Effects of quantum lattice fluctuations on multiquanta Davydov-like solitons in a molecular chain

The Journal of Chemical Physics

2012

Based on the operatorial formulation of the perturbation theory, the exciton-phonon problem is revisited for investigating exciton-mediated energy flow in a finite-size lattice. Within this method, the exciton-phonon entanglement is taken into account through a dual dressing mechanism so that exciton and phonons are treated on an equal footing. In a marked contrast with what happens in an infinite lattice, it is shown that the dynamics of the exciton density is governed by several time scales. The density evolves coherently in the short-time limit whereas a relaxation mechanism occurs over intermediated time scales. Consequently, in the long-time limit, the density converges toward a nearly uniform distributed equilibrium distribution. Such a behavior results from quantum decoherence that originates in the fact that the phonons evolve differently depending on the path followed by the exciton to tunnel along the lattice. Although the relaxation rate increases with the temperature and with the coupling, it decreases with the lattice size, suggesting that the decoherence is inherent to the confinement.

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Equation (4) shows that ∆H favors exciton scattering from state |k to state |k ′ via the exchange of a phonon p. The allowed transitions are specified by the selection rules M pkk ′ = 0 that generalize the concept of momentum conservation in a finite-size lattice.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Energy transfer in finite-size exciton-phonon systems: Confinement-enhanced quantum decoherence

The Journal of Chemical Physics

2012

“…To interpolate between the two asymptotic solutions of the Fröhlich Hamiltonian, Brown, Ivic, and coworkers introduced a unified theory whose starting point was also based on the MLF transformation. [25][26][27][28] In the partially dressed point of view, a trial quantum state is introduced in analogy with the D 1 Davydov's ansatz. 6 Combining time-dependent variational principles and an average over the phonon degrees of freedom, the dressing fraction is finally optimized by minimizing the system ground-state energy.…”

Section: Introductionmentioning

confidence: 99%

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

2009

Phys. Rev. B

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.

“…Nevertheless, the dressing effect leads to an attractive interaction between vibrons mediated by virtual phonons. Such an interaction is responsible for the formation of bound states and it has been suggested that proteins can support solitons formed by bound states involving a large number of vibrational quanta [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Relaxation channels of two-vibron bound states in α-helix proteins

Falvo

2004

Phys. Rev. E

Relaxation channels for two-vibron bound states in an anharmonic α-helix protein are studied. According to a recently established small polaron model [V. Pouthier, Phys. Rev. E68, 021909 (2003)], it is pointed out that the relaxation originates in the interaction between the dressed anharmonic vibrons and the remaining phonons. This interaction is responsible for the occurrence of transitions between two-vibron eigenstates mediated by both phonon absorption and phonon emission. At biological temperature, it is shown that the relaxation rate does not significantly depends on the nature of the two-vibron state involved in the process. Therefore, the lifetime for both bound and free states is of the same order of magnitude and ranges between 0.1 and 1.0 ps for realistic parameters. By contrast, the relaxation channels strongly depend on the nature of the two-vibron states which is a consequence of the breather-like behavior of the two-vibron bound states.