electron tunneling between quantum Hall systems on the same two dimensional plane separated by a narrow barrier is studied. We show that in the limit where inelastic scattering time is much longer than the tunneling time, which can be…

A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…

The effect of inelastic scattering on quantum tunneling through a rectangular potential barrier, of length $L$, containing randomly distributed impurities, is considered. It is shown that, despite the fact that the inelastic transition…

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we…

We quantize the 1-dimensional 3-body problem with harmonic and inverse square pair potential by separating the Schr\"odinger equation following the classic work of Calogero, but allowing all possible self-adjoint boundary conditions for the…

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 anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle's state as it approaches the origin when the attractive coupling parameter is…

Quantum phase transitions (QPTs) in the spin-boson model with/without the rotating-wave approximation (RWA) are systematically investigated through variational calculations using a sub-Ohmic bath with high spectral density. Four cases…

We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…