Related papers: WKB - Not So Bad After All
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an…
Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. While the WKB method generates an expansion in powers of h, the quasilinearization method (QLM) approaches the solution of the nonlinear equation…
A set of simple exactly solvable potentials are shown to have convergent WKB series. The resulting all-orders quantisation conditions provide a unified description of all known cases where an exact WKB quantisation condition has been…
For a single potential barrier, the barrier penetrability can be inverted based on the WKB approximation to yield the barrier thickness. We apply this method to heavy-ion fusion reactions at energies well below the Coulomb barrier and…
At low temperatures, the transport through a superconducting-normal tunnel interface is due to tunneling of electrons in pairs. The probability for this process is shown to depend on the layout of the electrodes near the tunnel junction,…
Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric…
It has been recently realized that, in the case of polynomial potentials, the exact WKB method can be reformulated in terms of a system of TBA equations. In this paper we study this method in various examples. We develop a graphical…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
A simple example of especially constructed potential barrier enables to show analytically (not numerically) the existence of tunneling effect for a Sommerfeld particle.
Wentzel, Kramers, Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case the wave function is constructed such that the phase factor is the same as 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…
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…
A hybrid model where the tunneling probability is estimated based on both sudden and adiabatic approaches has been proposed to understand the heavy ion fusion phenomena at deep sub-barrier energies. It is shown that under certain…
The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary…
Photon-assisted charge transport through a double barrier structure under a time periodic field in graphene is studied. Within the framework of the Floquet formalism and using the transfer matrix method, the transmission probabilities for…
Exact analytical solutions of the time-dependent Schr\"odinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value…
Time it takes to travel from one position to another, devoid of any quantum mechanical description, has been modeled variously, especially for quantum tunneling. The model time, if universally valid, must be subluminal, must hold everywhere…
A simple theory for the tunneling of two cold atoms out of a trap in the presence of an attractive contact force is developed. Two competing decay channels, respectively for single-atom and bound-pair tunneling, contribute independently to…
The complex-time formalism is developed in the framework of the path-integral formalism, to be used for analysis of the quantum tunneling phenomena. We show that subleading complex-time saddle-points do not account for the right WKB result.…