Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Abstract

For the system with one-dimensional spatially periodic potential we demonstrate that small periodic in time perturbation results in appearance of chaotic instanton solutions. We estimate parameter of local instability, width of stochastic layer and correlator for perturbed instanton solutions. Application of the instanton technique enables to calculate the amplitude of the tunneling, the form of the spectrum and the lower bound for width of the ground quasi-energy zone.

Quantum dynamics and delocalization in coherently driven one-dimensional double-well system

“…The critical value c (M) which divides the behavior of (2) Within the regular motion range, the period of the tunneling oscillation is reduced with the increase in the number of colors and/or strength of the perturbation. It could be explained by the increase in the instanton tunneling rate due to appearance of the stochastic layer near separatrix [28]. In this parameter regime the perturbed instanton picture is one of expression for chaos-assisted tunneling [32] and chaosassisted ionization picture reported for some quantum chaos systems [33].…”

“…The only manifestation of the perturbation in this approximation is the appearance of a number of additional solutions of the Euclidian equation of motion with energy close to the energy of the unperturbed one-instanton solution inside the stochastic layer. Accordingly, we can expect that the appearance of the stochastic layer enhances the tunneling rate as reported in the other systems [28]. However, we have to have in mind that the result is obtained in the first order on coupling constant of the time-periodic perturbation and does not take into account the structure of the stochastic layer.…”

“…In the coherent motions, the value of P L 's is almost the same as the unperturbed case, i.e. P L 0.3, in which case the instanton-like picture is valid [28]. A simple explanation of the perturbed instanton is given in Appendix B.…”

Controlling chaos in the Bose-Einstein condensate

“…Experimental and theoretical progress has been made in studying the properties of this new state of matter. Several remarkable phenomena, which strongly resemble well known effects in non linear optics, have been observed in the BEC, such as four wave mixing, vortices, dark and bright solitons, and chaos [3][4][5][6][7][8][9][10][11][12][13]. In a realistic experimental setting, an external electromagnetic field is used to produce, trap, and manipulate the BEC.…”

Chaotic instantons in scalar field theory

“…[7,8]. In particular, the wave function of a particle can be chaotized by a series of kicks inside a potential.…”