Excitonic-vibronic coupled dimers: A dynamic approach

Abstract

The dynamical properties of exciton transfer coupled to polarization vibrations in a two site system are investigated in detail. A xed point analysis of the full system of Bloch -oscillator equations representing the coupled excitonic -vibronic ow is performed. For overcritical polarization a bifurcation converting the stable bonding ground state to a hyperbolic unstable state which is basic to the dynamical properties of the model is obtained. The phase space of the system is generally of a mixed type: Above bifurcation chaos develops starting from the region of the hyperbolic state and spreading with increasing energy over the Bloch sphere leaving only islands of regular dynamics. The behaviour of the polarization oscillator accordingly changes from regular to chaotic.

Towards a generalized Landau-Zener formula for an interacting Bose-Einstein condensate in a two-level system

“…However, the crossing time is easily calculated by evaluating h N (t ℓ,N ) = h ℓ (t ℓ,N ), where h ℓ (t) are diabatic levels as defined above. This yields At all crossing times t ℓ,N , the level spacings w ℓ,N are calculated by diagonalizing the Hamiltonian matrix (8). As H is tridiagonal, this can be done very efficiently.…”

“…These considerations have let to a reformulation of the adiabatic theorem for nonlinear systems, based on the adiabatic theorem of classical mechanics [3]. Note also that the emergence of looped levels was previously studied for the quantum dimer [8]. Several approaches were made to derive a nonlinear Landau-Zener formula for this problem using methods from classical Hamiltonian mechanics [9,10].…”

Nonadiabatic couplings and incipience of quantum chaos

“…The main aim of this paper was to show how irregularities in the spectrum and associated eigenvectors of the fully quantized electronic two site system coupled to a vibration appear when a characteristic coupling parameter is increased. The considered system belongs to the class of models which show regular and chaotic dynamics in the mixed quantum -classical description when a stepwise quantization is applied treating the electronic subsystem in the quantum but the vibronic subsystem in the classical context [4]. Hence it is natural to ask for the "fingerprints" of the dynamical chaos in the mixed description after full quantization is performed.…”

“…The result of this research was that despite some irregularities in the spectrum the level spacing statistics is mostly regular. Here we demonstrate for one explicit system of this class, namely the excitonic -vibronic coupled dimer (for details of the model see [4]), that in fact in this kind of systems one can follow how the irregularities in the eigenvalue spectrum and the associated eigenstates appear through patterns of growing complexity when a characteristic coupling parameter is increased. Hence these systems have to be placed between systems with regular and completely irregular spectra.…”

Resonant ratcheting of a Bose–Einstein condensate

“…The symmetric case shows a pitchfork bifurcation with the appearance of two new states at the bifurcation point ( Fig.2a). These new states exhibit a population imbalance similar to the undriven system [18,20,21,22], despite the fact that the equations are symmetric.…”