Bernd Esser

Spin-boson Hamiltonian and optical absorption of molecular dimers

An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is performed by computing Bloch and Husimi projections. The eigenstate analysis is combined with the calculation of absorption bands of asymmetric dimer configurations constituted by monomers with nonidentical excitation energies and optical transition matrix elements. Absorption bands with regular and irregular fine structures are obtained and related to the transition from the coexistence to a mixing of adiabatic branches in the spectrum. It is shown that correlations between spin states allow for an interpolation between absorption bands for different optical asymmetries.

Excitonic-vibronic coupled dimers: a dynamic approach

The dynamical properties of exciton transfer coupled to polarization vibrations in a two site system are investigated in detail. A fixed point analysis of the full system of Bloch-oscillator equations representing the coupled excitonic-vibronic flow 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.

Energy transfer in an asymmetric nonlinear dimer model

A complete analysis of the transfer dynamics in an asymmetric nonlinear dimer model with different cubic site polarizations is given. The analysis is performed for both the dynamics of the full density matrix on the Bloch sphere (location of fixed points, bifurcation in dependence on the polarization strength) and of the reduced space of the occupation difference using a potential function. For a time dependent harmonic perturbation the appearance of chaotic transfer regimes near a homoclinic structure on the Bloch sphere is demonstrated. A comparison with spin models is performed. It is shown that the chaotic regime corresponds to chaotic motion in a classical spin model witha−Sz2 nonlinearity and an external magnetic field having its constant and time dependent parts in the same direction.

Spectral and time resolved optical emission of a nonlinear dimer model

The relations between the different stationary and nonstationary states of molecular excitations described by a nonlinear dimer model with cubic site polarization terms and the corresponding optical emission spectra are considered in detail. For the stationary states emission is explicitly calculated for both the symmetric case with equal optical coupling constants of both molecules constituting the dimer as well as the asymmetric case where one of the molecules is optically active only. The time-resolved emission from the nonstationary states is treated by using a quasistationary approximation based on slow transfer dynamics compared to the polarization. Of particular interest in the nonstationary case is the chaotic transfer regime induced by a harmonic perturbation. For the latter case the evolution of the spectrum from an ensemble of dimers spreading within the stochastic layer on the Bloch sphere is presented.

Spectrum, lifetime distributions and relaxation in a dimer with strong excitonic—vibronic coupling

The fine structure of the complex quantum spectrum of a dimer constituted by monomers with a finite lifetime in the excited states and a strong excitonic—vibronic coupling has been investigated in detail. Lifetime distributions of the spectrum are analysed for di⁄erent system parameter sets. It is shown that in case of an asymmetric configuration the spectrum may be characterised by a broad distribution of the lifetimes of the eigenstates. This can give rise to a strongly varying relaxation behaviour, which is due to the mixing of the monomer spectra with two di⁄erent excitonic lifetimes in the dimer spectrum. ( 1999 Elsevier Science B.V. All rights reserved.

Type II quantum chaos

A classification of quantum systems into three categories, type I, II and III, is proposed. The classification is based on the degree of sensitivity upon initial conditions, and the appearance of chaos. The quantum dynamics of type I systems is quasi periodic displaying no exponential sensitivity. They arise, e.g., as the quantized versions of classical chaotic systems. Type II systems are obtained when classical and quantum degrees of freedom are coupled. Such systems arise naturally in a dynamic extension of the first step of the Born-Oppenheimer approximation, and are of particular importance to molecular and solid state physics. Type II systems can show exponential sensitivity in the quantum subsystem. Type III systems are fully quantized systems which show exponential sensitivity in the quantum dynamics. No example of a type III system is currently established. This paper presents a detailed discussion of a type II quantum chaotic system which models a coupled electronic-vibronic system. It is argued that type II systems are of importance for any field systems (not necessarily quantum) that couple to classical degrees of freedom.

TRANSFER AND DECAY OF AN EXCITON COUPLED TO VIBRATIONS IN A DIMER

Transfer and decay dynamics of an exciton coupled to a polarization vibration in a dimer is investigated in a mixed quantum-classical picture with the exciton decay incorporated by a sink site. Using a separation of time scales, it is possible to explain analytically the most important characteristics of the model. If the vibronic subsystem is fast, these are the enhancement of nonlinear self-trapping due to the sink and the slowing down of the exciton decay for large coupling or sink strength. Numerical results obtained recently for the discrete self-trapping (DST) approximation to the model are quantitatively explained and dynamic effects beyond this approximation are found. If the vibronic subsystem is slow, the behavior of the system follows closely the predictions of the adiabatic approximation. In this regime, the exciton decay crucially depends on the initial conditions of the vibronic subsystem. In the transition regime between the adiabatic and DST approximation, complex dynamics is observed by numerical computation. We discuss the correspondence to the chaotic behavior of the excitonic-vibronic coupled dimer without trap. {copyright} {ital 1997} {ital The American Physical Society}

Theory of absorption bands in molecular dimers: Interpolating between optical asymmetries

Absorption band shapes of an asymmetric dimer system constituted by monomers with different excitation energies and optical transition matrix elements are considered in the semiclassical parameter region. Optical transition matrix elements originating from arbitrary initial vibrational states are analyzed on the basis of a spin representation of the eigenstates of an associated symmetry broken spin-boson Hamiltonian. Correlations between the spin-down and spin-up coefficients of these eigenstates are shown to exist and investigated in detail. Using these correlations, an asymmetry interpolation of the intensity of absorption lines between dimer configurations with different optical monomer transition matrix elements is proposed.

Emission spectra in non-symmetric dimer systems: fine structure of emission bands and dependence on asymmetry parameters

The fine structure of emission bands of asymmetric dimers with different excitation energies and optical transition matrix elements of the monomers constituting the dimer is investigated. Emission bands are calculated for various initial states which belong either to a single adiabatic branch or are due to a mixing of the adiabatic branches in the spectrum. Mixing of adiabatic branches is shown to result in spectral randomness and complex bands which spectral ranges can change drastically when the asymmetry is varied.