Assisted tunneling of a metastable state between barriers

Abstract

The assisted tunneling of a metastable state between barriers is investigated analytically by means of a simplified one dimensional model. A time dependent perturbation changes the pole spectrum of the wave function introducing a larger decay constant. New insights about the decay of a metastable state are found. The scheme is exemplified for parameters corresponding to the nuclear process of α decay.

Eigenstate suppressed activation

“…Resonant tunneling in the presence of changing perturbation is ubiquitous in electronics [2], nanotechnology [3][4][5], the foundations of quantum mechanics [1,[6][7][8][9][10][11][12][13], and even biology and biochemistry [14][15][16][17][18][19]. Therefore, understanding the complexity of dynamic resonant tunneling in general and the forbidden activation regime in particular is necessary to the understanding of this wealth of physical phenomena.…”

“…The problem of tunneling in the presence of an external timedependent potential has been extensively studied [1,5,[8][9][10][11][12][13][20][21][22][23][24][25][26]. It is well known that the tunneling particle can raise its energy by absorbing some phonons by which it can easily penetrate the barrier.…”

The Tunnelling Current through Oscillating Resonance and the Sisyphus Effect

“…Clearly, this expression is exponentially larger than the stationary current but is exponentially smaller than the adiabatic maximum (22). It is also of interest to mention that the smaller the oscillating frequency , the larger the maximum current.…”

“…As a consequence, the particle can be activated to much higher energies (close to the barrier's height) and penetrates through the well with much higher probability. This dynamic resonant tunnelling was investigated in a variety of fields: from the foundations of quantum mechanics [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] via nano-and microelectronics [14,[31][32][33] to biochemistry and biology [34][35][36][37][38][39][40].…”

Analyticity of the time dependence of resonance poles: Solving the Friedrichs model with a time-dependent interaction

“…In this work we shall address, from a mathematical oriented view, the question of the enhancement (or hindrance) of the resonant structure of a state, as suggested by Kälbermann [20,21]. In these papers, Kälbermann has discussed, based on numerical analysis, the assisted tunneling of a wave packet between square barriers, and concluded that the tunneling probability is enhanced by the perturbation [20,21].…”