Related papers: Tunneling in Fractional Quantum Mechanics
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A…
The tunneling conductance spectra of a normal-metal/insulator/quasi-one-dimensional superconductor is calculated by using the Blonder-Tinkham-Klapwijk formulation. The pairing symmetry of the superconductor is assumed to be $p$, $d$, and…
We derive exact sum-rules that relate the tunneling density of states (TDOS) of spinful electrons in the fractional quantum Hall (FQH) regime to the spin-dependent many body ground state correlation energy. Because the tunneling process is…
We used analytical methods to study the interaction of electrons with shunted models consisting of a rectangular, triangular, or delta function. potential barrier in series with a pre-barrier region at zero potential. In each model the…
We study the evolution of the most general initial Gaussian packet with nonzero correlation coefficient between the coordinate and momentum operators in the presence of a repulsive delta potential barrier, using the known exact propagator…
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 present a semiclassical study of a transport process, the tunneling, in the presence of a magnetic field and a dissipative environment. We have found that the problem can be mapped onto an effective one-dimensional one, and the tunneling…
We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the…
We consider the non-selfadjoint, semiclassical Schr\"odinger operator $\mathscr{L}(h) := -h^2\partial_x^2+e^{i\alpha}V$, where $\alpha \in (-\pi,\pi)$ and $V: \mathbb{R}\to \mathbb{R}_+$ is even and vanishes at exactly two (symmetric)…
We use chiral Luttinger liquid theory to study transport through a quantum dot in the fractional quantum Hall effect regime and find rich non-Fermi-liquid tunneling characteristics. In particular, we predict a remarkable…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient ($T$) as a function in incident…
We present a model of dissipative transport in the fractional quantum Hall regime. Our model takes account of tunneling through saddle points in the effective potential for excitations created by impurities. We predict the temperature range…
We investigate the confined states and transport of three-dimensional Weyl electrons around a one-dimensional external rectangular electrostatic potential. Confined states with finite transverse wave vector exist at energies higher than the…
The influence of a rectangular potential barrier on the quantum transport of fermions in silicene is explored. Specifically, analytical solutions are presented to derive transmission and reflection probabilities together with conductance.…
For the theory of a single scalar field $\varphi$ with a quartic potential $V(\varphi)$, we find semi-analytic expressions for the Euclidean action in both four and three dimensions. The action in four dimensions determines the quantum…
We explore dissipative quantum tunnelling, a phenomenon central to various physical and chemical processes, using a double-well potential model. This paper aims to bridge gaps in understanding the crossover from thermal activation to…
Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schr\"odinger-Langevin or Kostin quantum classical transition wave equation is used and applied resulting in a scaled…
Weyl semimetal is a recently discovered state of quantum matter, which generally possesses tilted energy dispersion. Here, we investigate the electron tunneling through a Weyl semimetal p-n-p junction. The angular dependence of electron…
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…