Two-site small polaron quantum states: Optimization of the dressing fraction

Abstract

A modified Lang-Firsov transformation is used to study the exciton-phonon interaction in a two-site system embedded in a one-dimensional lattice. It describes an exciton partially dressed by a virtual phonon cloud and depends on a single variational parameter, the so-called dressing fraction, whose optimization is achieved by using both the standard Bogoliubov inequality and its improved version defined by Decoster ͓J. Phys. A 37, 9051 ͑2004͔͒. The optimization procedure is applied to build a phase diagram in the parameter space which defines the different states of the exciton depending on the adiabaticity, the coupling strength, and the temperature. It is shown that the two Bogoliubov inequalities yield different variational principles that give rise to two optimal dressing fractions. Special attention is thus paid to characterize their differences in the nonadiabatic limit, where the exciton evolves continuously from a partially dressed state in the weak-coupling limit to a fully dressed state in the strong-coupling limit, and in the adiabatic limit where a self-trapped transition takes place.

Nature of the vibron self-trapped states in hydrogen-bonded macromolecular chains

“…Note that in this way, each single-particle energy level is minimized individually by this scheme, consequently the free energy is also minimized and the present ansatz is consistent with some other mean-field approaches based upon the Bogolyubov variational principle [16][17][18][20][21][22].…”

Quantum decoherence in finite size exciton–phonon systems

“…42 Moreover, the dressed exciton delocalizes according to a reduced hopping constant ≈ exp(−S), where the band-narrowing factor at zero temperature is S = 8E B /(3π c ). The first parameter, δω k , describes the energy shift experienced by the exciton when it is dressed by a virtual phonon cloud.…”

On the vibron nature in the system of two parallel macromolecular chains: The influence of interchain coupling

“…In order to facilitate an analytic treatment, we assume the equal dressing fraction for all phonon modes introducing the new variational parameter-dressing fraction (δ) taking [5,22,32]…”

“…Contrary to the problem of the single excitation interacting with the dispersionless optical phonons at zero temperature where numerically exact solutions were found recently [21], the finite temperature treatment is much more complicated and exact solutions, both analytical or numerical, are yet unknown. For this reason we base our study on an approximate, variational mean field approach, which has been used for years as a theoretical framework of the understanding of the various phenomena in the strongly coupled exciton-phonon systems [5,22,25,26,27]. At zero temperature this approach reduces to the variational theories of Toyozawa-Merriefild-Emin (TME) [11,28,29] whose predictions for 3D systems are consistent with the numerical ones [21].…”

“…In this paper we study the influence of the temperature and the interchain coupling on the properties of the small polarons in media composed of the two coupled infinite parallel molecular chains. For that purpose we employ variational treatment based on the modified Lang-Firsov transformation [5,22,23].…”