We investigate the properties of phase separation in a mixture of two bosonic species by means of path-integral quantum Monte Carlo by the two-worm algorithm. The mixture is trapped in a square optical lattice at different filling and temperature conditions. The work is focused on the study of the ground-state phase diagram where various quantum phases can arise depending on the interplay between intra-and inter-species interactions. Demixed phases, characterized by spatial separation of the two species, are studied in details determining under which conditions they can be stabilized. The influence of temperature, filling factor and harmonic trap on phase separation is also investigated. An interesting dependence of the degree of demixing from temperature has been found, suggesting new ways to measure the temperature of a two-component bosonic mixture.

Heilmann and Lieb (J.Stat.Phys. 1979) proposed a monomer-dimer model on the square lattice in order to describe a liquid crystal. They proved the existence of a long range orientational order induced by a short-range attractive intraction favoring colinear dimers. On the other hand they conjectured the absence of a complete translational order in the system. This conjecture is still open. In this talk I will show how cluster expansion methods have been recently used (J.Stat.Phys. 2016) to prove the absence of translational order in a modified system. In the future this approach could be extended to study the original problem.

Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, varying the noise source intensity and the bias frequency. Moreover the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources, Levy type, is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the resonant activation. The analysis of the time evolution of the order parameter highlights the influence of the noise induced solitons on the mean switching time behavior and the observation of breathers. Effect of non-Gaussian noise sources on the distributions of switching currents in graphene Josephson junctions will be presented [1]. (ii) Second, the electron spin relaxation process in n-type GaAs crystals driven by a fluctuating electric field and two different noise sources is investigated. Monte Carlo numerical simulations show, in both cases, an enhancement of the spin relaxation time by increasing the amplitude of the external noise [2]. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system-bath coupling and the temperature, producing a stabilizing effect [3].
References 1. Claudio Guarcello, Davide Valenti, and Bernardo Spagnolo, Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations, Phys. Rev. B 92, 174519 (2015). 2. B. Spagnolo, D. Valenti, C. Guarcello, A. Carollo, D. Persano Adorno, S. Spezia, N. Pizzolato, B. Di Paola, Noise-induced effects in nonlinear relaxation of condensed matter systems, Chaos Solitons and Fractals 81, 412-424 (2015). 3. D. Valenti, L. Magazzu', P. Caldara, and B. Spagnolo, Stabilization of quantum metastable states by dissipation, Physical Review B 91, 235412 (7) (2015).

We continue the study of the Quench Action Method (QAM) for a recently considered geometrical quantum quench: two free fermionic chains initially separated by an hard wall and after put in contact and let evolve unitarily with a translation invariant Hamiltonian. Every time un unbalanced of energy, chemical potential or number of particles is present two di fferent stationary regimes are reached at long times, depending on the ratio t/L, where t is the observation time scale and L is the total system size. To captured the two quasi-stationary states (before the quantum recurrence) with the QAM is necessary to distinguish the two case with the introduction of the time in the saddle point equation as just shown in a previous paper, and we show how this modification works also for a domain wall initial state. In this paper we compute the total time evolution for three di fferent initial state of a XX chain, conjecturing that our master equation is valid for any initial state. We also review the derivation of the GGE state in the case of the two temperatures showing that this is an effect of finite volume, as for a domain wall initial condition.

Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process. These exponents are also recovered in neuronal network simulations implementing various neuronal dynamics on different network topologies. They can therefore be considered a very robust feature of spontaneous neuronal activity. Interestingly, this scaling behaviour is also observed on regular lattices in finite dimensions, which raises the question about the origin of the mean field behaviour observed experimentally. We provide an answer to this open question by investigating the effect of activity dependent plasticity in combination with the neuronal refractory time in a neuronal network. Results show that the refractory time hinders backward avalanches forcing a directed propagation. Hebbian plastic adaptation plays the role of sculpting these directed avalanche patterns into the topology of the network slowly changing it into a branched structure where loops are marginal.

Active fluids are inherently far-from-equilibrium systems whose internal self-propelled constituents convert chemical energy into work [1]. This non-equilibrium feature unveils several novel striking effects, such as giant density fluctuations [2], spontaneous flows [3] and unexpected phase separation [4,5]. Of particular importance is the so-called motility induced phase separation (MIPS), a phenomenon which is attracting a remarkable amount of interest in the physics community. If the propulsion speed of the motile particles decreases fast enough with the density due to the crowding, phase separation occurs even without any attractive interaction [6]. Several theoretical models, both particle [5,7] and continuum-based [5,6,8], have been proposed in order to shed light on the physics of MIPS. In particular simulations show that, when hydrodynamic interactions are negligible, the kinetics of domain growth exhibits a diffusive behavior [5]. On the other hand, motile particles with orientational order (such as bacteria, whose shape can be assumed as rod-like with no head-tail symmetry) phase separate too. Their intrinsic tendency to align each other [9], in presence of fluctuations in the local density, can induce phase separation [2]. By using a relatively simple model (already adopted to describe active polar liquid crystals [10]) in which the degree of order (namely the alignment among particles) is encoded in a vector field whose evolution is governed by advection-relaxation-like equations, the concentration of active material is described by using a scalar field governed by a Cahn-Hilliard-like equation and hydrodynamic interactions are described by the Navier-Stokes equation, we will elucidate how hydrodynamics affect domain coarsening and will show that, regardless the mechanisms responsible for generating fluid flows, phase separation is arrested. In particular we will show the physics of active phase separation for mixtures of active (namely contractile and extensile) particles at symmetric and off-symmetric concentration and for mixtures of active and passive particles.
References [1] S. Ramaswamy, Annu. Rev. Condens. Matt. Phys. 1, 323 (2010); M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Rev. Mod. Phys. 85, 1143 (2013). [2] V. Narayan, S. Ramaswamy, M. Menon, Science 317, 105 (2007). [3] H. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. E. Goldstein, H. Lowen, and J. M. Yeomans, Proc. Natl. Acad. Sci. USA 109, 14308 (2012). [4] I. Buttinoni, J. Bialk? F. Kummel, H. Lowen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013); R. Wittkowski, A. Tiribocchi, J. Stenhammar, R. J. Allen, D. Marenduzzo and M. Cates, Nature Comm. 6, 5420 (2014); G. S. Redner, M. F. Hagan, and A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013). [5] J. Stenhammar, A. Tiribocchi, R. J. Allen, D. Maren-duzzo, M. E. Cates, Phys. Rev. Lett. 111, 145702 (2013); J. Stenhammar, R. J. Allen, D. Marenduzzo, M. E. Cates, Soft Matter 10, 1489 (2014) [6] J. Tailleur and M. E. Cates, Phys. Rev. Lett. 100, 218103 (2008). [7] G. S. Redner, M. F. Hagan, and A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013).; Y. Fily and M. C. Marchetti, Phys. Rev. Lett. 108, 235702 (2012). [8] A. Suma, G. Gonnella, D. Marenduzzo, E. Orlandini, Europhys. Lett. 108,56004 (2014). [9] J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995); S. Ramaswamy, R. Simha, and J. Toner, Europhys. Lett. 62, 196 (2003); A. Baskaran and M. C. Marchetti, Phys. Rev. Lett. 101, 268101 (2008). [10] E. Tjhung, D. Marenduzzo, M. E. Cates, Soft Matter 7 , 7453 (2011); E. Tjhung, D. Marenduzzo, M. E. Cates Proc. Natl. Acad. Sci. USA 109,12381(2012); E. Tjhung, A. Tiribocchi, D. Marenduzzo, M. E. Cates, Nature Comm. 6, 5420 (2015).

A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The consistency equation characterising the monomer density is studied in the phasespace (h, J), where h tunes the monomer potential and J the attractive potential. The number of monomers fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.

We immediately perceive beauty, although the criteria involved in this complex process are unknown in general. Focusing on the case of facial attractiveness, we pose some questions from a complex-systems perspective. What are the relevant features, (shapes, distances, or proportions), determining attractiveness, and to what extent their mutual correlations matter? Can beautiful faces be characterised as local maxima in some space (so that local variations lower their attractiveness)? To what extent our preferences are universal in such a space? We propose an experimental scheme leading quantitative answers to these questions.

Competition for limited molecular resources (nutrients, ribosomes, RNAp, tRNA, etc.) can influence cellular functions up to the highest levels. Here we review recent modeling work aimed at characterizing how gene expression is affected by competition for small regulatory RNAs. We shall argue that control through competition may outperform direct transcriptional regulation in reliably generating expression profiles, and that the effects of competition can build-up to establish system-level regulatory modes carrying out distinct functions, from the buffering of gene expression noise to the selective activation of specific pathways. In this light, the RNA-mediated post-transcriptional regulatory layer appears to orchestrate a flexible collective control over gene expression, contributing crucially both to the fine tuning of expression levels and to large-scale re-organizations of the transcriptome as required e.g. for differentiation.

We use a micro-canonical Wang-Landau technique to study the equilibrium properties of a single flexible homopolymer where consecutive monomers are represented by impenetrable hard spherical beads tangential to each other, and non-consecutive monomers interact via a square-well potential. To mimic the characteristics of a protein-like system, the model is then refined in two different directions. Firstly, by allowing partial overlap between consecutive beads, we break the spherical symmetry and thus provide a severe constraint on the possible conformations of the chain. Alternatively, we introduce additional spherical beads at specific positions in the direction normal to the backbone, to represent the steric hindrance of the side chains in real proteins. Finally, we consider also a combination of these two ingredients. In all three systems, we obtain the full phase diagram in the temperature-interaction range plane and find the presence of helicoidal structures at low temperatures in the intermediate range of interactions. The effect of the range of the square-well attraction is highlighted, and shown to play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.
Reference: T. Skrbic, A. Badasyan, T.X. Hoang, R. Podgornik and A. Giacometti Soft Matter. 2016 May 25;12(21):4783-93. doi: 10.1039/c6sm00542j.