We have numerically investigated by using Brownian dynamics, semiflexible polymers confined in a plane in two cases: under an external force for a tethered chain and in shear flow for a free one. Such situations are relevant for adsorbed biological filaments. Our results confirm experimental results and extend earlier theoretical predictions.

The dynamics of sparse networks is investigated both at the microscopic and macroscopic level, upon varying the connectivity. In all cases (chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neuron models), we find that a few tens of random connections are sufficient to sustain a nontrivial (and possibly irregular) collective dynamics. At the same time, the microscopic evolution turns out to be extensive, both in the presence and absence of a macroscopic evolution. This result is quite remarkable, considered the non-additivity of the underlying dynamical rule.

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest) –regardless of the species they belong to– have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species while treating the dynamics in a species symmetric manner. We demonstrate that the dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.

Population models, such as those for plankton dynamics, are often based on a mean-field approximation of individual behaviors. A weakly stable mean-field configuration, however, can be destabilized by demographic noise. In certain cases, such destabilization persists even in the thermodynamic limit. It is shown how this effect can be exploited, in a simple predator-prey model, to produce behaviors similar to algal blooms.

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The possibility of inducing domain-wall (DW) motion in magnetic nanowires by means of spin polarised electric currents has recently renewed theoretical interest in this field. The problem is usually modelled on a micro-magnetic approach, but ignoring any thermal fluctuations. However, some relevant experimental facts - like the correct order of magnitude of the critical current needed for DW motion - still lack satisfactory explanations. We thus developed a general theoretical framework, which highlights the crucial role played by thermal fluctuations at the centre of DWs. The latter qualitatively and quantitatively accounts for a variety of problems relating to DWs at finite temperatures. Examples are the shrinking of magnetic domains observed in Fe ultra-thin films on Cu(001) substrates with increasing temperature, the inverse symmetry breaking in ultra-thin films and the renormalisation of the critical current for domain- wall motion at finite temperatures.

An effective one-dimensional hopping model can be realized in several systems, such as spin chains, arrays of quantum dots or optical lattices. Each site of the array can be thought of as a `qubit', i.e. an object endowed with a 2-dimensional Hilbert space of states, and the natural dynamics of such an open chain of qubits can be exploited for transferring a quantum state between its ends, a task which is required for connecting registers in a quantum computer. Indeed, assuming that the first qubit is initially in a given state, the purpose of state transfer is that the dynamics of the chain leads at some time the same state to belong to the qubit sitting on the opposite end.
In a uniform chain (with uniform hopping amplitudes) the quantum-transfer process is found to be impossible due the effect of dispersion. It is known that perfect transmission can occur if the hopping amplitudes are properly modulated along the channel; however, such an engineered setup is not likely to be realizable in a lab.
Therefore we consider a chain with uniform hopping amplitudes and just allow the two extremal pairs of them to be weaker. Surprisingly, provided that the extremal couplings have suitable optimal values depending on the channel length, our setup gives an extremely high transfer quality, with average fidelity larger that 0.99 even in the limit of an infinitely long channel. The transmission time is ballistic and the quality of quantum transfer keeps being high in a large neighborhood of the optimal values so there is no need to finely tune the extremal hopping amplitudes in an experiment.

Le applicazioni degli atomi ultrafreddi, in diversi settori della fisica, sono in continua crescita. Ciò è dovuto alla grande versatilità che questi sistemi fisici offrono. L'alto grado di controllo con cui essi possono essere "preparati", le nuove possibilità di osservazione (in situ) sviluppate, ed il fatto che la fisica che sta alla loro base consenta di interpolare tra regimi dinamici che vanno da quelli più fortemente quantistici a quelli classici, li rendono dei sistemi fisici "speciali". Oggigiorno i gas di atomi ultrafreddi trovano applicazione nell'ambito dell'informazione quantistica, sono stati proposti come sistemi per realizzare simulatori quantistici, per esempio di teorie di campo relativistiche. Nel presente intervento vedremo come condensati in reticoli ottici e nel regime superfluido, possano essere utilizzati nell'ambito della meccanica statistica per realizzare stati dinamici localizzati ("breathers") e stati termodinamici a temperature negative. In particolare vedremo che l'equazione non lineare di Schrödinger discretizzata, che descrive appunto la dinamica nel regime superfluido di condensati in un reticolo ottico, presenta una regione dei parametri dove tale sistema evolve verso uno stato caratterizzato da una densità finita di "breathers" e una temperatura negativa. Tale stato è metastabile ma converge verso quello di equilibrio su scale di tempo astronomiche. Stati stazionari a temperatura negativa sono sperimentalmente accessibili sfruttando meccanismi di dissipazione, o tramite un'espansione libera di pacchetti inizialmente a temperatura positiva.

S. Iubini, R. Franzosi, R. Livi, G.-L. Oppo and A. Politi, "Negative Temperature States in the Discrete Nonlinear Schroedinger Equation", in preparazione.
R. Franzosi, "Geometric microcanonical thermodynamics for systems with first integrals", Phys. Rev. E 85, 050101 (2012).
R. Franzosi, R. Livi, G-L. Oppo, and A Politi, "Discrete Breathers in Bose-Einstein Condensates", Nonlinearity 24, R89 (2011).
R. Franzosi, "Microcanonical entropy and dynamical measure of temperature for systems with two first integrals", J. Stat. Phys. (2011) 143: 824-830.
R. Livi, R. Franzosi and G.-L. Oppo, "Selflocalization of Bose-Einstein condensates in optical lattices via boundary dissipation", Phys. Rev. Lett. 97, 060401 (2006).

We have developed a parallel GPU-based Monte-Carlo algorithm devoted to the analysis of continuous spin models in disordered graphs. This tool facilitates the study of the critical behaviour of the XY model on a Levy graph, such that the bond probability decays as a power, rho, of the distance between bonds with respect to their position in a given (short-range) lattice. Varying rho from infinity to zero, the Levy graph interpolates between the lattice and the uncorrelated (Erdos-Rany) graph. Renormalization group arguments allow to define three regimes of rho in correspondence with different critical behaviours of the model: for sufficiently low rho the model presents a phase transition of the mean-field type, whether for large values of rho the transition is supposed to belong to the Kosterlitz-Thouless universality class. We provide numerical support of these results, which are in agreement with previous studies of the XY model in complex topologies (Cassi, Phys. Rev. Lett. 68 3631 (1992)). Our research is motivated by the study of continuous spin models with disordered, long-range interactions, relevant in the statistical description of modes in random lasers (Conti and Leuzzi Phys. Rev. E 83 134204 (2011)).