Analytical approximations to the dynamics of cubic level crossing model

Efficient electron transfer in quantum dot chains controlled by a cubic detuning profile via shortcuts to adiabaticity

“…Nevertheless, using an accelerated nonlinear field profile could improve the speed and efficiency for charge transfer. Nonlinear level crossing dynamics have studied analitically in two-level systems [32,35]. In particular, we consider here a cubic detuning electric field ε C (t) = ε C 0 (t/τ E ) 3 , with amplitude ε C 0 and time scale τ E = /V .…”

Analytical Approximations for Generalized Landau-Zener Transitions in Multi-level Non-Hermitian Systems

“…Compared to the two-state scenario, the research of generalized Landau-Zener transition for complicated systems with more than two states, even in ordinary Hermitian quantum mechanics, has been arduous and in most cases inconclusive. The main reason is that in conventional Landau-Zener transition, the coupling equations which govern the non-adiabatic transition amplitudes between the two energy levels can be reduced to a single second-order differential equation, e.g., the parabolic cylinder function for linear separation of diabatic energies [16], or the confluent Heun functions for quadratic and cubic separations of diabatic energies [23,24]. In contrast, in the general multi-state scenario, if one attempts to re-duce the coupling equations which govern the non-adiabatic transition amplitudes between different energy levels in a single equation, one would probably obtain an ordinary differential equation with order greater than two.…”

“…Recently, the three-state non-Hermitian Landau-Zener model in the presence of an interaction with the outer environment has been considered [28], and the Landau-Zener transitions through a pair of higher order exceptional points has been analyzed by Melanathuru [29]. In this work, based on our analytical approximation methods used in previous researches [23,24,27], we will analyze the dynamics of a four-state non-Hermitian PT -symmetric system which directly passes through a collection of exceptional points.…”