Related papers: Semi-classical formula for quantum tunneling in as…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution…
We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field…
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…
An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the…
As an application of the polymer quantization scheme, in this work we investigate the one dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle and derive the…
A spin interaction Hamiltonian for topological basis is constructed in this paper. When we select proper parameters, this Hamiltonian system can be simulated by a quantum double well potential system. If the parameter $\Delta=0$, the…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting…
We investigate numerically the tunneling effect under influence of another particle in a double well system. Such influence from only one degree of freedom makes decoherence and quantum-classical transition, i.e., suppression of the…
We present the mathematical model and numerical calculation results for the tunneling of the wave function in a time-periodic double-well potential. The bi-quadratic potential of a double-well form is used. Based on a mathematical model of…
The semi-classical study of the integer Quantum Hall conductivity is investigated for electrons in a bi-periodic potential $V(x,y)$. The Hall conductivity is due to the tunnelling effect and we concentrate our study to potentials having…
The complex-time method for quantum tunneling is studied. In one-dimensional quantum mechanics, we construct a reduction formula for a Green function in the number of turning points based on the WKB approximation. This formula yields a…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
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 study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal…
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral…
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian…
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…
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…