Tunneling effects between tori in double wells

Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2

We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational tori, we obtain an accurate description of the spectrum in a suitable window in the complex spectral plane, provided that the strength of the non-selfadjoint perturbation $\gg h$ (or sometimes $\gg h^…

Multidimensional tunneling between potential wells at non degenerate minima

We consider tunneling between symmetric wells for a 2-D semi-classical Schrödinger operator for energies close to the quadratic minimum of the potential V in two cases: (1) excitations of the lowest frequency in the harmonic oscillator approximation of V; (2) more general excited states from Diophantine tori with comparable quantum numbers.

The calculus of the electric potential and field intensity in multiple electrodes lateral tunneling transistors with double gate

The paper presents an adaptive over-relaxation method for calculating the electric potential and field intensity, for a complex tunnel transistor structure involving a split gate and a shielding boundary. The accuracy and speed of the method has been numerically tested and found satisfactory for the study of such devices by calculating the tunneling currents for the obtained potential distribution.

Quantum Transport on KAM Tori

Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit $\hbar\searrow 0$ for the Schrödinger equation of a particle in $\bR^d$ under the influence of a smooth periodic potential. In particular this implies that the distribution of quantum group velocities near energy $E$ converges to the distribution of the classical asymptotic velocities near $E$, up to a term of the order $\cO(1/\sqrt{E})$.

The bosonic string on string-size tori from double field theory

We construct the effective action for toroidal compactifications of bosonic string theory from generalized Scherk-Schwarz reductions of double field theory. The enhanced gauge symmetry arising at special points in moduli space is incorporated into this framework by promoting the $O(k,k)$ duality group of $k$-tori compactifications to $O(n,n)$, $n$ being the dimension of the enhanced gauge group, which allows to account for the full massless sector of the theory. We show that the effective action reproduces the right masses of scalar and vector fields when moving sligthly away from the points o…

磁双势阱：隧穿的缺失

Magnetic Double-Wells: Absence of Tunneling

本研究提出一种磁双势阱哈密顿量，证实该体系中两势阱间不存在隧穿效应，呼应了近期的相关公布结果。