Ultracold Bose-Fermi mixtures with pairing: quantum phase transition, mechanical stability, and trap confinement

Ultracold dilute gases occupy an important role in modern physics and they are employed to verify fundamental quantum theories in most branches of theoretical physics. The scope of this thesis work is the study of Bose-Fermi (BF) mixtures at zero temperature with a tunable pairing between bosons and fermions. The mixtures are treated with diagrammatic quantum many-body methods based on the so-called T-matrix formalism. Starting from the Fermi-polaron limit, I will explore various values of relative concentrations up to mixtures with a majority of bosons, a case barely considered in previous works. An unexpected quantum phase transition is found to occur in a certain range of BF coupling for mixture with a slight majority of bosons. The mechanical stability of mixtures has been analysed, when the boson-fermion interaction is changed from weak to strong values, in the light of experimental results recently obtained for a double-degenerate Bose-Fermi mixture of 23 Na - 40 K. A possible improvement in the description of the boson-boson repulsion based on Popov's theory is proposed. Finally, the effects of a harmonic trapping potential are described, with a comparison with the experimental data for the condensate fraction recently obtained for a trapped 23 Na - 40 K mixture.

Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton

Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960s as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well understood nowadays, the model never received a full numerical treatment to investigate its critical behavior. In this Brief Report we characterize the critical behavior of Stavskaya's PCA by means of Monte Carlo simulations and finite-size scaling analysis. The critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior, as would be expected on the basis of the directed percolation conjecture. We also explicitly establish the relationship of the model with the Domany-Kinzel PCA on its directed site percolation line, a connection that seems to have gone unnoticed in the literature so far.

The n-site approximation for the triplet-creation model

The nonequilibrium phase transition of the one-dimensional triplet-creation model is investigated using the n-site approximation scheme. We find that the phase diagram in the space of parameters (gamma, D), where gamma is the particle decay probability and D is the diffusion probability, exhibits a tricritical point for n >= 4. However, the fitting of the tricritical coordinates (gamma(t), D(t)) using data for 4 <= n <= 13 predicts that gamma(t) becomes negative for n >= 26, indicating thus that the phase transition is always continuous in the limit n -> infinity. However, the large discrepancies between the critical parameters obtained in this limit and those obtained by Monte Carlo simulations, as well as a puzzling non-monotonic dependence of these parameters on the order of the approximation n, argue for the inadequacy of the n-site approximation to study the triplet-creation model for computationally feasible values of n.

The mass media destabilizes the cultural homogenous regime in Axelrod`s model

An important feature of Axelrod`s model for culture dissemination or social influence is the emergence of many multicultural absorbing states, despite the fact that the local rules that specify the agents interactions are explicitly designed to decrease the cultural differences between agents. Here we re-examine the problem of introducing an external, global interaction-the mass media-in the rules of Axelrod`s model: in addition to their nearest neighbors, each agent has a certain probability p to interact with a virtual neighbor whose cultural features are fixed from the outset. Most surprisingly, this apparently homogenizing effect actually increases the cultural diversity of the population. We show that, contrary to previous claims in the literature, even a vanishingly small value of p is sufficient to destabilize the homogeneous regime for very large lattice sizes.

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

Numerical study of a model for nonequilibrium wetting

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

Noise-induced scenario for inverted phase diagrams

We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions.

Universality in models for disorder induced phase transitions

We have systematically analyzed six different reticular models with quenched disorder and no thermal fluctuations exhibiting a field-driven first-order phase transition. We have studied the nonequilibrium transition, appearing when varying the amount of disorder, characterized by the change from a discontinuous hysteresis cycle (with one or more large avalanches) to a smooth one (with only tiny avalanches). We have computed critical exponents using finite size scaling techniques and shown that they are consistent with universal values depending only on the space dimensionality d.

Dynamics of the deconfinement transition of quarks and gluons in a finite volume

We employ finite elements methods for the approximation of solutions of the Ginzburg-Landau equations describing the deconfinement transition in quantum chromodynamics. These methods seem appropriate for situations where the deconfining transition occurs over a finite volume as in relativistic heavy ion collisions. where in addition expansion of the system and flow of matter are important. Simulation results employing finite elements are presented for a Ginzburg-Landau equation based on a model free energy describing the deconfining transition in pure gauge SU(2) theory. Results for finite and infinite system are compared. (C) 2009 Elsevier B.V. All rights reserved.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

CDP/cut is the DNA-binding subunit of histone gene transcription factor HiNF-D: a mechanism for gene regulation at the G1/S phase cell cycle transition point independent of transcription factor E2F.

Transcription of the genes for the human histone proteins H4, H3, H2A, H2B, and H1 is activated at the G1/S phase transition of the cell cycle. We have previously shown that the promoter complex HiNF-D, which interacts with cell cycle control elements in multiple histone genes, contains the key cell cycle factors cyclin A, CDC2, and a retinoblastoma (pRB) protein-related protein. However, an intrinsic DNA-binding subunit for HiNF-D was not identified. Many genes that are up-regulated at the G1/S phase boundary are controlled by E2F, a transcription factor that associates with cyclin-, cyclin-dependent kinase-, and pRB-related proteins. Using gel-shift immunoassays, DNase I protection, and oligonucleotide competition analyses, we show that the homeodomain protein CDP/cut, not E2F, is the DNA-binding subunit of the HiNF-D complex. The HiNF-D (CDP/cut) complex with the H4 promoter is immunoreactive with antibodies against CDP/cut and pRB but not p107, whereas the CDP/cut complex with a nonhistone promoter (gp91-phox) reacts only with CDP and p107 antibodies. Thus, CDP/cut complexes at different gene promoters can associate with distinct pRB-related proteins. Transient coexpression assays show that CDP/cut modulates H4 promoter activity via the HiNF-D-binding site. Hence, DNA replication-dependent histone H4 genes are regulated by an E2F-independent mechanism involving a complex of CDP/cut with cyclin A/CDC2/ RB-related proteins.

Interacting nonequilibrium systems with two temperatures

We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being interconnected with each other. Using generating functional analysis, commonly used in statistical mechanics, we find exactly soluble expressions for their individual magnetization that define a two-dimensional nonlinear map, the equations of which have the same form as those obtained for densely connected equilibrium systems. Steady states correspond to the fixed points of this map, separating the parameter space into a rich set of nonequilibrium phases that we analyze in asymptotically high and low (nonequilibrium) temperature limits. The theoretical formalism is shown to revert to the classical nonequilibrium steady state problem for two interacting systems with a nonzero heat transfer between them that catalyzes a phase transition between ambient nonequilibrium states. © 2013 American Physical Society.

Superconducting Transition-Edge Sensor Physics

Despite record-setting performance demonstrated by superconducting Transition Edge Sensors (TESs) and growing utilization of the technology, a theoretical model of the physics governing TES devices superconducting phase transition has proven elusive. Earlier attempts to describe TESs assumed them to be uniform superconductors. Sadleir et al. 2010 shows that TESs are weak links and that the superconducting order parameter strength has significant spatial variation. Measurements are presented of the temperature T and magnetic field B dependence of the critical current Ic measured over 7 orders of magnitude on square Mo/Au bilayers ranging in length from 8 to 290 microns. We find our measurements have a natural explanation in terms of a spatially varying order parameter that is enhanced in proximity to the higher transition temperature superconducting leads (the longitudinal proximity effect) and suppressed in proximity to the added normal metal structures (the lateral inverse proximity effect). These in-plane proximity effects and scaling relations are observed over unprecedentedly long lengths (in excess of 1000 times the mean free path) and explained in terms of a Ginzburg-Landau model. Our low temperature Ic(B) measurements are found to agree with a general derivation of a superconducting strip with an edge or geometric barrier to vortex entry and we also derive two conditions that lead to Ic rectification. At high temperatures the Ic(B) exhibits distinct Josephson effect behavior over long length scales and following functional dependences not previously reported. We also investigate how film stress changes the transition, explain some transition features in terms of a nonequilibrium superconductivity effect, and show that our measurements of the resistive transition are not consistent with a percolating resistor network model.

Entropy, chaos, and excited-state quantum phase transitions in the Dicke model

We study nonequilibrium processes in an isolated quantum system-the Dicke model-focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos, and the excited-state quantum phase transition is more clear for the entanglement entropy.