F. de Pasquale

DYNAMICAL MEAN-FIELD THEORY OF THE SMALL POLARON

A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground-state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion, at both zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground-state properties, such as the effective polaron mass, which show a continuous behavior as the coupling is increased, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more open in the density of states at low energy, while the high-energy part of the spectrum is broad and can be qualitatively explained by a strong coupling adiabatic approximation. As a consequence, narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such an effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum always has a multipeaked structure.

SQUEEZING PHENOMENA IN INTERACTING ELECTRON-PHONON SYSTEMS

The molecular crystal model of electrons coupled to Einstein phonons is studied as a function of the two parameters: the coupling constant A and the ratio of the electron-phonon coupling energy to the phonon energy, denoted by α. Both the one-electron and the many-electron models are studied, starting (for the former) from the adiabatic limit and (for the latter) from the anti-adiabatic one. In the “multiphonon” regime α>1, the sharp crossover between quasi-free electrons (λ≪1) and small polarons (λ≫1) is investigated, emphasizing the anomalous lattice fluctuations which occur in the intermediate regime (λ≈1). These fluctuations are due to the band motion of the electrons strongly coupled to the lattice and are shown in turn to weaken the electron mass renormalization inherent to self-trapping. In a relevant part of the intermediate region the effective electron mass slowly increases with λ, due to a competition between the phonon dressing effect and the reduction of lattice momentum fluctuations. This re...

On the stochastic correlations in a randomly perturbed chemical front

A stochastic reaction-diffusion equation, which describes the time evolution of a front of concentration in a chemical system characterized by a single active component and influenced by the presence of external noise, is solved within the small noise approximation. The spatial correlations of concentration are studied. The relationship between the spectrum of the evolution operator and the correlation function is discussed and two examples (the trigger wave and the wave between a stable and an unstable state) are discussed.

Teleportation on a quantum dot array.

We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, with one excess electron, coupled by tunneling. It is shown how to create a maximally entangled state using an adiabatically increasing Coulomb repulsion between different dot pairs. This entangled state is exploited to perform teleportation again using an adiabatic coupling between itself and the incoming unknown state. Finally, a sudden separation of Bobs qubit allows a time evolution of Alices, which amounts to a modified version of standard Bell measurement. A transmission over a long distance could be obtained by considering the entangled state of a chain of N coupled double quantum dots. The system is shown to be increasingly robust with N against decoherence due to phonons.

Charge-ordered state from weak to strong coupling

We apply the dynamical mean field theory to the problem of charge ordering. In the normal state as well as in the charge-ordered (CO) state, the existence of polarons (i.e., electrons strongly coupled to local lattice deformation) is associated to the qualitative properties of the lattice polarization distribution function (LPDF). At intermediate and strong coupling, a CO state characterized by acertain amount of thermally activated defects arises from the spatial ordering of preexisting, randomly distributed polarons. Properties of this particular CO state give a qualitative understanding of the low frequency behavior of optical conductivity of Ni perovskites.

Superconductivity and Density Waves in High Dimensions

Density and pairing responses are studied for the Holstein molecular crystal model. The charge density wave (CDW) and the superconductivity (SC) instabilities of the normal phase are investigated. Analytical results are obtained for small electron-phonon coupling in a simple cubic lattice in the limit of large dimensionality (d = ∞). Near half-filling the dominant instability is a CDW, due to nesting at q = (π, π,...). For larger deviations from half-filling the CDW becomes incommensurate in a narrow filling range and finally disappears. Then the SC instability dominates.

Exact Solution of the Small-Polaron Problem in Infinite Dimensions

The spectral function of a single electron coupled to Einstein phonons (Holstein model) is calculated exactly in the limit of large space dimensionality, for any coupling strength and phonon frequency. A self-consistent mapping onto an effective impurity model leads to the solution in terms of a continued-fraction expansion for the electron propagator at zero temperature. True self-trapping is obtained only for finite bandwidth, such as the case of a Bethe lattice in infinite dimensions. It is shown that at intermediate coupling multiphonon resonances develop, corresponding to polaron states. Only the lowest one has long lifetime, and the polaron mass is calculated.

Transient laser radiation as a stochastic process near an instability point

A new approximate solution of the stochastic process associated to the laser transient radiation is proposed. It is shown that, by means of the classical equation of motion, it is possible to introduce a non-linear time-dependent mapping between the original stochastic process and a new process which, near an unstable state, has a limited range for short times. Detailed comparisons with numerical results and experimental data are also performed.

Optimized electron propagation on a quantum chain by a topological phase

8 pages, 6 figures.-- Published in Fortschritte der Physik 57(11-12): 1094-1102 (2009).-- http://dx.doi.org/10.1002/prop.200990010

Analysis of the coexistence curve of a liquid system with a global equation of state

The data of Green (1976) on the difference of volume fractions in the coexisting phases of the isobutyric acid-water system are analysed in terms of an equation of state, which is a model for the crossover from the critical region to a van der Waals-like behaviour. The results provide evidence of the importance of non-scaling correction terms even in a small range close to the critical point. Correspondingly the effective critical index describing the coexistence curve shows a significant departure from its asymptotic value.