Related papers: WKB - Not So Bad After All
We show how a potential that is well-defined everywhere on the positive half-line, but diverges to $-\infty$ as $x\rightarrow 0^+$, may still be able to dynamically confine a particle to the (positive) half-line. We shall call this effect…
In present work, we present a couple-channel formalism for the description of tunneling time of a quantum particle through a composite compound with multiple energy levels or a complex structure that can be reduced to a…
In this paper we revisit the one-dimensional tunnelling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the…
Since Parikh and Wilczek's tunneling method was proposed, there have been many generalizations, such as its application to massive charged particles' tunneling and other spacetimes. Moreover, a variant tunneling method was also recently…
We report on numerical procedures for, and preliminary results on the search for, tunnelling centres in Lennard-Jones clusters, seen as simple model systems of glasses. Several of the double-well potentials identified are good candidates to…
Tunneling of a particle through a potential barrier remains one of the most remarkable quantum phenomena. Owing to advances in laser technology, electric fields comparable to those electrons experience in atoms are readily generated and…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…
The fusion of two interacting heavy ions traditionally has been interpreted in terms of the penetration of the projectile into the target. Observed rates well below the Coulomb barrier are considerably lower than estimates obtained from…
We perform a systematic WKB expansion to all orders for a one--dimensional system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the series to the exact energy spectrum. Then we show that any finite order WKB approximation…
The tunneling effect is the most popular phenomenon of quantum physics and is present in modern physical theories. Still, the most important features of this effect are already present in toy models - low dimensional quantum mechanics with…
There are several exotic tunneling processes that can be realized only by incorporating the effect of gravity. Here, we point out that we encounter difficulties in constructing the WKB wave function, once we try to describe quantum…
We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for…
Recently, the Lorentzian path integral formulation using the Picard-Lefschetz theory has attracted much attention in quantum cosmology. In this paper, we analyze the tunneling amplitude in quantum mechanics by using the Lorentzian…
The extremely small probability of tunneling through an almost classical potential barrier may become not small under the action of the specially adapted non-stationary signal which selects the certain particle energy E_R. For particle…
Optimizing the probability of quantum tunneling between two states, while keeping the resources of the underlying physical system constant, is a task of key importance due to its critical role in various applications. We show that, by…
We point out that a non-overlapping well (at negative energies) adjacent to a finite barrier (at positive energies) is a simple potential which is generally missed out while discussing the one-dimensional potentials in the textbooks of…
In this paper we look at transmission through one-dimensional potential barriers that are piece wise constant. The Transfer Matrix approach is adopted and a new formula is derived for multiplying long matrix sequences that not only leads to…
Quantum tunneling through an almost classical potential barrier can be strongly enhanced by a nonstationary field so that the penetration through the barrier becomes not exponentially small. This constitutes an extremely unusual phenomenon…
It has been shown that the cases of the JWKB formulae in 1--dim QM quantizing the energy levels exactly are results of essentially one global symmetry of both potentials and their corresponding Stokes graphs. Namely, this is the invariance…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…