Related papers: Tunnelling in Quantum Cosmology: WKB vs SWKB
It was found recently that tunneling probabilities over a barrier is roughly twice as large as that given by standard WKB formula. Here we explained how this come from and showed that WKB method does give a good approximation over almost…
The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb…
The phenomenon of quantum tunneling is reviewed and an overview of applying approximate methods for studying this effect is given. An approach to a time-dependent formalism is proposed in one dimension and generalized to higher dimensions.…
The tunneling probability for a system modelling macroscopic quantum tunneling is computed. We consider an open quantum system with one degree of freedom consisting of a particle trapped in a cubic potential interacting with an environment…
In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
In this paper, we use the WKB approximation method to approximately solve a deformed Schrodinger-like differential equation: $\left[ -\hbar^{2} \partial_{\xi}^{2}g^{2}\left( -i\hbar\alpha\partial_{\xi}\right) -p^{2}\left( \xi\right) \right]…
We formulate a ''minimal'' interpretational scheme for fairly general (minisuperspace) quantum cosmological models. Admitting as few exact mathematical structure as is reasonably possible at the fundamental level, we apply approximate…
We analyse the accuracy of the approximate WKB quantization for the case of general one-dimensional quartic potential. In particular, we are interested in the validity of semiclassically predicted energy eigenvalues when approaching the…
Cosmologies with a Chaplygin gas have recently been explored with the objective of explaining the transition from a dust dominated epoch towards an accelerating expansion stage. We consider the hypothesis that the transition to the…
We study Hawking-like radiation in a Friedmann-Robertson-Walker (FRW) universe using the quasi-classical WKB/tunneling method which pictures this process as a "tunneling" of particles from behind the apparent horizon. The correct…
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…
We present a formalism based on the functional Schr\"odinger equation to analyse time-dependent tunneling in quantum field theory at the semi-classical level. The full problem is reduced step by step to a finite dimensional quantum…
Using a method of local transmission matrix, we generalize the well-known WKB formula for a barrier penetrability to multi-channel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that…
We revisit the formalism for tunneling in quantum field theory developed by Coleman and collaborators. In particular using the generalization of WKB methods for tunneling in quantum mechanics we avoid the problems with negative eigenvalues…
We consider a symmetric double barrier heterostructure enclosing a well and propose a solution for the transmission problem using a generalized WKB approach which accounts for the amplitude suppression and phase shift due to the barriers.…
In this work, we develop and apply the WKB approximation to several examples of noncommutative quantum cosmology, obtaining the time evolution of the noncommutative universe, this is done starting from a noncommutative quantum formulation…
In the deformed quantum mechanics with a minimal length, one WKB connection formula through a turning point is derived. We then use it to calculate tunnelling rates through potential barriers under the WKB approximation. Finally, the…
We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found…
We compute the corrections, using the tunneling formalisim based on a quantum WKB approach, to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are…