Long-range interacting systems include neutral plasma, gravitational systems, two-dimensional and geophysical fluid models. We consider long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic fields. The system reaches stationary states where the external forces balance the dissipation on average. These states do not respect detailed balance and support non-vanishing fluxes of conserved quantities. I will discuss how the classical tools of kinetic theory can be extended to describe these systems when the large structures evolve slowly. Comparisons with numerical simulations in a case of a particularly simple system, show an excellent agreement between the theory and simulations. I will also discuss some results on non-equilibrium phase transitions that we numerically observed in these systems.

Long-range interacting systems, while relaxing to equilibrium, often get trapped in long- lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system in a quasistationary state (QSS) responds to an external perturbation. We consider a long-range system that evolves under deterministic Hamilton dynamics. The perturbation is taken to couple to the canonical coordinates of the individual constituents. Our study is based on analyzing the Vlasov equation for the single-particle phase space distribution. The QSS represents stable sta- tionary solution of the Vlasov equation in the absence of the external perturbation. In the presence of small perturbation, we linearize the perturbed Vlasov equation about the QSS to obtain a formal expression for the response observed in a single-particle dynami- cal quantity. We apply our analysis to a paradigmatic model, the Hamiltonian mean-field model, that involves particles moving on a circle under Hamilton dynamics. Our prediction for the response of some representative QSSs in this model (the water-bag QSS and the Gaussian QSS) is found to be in good agreement with N-particle simulations for large N.

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. We present empirical and theoretical evidence for a new macro-ecological pattern related to the distributions of local species persistence times, defined as the timespans between local colonization and extinctions in a given geographic region, and empirically estimated from local observations of species' presence- absence time series. Empirical distributions exhibit power-law scaling limited by a cut-off determined by the rate of emergence of new species. The scaling exponents depend solely on the structure of the spatial interaction network, regardless of the details of the ecological interactions, suggesting similarities between ecosystem dynamics and critical systems in physics. We also present generalize and solve analytically a related sampling problem. The framework developed here also allows to link the cut-off timescale with the spatial scale of analysis, and the persistence-time distribution to the species-area relationship. We conclude that the inherent coherence obtained between spatial and temporal macro-ecological patterns points at a seemingly general feature of the dynamical evolution of ecosystems.

There has been a considerable effort to understand and quantify the spatial distribution of species across different ecosystems. The Species Area Relationship (SAR), which relates the area with the number of species that it supports, is probably one of the most studied quantity in ecology. We introduce a simple phenomenological model based on Poisson cluster processes which allows us to derive an analytical expression for the SAR which reproduces the empirical behavior as sample area increases from local to continental scales, explaining how it can be understood in terms of simple geometric arguments. Within our framework we also obtain interesting prediction for other spatial ecological quantities.

Joining two different spectral methods, we are allowed to arrange the promoters of a given species in equivalence classes, each of which is found to be characterized by particular regular subsequences.

We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The dissipation due to the coupling of the complex to a reaction center is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, the maximum efficiency in energy transport is achieved at the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. This approach allows one to study various couplings to the reaction center. We show that the maximal efficiency at room temperature is sensitive to the coupling of the system to the reaction center.

General properties are presented for transfer matrices originating from the eigenvalue equation of Hamiltonian matrices with band structure (for example: tight binding model for crystals, Anderson model for localization). Their eigenvalues are linked by a spectral identity. A general statement by Demko, Moss and Smith on the exponential decay of matrix elements of the inverse of a band matrix, translates into statements on the matrix elements and singular values of transfer matrices.

Quantum Monte Carlo (QMC) techniques have become very powerful tools providing deep insight into the physical behaviour of strongly correlated systems. As far as equilibrium properties of bosonic systems are concerned, nowadays QMC simulations are able to provide "exact" predictions. Ordinary matter is made of fermions and dynamical properties hide plenty of physical informations: if one could ever achieve the accuracy that is now currently available for the equilibrium behavior of bosonic models, the importance for Condensed Matter Physics would be outstanding. For Fermi systems, it is very interesting to study approaches different from the traditional ones (fixed node), which may hopefully help in facing the severe challenge due to the famous sign problem. Here we address two novel methodologies to study dynamical properties of Fermi systems. One relies on bosonic imaginary-time correlation functions, providing fermionic eigenstates as excitations over the bosonic ground state in a bigger Hilbert space, not imposing quantum statistics [1,2]; such approach requires to pay the fee of inverting Laplace transform in ill-posed conditions. We have faced such a problem via the GIFT methodology [3]. Within this approach, we have studied the equation of state, the magnetic properties and the low energy excitations of two-dimensional 3He [2,4]. We have been able to extract for the first time the zero sound mode from ab-initio calculations, finding good agreement with experiments [5]. In principle this methodology provides "exact" results for energies and their derivatives; it gives access also to a variational estimation of dynamic structure factors. The main difficulty concernes the extrapolation to the thermodynamic limit. The second approach relies on a phaseless fermionic Auxiliary-Fields QMC algorithm [6]. This method is based on a random walk taking place in the Slater Determinants space, authomatically taking into account Fermi statistics; in a "Diffusion Monte Carlo" strategy, the sign approximation is translated into a non-local and somehow weaker condition, involving only the overlap of one Determinant on a given guiding function, resembling the typical importance sampling recypes. From a formal point of view the method relies on the Hubbard-Stratonovich transformation. We have preliminary results for dynamical properties of a three-dimensional jellium model.

References:
[1] G. Carleo, S. Moroni, F. Becca, and S. Baroni, Phys. Rev. B 83, 060411 (2011).
[2] M. Nava, E. Vitali, A. Motta, D.E. Galli, and S. Moroni, arXiv:1103.0915.
[3] E. Vitali, M. Rossi, L. Reatto, and D.E. Galli, Phys. Rev. B 82, 174510 (2010).
[4] M. Nava, D.E. Galli, S. Moroni, and E. Vitali, in preparation.
[5] H. Godfrin, M. Meschke, H.J. Lauter, A. Sultan, H.M. Bohm, E. Krotscheck, and M. Panholzer, Nature 483, 576 (2012).
[6] M. Suewattana, W. Purwanto, S. Zhang, H. Krakauer, and E.J. Walter, Phys. Rev. B 75, 245123 (2007).

Quantum transport is deeply influenced by interference. When considering excitation propagation through a quantum multi-body system, interference is determined by the spatial disposition of the components.
Notwithstanding, a clear link between structure and fast, efficient transport is still missing. Here, we present a complex network analysis of quantum transport to elucidate the relationship between efficiency and structural organisation. Our analysis reveals a well defined classification related to the dynamical behaviour.