Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape

We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving under identical but arbitrarily correlated noises, we demonstrate that there exists a critical temperature T0 which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high temperatures, being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations, we show that the asymptotic damage has the good properties of a dynamical order parameter, such as (i) independence of the initial damage; (ii) independence of the class of initial condition; and (iii) stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as metastable states) in the thermodynamic limit consequence of the ruggedness of the free-energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading an interesting tool to probe the ruggedness of the configurational landscape.

Reaction-diffusion lattice gas: Theory and computer results

We report on the study of nonequilibrium ordering in the reaction-diffusion lattice gas. It is a kinetic model that relaxes towards steady states under the simultaneous competition of a thermally activated creation-annihilation $(reaction$) process at temperature T, and a diffusion process driven by a heat bath at temperature T?T. The phase diagram as one varies T and T, the system dimension d, the relative priori probabilities for the two processes, and their dynamical rates is investigated. We compare mean-field theory, new Monte Carlo data, and known exact results for some limiting cases. In particular, no evidence of Landau critical behavior is found numerically when d=2 for Metropolis rates but Onsager critical points and a variety of first-order phase transitions.

Incompressibility of neutron-rich matter

The saturation properties of neutron-rich matter are investigated in a relativistic mean-field formalism using two accurately calibrated models: NL3 and FSUGold. The saturation properties density, binding energy per nucleon, and incompressibility coefficient are calculated as a function of the neutron-proton asymmetry α≡(N-Z)/A to all orders in α. Good agreement (at the 10% level or better) is found between these numerical calculations and analytic expansions that are given in terms of a handful of bulk parameters determined at saturation density. Using insights developed from the analytic approach and a general expression for the incompressibility coefficient of infinite neutron-rich matter, i.e., K0(α)=K0+Kτα2+ , we construct a hybrid model with values for K0 and Kτ as suggested by recent experimental findings. Whereas the hybrid model provides a better description of the measured distribution of isoscalar monopole strength in the Sn isotopes relative to both NL3 and FSUGold, it significantly underestimates the distribution of strength in 208Pb. Thus, we conclude that the incompressibility coefficient of neutron-rich matter remains an important open problem.

Dinàmica de sistemes mesoscòpics amb correlacions quàntiques mitjançant la formulació de de Broglie-Bohm

Per a determinar la dinàmica espai-temporal completa d’un sistema quàntic tridimensional de N partícules cal integrar l’equació d’Schrödinger en 3N dimensions. La capacitat dels ordinadors actuals permet fer-ho com a molt en 3 dimensions. Amb l’objectiu de disminuir el temps de càlcul necessari per a integrar l’equació d’Schrödinger multidimensional, es realitzen usualment una sèrie d’aproximacions, com l’aproximació de Born–Oppenheimer o la de camp mig. En general, el preu que es paga en realitzar aquestes aproximacions és la pèrdua de les correlacions quàntiques (o entrellaçament). Per tant, és necessari desenvolupar mètodes numèrics que permetin integrar i estudiar la dinàmica de sistemes mesoscòpics (sistemes d’entre tres i unes deu partícules) i en els que es tinguin en compte, encara que sigui de forma aproximada, les correlacions quàntiques entre partícules. Recentment, en el context de la propagació d’electrons per efecte túnel en materials semiconductors, X. Oriols ha desenvolupat un nou mètode [Phys. Rev. Lett. 98, 066803 (2007)] per al tractament de les correlacions quàntiques en sistemes mesoscòpics. Aquesta nova proposta es fonamenta en la formulació de la mecànica quàntica de de Broglie– Bohm. Així, volem fer notar que l’enfoc del problema que realitza X. Oriols i que pretenem aquí seguir no es realitza a fi de comptar amb una eina interpretativa, sinó per a obtenir una eina de càlcul numèric amb la que integrar de manera més eficient l’equació d’Schrödinger corresponent a sistemes quàntics de poques partícules. En el marc del present projecte de tesi doctoral es pretén estendre els algorismes desenvolupats per X. Oriols a sistemes quàntics constituïts tant per fermions com per bosons, i aplicar aquests algorismes a diferents sistemes quàntics mesoscòpics on les correlacions quàntiques juguen un paper important. De forma específica, els problemes a estudiar són els següents: (i) Fotoionització de l’àtom d’heli i de l’àtom de liti mitjançant un làser intens. (ii) Estudi de la relació entre la formulació de X. Oriols amb la aproximació de Born–Oppenheimer. (iii) Estudi de les correlacions quàntiques en sistemes bi- i tripartits en l’espai de configuració de les partícules mitjançant la formulació de de Broglie–Bohm.

Response of doped 4He droplets

In the framework of a finite-range density-functional theory, we compute the response of 4HeN clusters doped with a rare-gas molecule. For this purpose, the mean field for the 4He atoms, their wave functions and effective quasiparticle interaction, are self-consistently calculated for a variety of particle numbers in the cluster. The response function is then evaluated for several multipolarities in each drop and the collective states are consequently located from the peaks of the strength function. The spectra of pure droplets approach those previously extracted with a similar algorithm resorting to a zero-range density functional. The spectra of doped clusters are sensitive to the presence of the impurity and are worth a future systematic investigation.

Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

K-Rb Fermi-Bose mixtures: Vortex states and sag

We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean-field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the Fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.

Polymer-induced tubulation in lipid vesicles

A mechanism of extraction of tubular membranes from a lipid vesicle is presented. A concentration gradient of anchoring amphiphilic polymers generates tubes from budlike vesicle protrusions. We explain this mechanism in the framework of the Canham-Helfrich model. The energy profile is analytically calculated and a tube with a fixed length, corresponding to an energy minimum, is obtained in a certain regime of parameters. Further, using a phase-field model, we corroborate these results numerically. We obtain the growth of tubes when a polymer source is added, and the budlike shape after removal of the polymer source, in accordance with recent experimental results.

Shell structure in mixed 3He-4He droplets

Due to the immiscibility of 3He into 4He at very low temperatures, mixed helium droplets consist of a core of 4He atoms coated by a 3He layer whose thickness depends on the number of atoms of each isotope. When these numbers are such that the centrifugal kinetic energy of the 3He atoms is small and can be considered as a perturbation to the mean-field energy, a novel shell structure arises, with magic numbers different from these of pure 3He droplets. If the outermost shell is not completely filled, the valence atoms align their spins up to the maximum value allowed by the Pauli principle.

Lateral instability in normal viscous fingers

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

Dynamical scaling of imbibition in columnar geometries

compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

Pattern formation during mesophase growth in a homologous series

Remarkable differences in the shape of the nematic-smectic-B interface in a quasi-two-dimensional geometry have been experimentally observed in three liquid crystals of very similar molecular structure, i.e., neighboring members of a homologous series. In the thermal equilibrium of the two mesophases a faceted rectanglelike shape was observed with considerably different shape anisotropies for the three homologs. Various morphologies such as dendritic, dendriticlike, and faceted shapes of the rapidly growing smectic-B germ were also observed for the three substances. Experimental results were compared with computer simulations based on the phase field model. The pattern forming behavior of a binary mixture of two homologs was also studied.

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

Critical frequency for vortex nucleation in Bose-Fermi mixtures in optical lattices

We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since 87Rb-40K mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system.

Scaling calculation of isoscalar giant resonances in relativistic Thomas-Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended ThomasFermi approach to relativistic mean-field theory. We study the ability of several nonlinear σω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.