Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.Comment: 14 pages, 12 fig

Two-vibron bound states in alpha-helix proteins : the interplay between the intramolecular anharmonicity and the strong vibron-phonon coupling

The influence of the intramolecular anharmonicity and the strong vibron-phonon coupling on the two-vibron dynamics in an $\alpha$-helix protein is studied within a modified Davydov model. The intramolecular anharmonicity of each amide-I vibration is considered and the vibron dynamics is described according to the small polaron approach. A unitary transformation is performed to remove the intramolecular anharmonicity and a modified Lang-Firsov transformation is applied to renormalize the vibron-phonon interaction. Then, a mean field procedure is realized to obtain the dressed anharmonic vibron Hamiltonian. It is shown that the anharmonicity modifies the vibron-phonon interaction which results in an enhancement of the dressing effect. In addition, both the anharmonicity and the dressing favor the occurrence of two different bound states which the properties strongly depend on the interplay between the anharmonicity and the dressing. Such a dependence was summarized in a phase diagram which characterizes the number and the nature of the bound states as a function of the relevant parameters of the problem. For a significant anharmonicity, the low frequency bound states describe two vibrons trapped onto the same amide-I vibration whereas the high frequency bound states refer to the trapping of the two vibrons onto nearest neighbor amide-I vibrations.Comment: may 2003 submitted to Phys. Rev.

Relaxation channels of two-vibron bound states in \alpha-helix proteins

Relaxation channels for two-vibron bound states in an anharmonic alpha-helix protein are studied. 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.Comment: octobre 2003 - soumis Phys. Rev.

From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states

The self-consistent propagation of generalized $D_{1}$ [coherent-product] states and of a class of gaussian density matrix generalizations is examined, at both zero and finite-temperature, for arbitrary interactions between the localized lattice (electronic or vibronic) excitations and the phonon modes. It is shown that in all legitimate cases, the evolution of $D_{1}$ states reduces to the disentangled evolution of the component $D_{2}$ states. The self-consistency conditions for the latter amount to conditions for decoherence-free propagation, which complement the $D_{2}$ Davydov soliton equations in such a way as to lift the nonlinearity of the evolution for the on-site degrees of freedom. Although it cannot support Davydov solitons, the coherent-product ansatz does provide a wide class of exact density-matrix solutions for the joint evolution of the lattice and phonon bath in compatible systems. Included are solutions for initial states given as a product of a [largely arbitrary] lattice state and a thermal equilibrium state of the phonons. It is also shown that external pumping can produce self-consistent Frohlich-like effects. A few sample cases of coherent, albeit not solitonic, propagation are briefly discussed.Comment: revtex3, latex2e; 22 pages, no figs.; to appear in Phys.Rev.E (Nov.2001

The ves hypothesis and protein misfolding

Proteins function by changing conformation. These conformational changes, which involve the concerted motion of a large number of atoms are classical events but, in many cases, the triggers are quantum mechani- cal events such as chemical reactions. Here the initial quantum states after the chemical reaction are assumed to be vibrational excited states, something that has been designated as the VES hypothesis. While the dynamics under classical force fields fail to explain the relatively lower structural stability of the proteins associated with misfolding diseases, the application of the VES hy- pothesis to two cases can provide a new explanation for this phenomenon. This explanation relies on the transfer of vibrational energy from water molecules to proteins, a process whose viability is also examined

Multi-soliton energy transport in anharmonic lattices

We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons [see Phys. Rev. Lett. {\bf 83}, 296 (1999)], our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models.Comment: 4 pages, 4 figure

Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer

The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A field-induced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure

Energy funneling in a bent chain of Morse oscillators with long-range coupling

A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions.Comment: 6 pages, 12 figures. Submitted to Physical Review E, Oct. 13, 200

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.