Tunneling and quantum localization in chaos‐driven symmetric triple well potential: An approach using quantum theory of motion

Abstract

For a symmetric triple well potential, driven by the forces associated with the bifurcation diagram of a logistic map, the tunneling and quantum localization are studied using quantum theory of motion and time‐dependent Fourier grid Hamiltonian methods. Detailed analysis reveals that application of only asymmetric or symmetric perturbation results into either quantum localization or over‐barrier transition and no tunneling while application of mixed symmetry perturbation gives either tunneling or over‐barrier transition, depending on temporal nature and initial position of the particle. For bifurcative and chaotic symmetric‐asymmetric perturbation, with truncation of mixed symmetry perturbation, a sudden jump in energy causes a transition from the tunneling phenomenon to the over‐barrier transition. With particle located initially near to either of the minima of the unperturbed well, quantum localization, or over‐barrier transition is observed, depending on types of perturbation used.

Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

“…The results indicate that no quantum localization with CDT takes place, irrespective of the spatial symmetry of the perturbation applied to the SDWP either with fixed or randomly changing $${\tau _r }$$ . In literature, the CDT has always been reported for time‐periodic perturbations that break spatial symmetry [3,32,34,44–46] . Our experiments (numerical) indicate that the symmetry breaking perturbations must also be continuous in time in‐order that CDT can take place thereby providing a route to complete tunnelling control.…”

“…In literature, the CDT has always been reported for time-periodic perturbations that break spatial symmetry. [3,32,34,[44][45][46] Our experiments (numerical) indicate that ChemPhysChem the symmetry breaking perturbations must also be continuous in time in-order that CDT can take place thereby providing a route to complete tunnelling control.…”

Controlling Tunneling Oscillation and Quantum Localization in an Asymmetric Double-Well Potential: A Bohmian Perspective

“…Now, QTM phase space can be constructed by solving either eq or . As suggested by Kar et al, we solve eq to construct the corresponding QTM phase space. We can express eq as follows, using the knowledge of the initial position of the particle where ψ = ψ real + iψ img .…”

Moving boundary truncated grid method: Multidimensional quantum dynamics

“…[26] In contrast to conventional methods of integrating the TDSE on a fixed lattice, nontraditional computational techniques have been developed for solving quantum dynamical problems. For example, quantum trajectories following the evolving wave packet density have been utilized to analyze a broad spectrum of physical systems, [27][28][29][30][31][32][33][34][35][36][37][38] and they have been employed as "optimal" moving grids to integrate the TDSE. [39][40][41][42][43][44][45][46][47][48][49][50][51] As an alternative to numerical integration of the TDSE, the arbitrary Lagrangian-Eulerian picture that allows for adaptive grid point motion has been utilized to solve the quantum hydrodynamic equations of motion.…”