Nonadiabatic couplings and incipience of quantum chaos

Abstract

The quantization of the electronic two site system interacting with a vibration is considered by using as the integrable reference system the decoupled oscillators resulting from the adiabatic approximation. A specific Bloch projection method is applied which demonstrates how besides some regular regions in the fine structure of the spectrum and the associated eigenvectors irregularities appear when passing from the low to the high coupling case. At the same time even for strong coupling some of the regular structure of the spectrum rooted in the adiabatic potentials is kept intact justifying the classification of this situation as incipience of quantum chaos.Comment: 16 pages including figure

Transfer and decay of an exciton coupled to vibrations in a dimer

“…First we note, that as g → 0 the two fixed points approach the well known lower and upper adiabatic states of the system without trap (see e. g. [23]) which are given by…”

Spin-boson Hamiltonian and optical absorption of molecular dimers

“…A central point in our eigenstate analysis will be to find out to what extent the adiabatic reference systems of the spin-boson Hamiltonian are present in its exact eigenstates and how the appearance of spectral randomness can be interpreted as a mixing of such reference systems. Following [13] we show that Bloch projections are a useful quantitative characteristic to describe this mixing. Computing the Bloch projections of the eigenstates, it is possible to distinguish the spectral region where the adiabatic branches of the spectrum are still intact from the region with a substantial mixing of adiabatic reference systems.…”

“…where |↑ = 1 0 , |↓ = 0 1 denote the spin up (down) states, |m the harmonic oscillator eigenstates and c zm (z =↑, ↓) for a given oscillator state as indicated in the second part of (13). The matrix dimension in the numerical diagonalization was N = 4000, for the eigenstate analysis the first 1100 eigenstates were used.…”

“…The matrix element (20) is representable in the form of a particular projection of the spin vector associated with the m = 0 vibrational state in (13), s (λ) 0…”

“…In particular, we show how the intensity variations in the Husimi projections are related to the spectral randomness in the fine structure of absorption bands. Such spectral randomness in the eigenstates of the spin-boson Hamiltonian is also known as incipience of quantum chaos [11][12][13]. In this case random features of the spectrum are just appearing while the system is still far from displaying universal spectral fluctuations described by random matrix theory and known for excited states of spectra of polyatomic molecules [14].…”