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We study the motion of an electric excitation between the ferroelectric (FE) and the ferromagnetic (FM) components of a MultiFerroic (MF) composite material by analysing the transfer of energy from the FE side to the FM one. The transmission process of the electric excitation, which has an envelope soliton shape, is studied for a one-dimensional model of the barium titanate/iron (BaTiO3/Fe) composite. From the transmission spectrum, we determine the most favourable range of the values of the amplitude and of the width of the initial excitation for the transmission of the FE energy to the FM part of the MF material. From the numerical analysis, it is shown that the position in which we excite the FE component strongly impacts on the solitary wave dynamics. We have also realised that, for some initial positions and suitable range of values of the amplitude and width of the excitation of the polarization, we get a stationary localised magnetic excitation in the FM part of the MF material that lasts for a long time. Such a phenomenon, which originates from a curvilinear trajectory of the incoming excitation is promising enough for the implementation of non-volatile memories based on MF composite materials.

This chapter begins with a rapid introduction to the definition and construction of the statistical ensembles, following the lines that are usually offered in the basics courses on statistical mechanics. The reader is assumed to be already acquainted with thermodynamics and basic statistical mechanics, but the introduction is self-contained. It is then shown that with short-range interactions the ensembles are physically equivalent, even in the presence of phase transitions. This is done by introducing the notions of concave functions, of stable and tempered potentials, and the Legendre-Fenchel transform of thermodynamic functions. The concavity of the entropy is at the basis of ensemble equivalence. Finally, the concepts of microstate and macrostate are analysed; they are very important for the study of ensemble equivalence or inequivalence in long-range systems.

In this Chapter the statistical mechanics theory of long-range interactions is applied to hydrodynamics problems. The Euler equation is derived as a limiting case of the two dimensional Navier-Stokes equation for incompressible fluids. A logarithmic coupling between distant vortices is found, an observation which points to the long-range character of the interactions. The Onsager point vortex model is then introduced and its statistical mechanics treatment reviewed. Moreover, the Robert-Sommeria-Miller theory for the 2D Euler equation is discussed. Finally, the quasi-geostrophic model is presented and a statistical mechanics theory developed to explain the formation of coherent structures in geophysical fluid dynamic (as seen in e.g. planets’ atmosphere and oceans).

This chapter opens with the notion of stable interaction in quantum systems, somewhat different from classical systems. It is shown that an unstable classical system can become stable when treated quantum mechanically. The remaining of the chapter is devoted to a brief survey of the main results concerning the stability of Coulomb systems. Explicit evaluations of the total energy show that the exclusion principle is essential for their stability. The final part of the chapter deals with the thermodynamic limit of globally neutral Coulomb systems. The limit exists in spite of the long-range character of the interaction, and contrary to the stability property, the existence of the limit does not require quantum mechanics, being valid also in classical Coulomb systems.

This chapter deals with the peculiarities that are present in the statistical mechanics treatment and in the equilibrium properties of system with long-range interactions. In dimension d they are characterized at large distance r by a decay slower than 1/rd. The important concepts of additivity and extensivity are analysed. It is shown that long-range systems are intrinsically nonadditive: the interaction energy between macroscopic subsystems is not negligible with respect to the total energy of the system. This can often give rise to ensemble inequivalence. In particular, also with the help of a simple model, the possibility to have convex regions in the entropy is demonstrated. These regions can cause a negative specific heat in the microcanonical ensemble, while in the canonical ensemble this quantity is always positive. A negative magnetic susceptibility is possible, as well, in the microcanonical ensemble.

This chapter is devoted to the study of a very useful mathematical tool for the computation of the entropy in long-range systems. The method is based on large deviation theory, and it is very well suited for purely mean-field systems, in which the interaction does not decay at all with the distance. However, it can be applied also to the other long-range systems. The three steps of the method are described: the expression of the energy in terms of global variables, the mean fields; the computation of the entropy of the macrostates, defined by given values of the mean fields; the computation of the entropy, maximizing on the macrostates. Finally, the method is illustrated by applying it to two simple models.

This chapter describes the derivation of kinetic equations for long-range systems. This is done on the basis of the Klimontovich equation, following an approach which is alternative but equivalent to the BBGKY hierarchy. After the derivation of the Klimontovich equation, that mathematically is equivalent to the full equations of motion, the Vlasov and the Lenard-Balescu equations are obtained. The former approximates the interaction in the system with a mean-field force, and for this it is considered a collisionless approximation; the latter takes into account the collisional corrections to the Vlasov equation. In the last section, with the background of the general theory presented in chapter 2 and in this chapter, there is a description of the physical meaning of the Kac’s prescription, often used as a convenient tool for the study of long-range systems.

In this Chapter the equilibrium and out-of-equilibrium dynamics of self-gravitating systems is discussed. The case of 1D planar systems is in particular investigated and the equilibrium statistical mechanics solution presented in some details. Long-lived quasi stationary states are found and successfully explained with the Lynden Bell statistical mechanics theory. The problem of structure formation in an expanding Universe is also introduced. The classical Vlasov-Poisson model and the adhesion approximation are recovered starting from relevant general relativity setting. In one dimension an exact event-driven scheme can be implemented which enables one to efficiently track the evolution of the system. Different simulations strategies in 3D are shortly discussed.

In this Chapter the statistical mechanics of charged particles subject to Coulomb interactions is discussed. The relevant physical parameters are introduced which enable one to classify the different systems under inspection. The classification is drawn for the reference case of globally neutral systems, with two species of charges, one positive and the other negative, equal in magnitude. The case of strongly interacting plasma is discussed and the equilibrium properties analyzed in the framework of the Debye-Huckel theory. In the final part of the Chapter, degenerate electron systems and the concept of Wigner crystal are reviewed.

This chapter aims at showing that the features occurring in mean-field models, described in the previous chapters, can be found also in the other long-range systems. The first four sections are dedicated to generalizations of the models of chapter 4, in which either the mean-field interaction is augmented with a nearest neighbour interaction, or it is replaced by a slowly decaying interaction. It is shown that the long-range characteristics of the associated mean-field models are preserved, and in addition ensemble inequivalence, microcanonical negative specific heat and ergodicity breaking are induced in some cases. The final section introduces the dipolar interaction, a marginal long-range system. Dipolar systems are treated in details in chapter 15, and in this chapter few relevant properties are presented, focussing in particular on elongated ferromagnets and on ergodicity breaking.

In this Chapter an alternative derivation of the self-consistent Vlasov-Maxwell equations for wave-particles interaction is given. The analysis is carried out under a rigorous Hamiltonian framework and targeted to modeling the dynamics of the Free Electron Laser. A universal one dimensional Hamiltonian is eventually recovered which proves of interest in all domains of applications where particles and waves are mutually interacting. The same Hamiltonian is obtained via an heuristic derivation that moves from the concept of Langmuir waves, as introduced in the preceding Chapter. The physics of Free Electron Laser is then discussed and the large deviation method applied to determine the intensity of the laser at equilibrium. The Lynden-Bell theory returns adequate predictions for the average laser intensity and bunching degree in the quasi stationary regime. Finally, the analogies between Free Electron Laser, plasma and Travelling Wave Tubes are discussed.

In this Chapter the peculiar out-of-equilibrium behaviour of systems subject to long-range coupling is discussed. The existence of the so called quasi stationary states (QSS) is numerically demonstrated using the Hamiltonian Mean Field model as a reference case study. The process of relaxation of a test particle in contact with a thermal reservoir is studied and shown to yield a Fokker Planck equation at the leading order of a system size expansion. The emergence of QSS is then analyzed in terms of attractive Vlasov equilibria. The statistical maximum entropy theory pioneered by Lynden-Bell allows one to explicitly calculate the equilibrium solution of the Vlasov equation and quantitatively explain the QSS features. The method is successfully applied to the HMF model and shown to predict out-of-equilibrium phase transitions from magnetized to homogeneous phases. The core halo solution, an alternative approach to the QSS, is finally reviewed.

In this chapter the theory and the tools described in the previous two chapters are applied to several simple mean-field models, computing both the microcanonical and the canonical partition functions. It is shown that in the first model, the Hamiltonian Mean Field model, ensembles are equivalent, while in the others, the generalized XY model, the phi-4 model and the Self-Gravitating Ring model, ensembles are nonequivalent, with the occurrence of negative specific heat or negative susceptibility in the microcanonical ensemble. A feature that can appear in long-range systems is presented, namely the occurrence of ergodicity breaking. Mentioned in chapter 2 as a consequence of the possibility to have not connected regions in the thermodynamic parameter space, it is here explicitly shown in the XY model. Ergodicity breaking clearly manifests itself in the dynamical behaviour.

In this Chapter a short introduction to the physics of hot plasma is given. The concepts of Debye shielding and quasi-neutrality are in particular discussed. The Vlasov-Maxwell equations are derived following the Klimontovich approach. Working within the collisionless Vlasov picture, the case of electrostatic waves is presented and the phenomenon of linear Landau damping reviewed in some details. The non linear regime of the wave-particles interaction is also briefly analyzed. Explicit reference is made to the collective BGK and Case-van Kampen modes.

This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distance. In particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples. However, it has become clear that long-range interactions are more common than previously thought. This has stimulated a growing interest in the study of long-range interacting systems, which has led to a much better understanding of the many peculiarities in their behaviour. The seed of all particular features of these systems, both at equilibrium and out-of-equilibrium, is the lack of additivity. It is now well understood that this does not prevent a statistical mechanics treatment. However, it does require a more in-depth study of the thermodynamic limit and of all related theoretical concepts. A satisfactory understanding of properties generally considered as oddities only a couple of decades ago has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion, etc. The first two parts describe the theoretical and computational instruments needed for addressing the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to discussing the applications of such techniques to the most relevant examples of long-range systems. The only prerequisite is a basic course in statistical mechanics.

We investigated experimentally and theoretically the valence-band structure of wurtzite InP nanowires. The wurtzite phase, which usually is not stable for III-V phosphide compounds, has been observed in InP nanowires. We present results on the electronic properties of these nanowires using the photoluminescence excitation technique. Spectra from an ensemble of nanowires show three clear absorption edges separated by 44 meV and 143 meV, respectively. The band edges are attributed to excitonic absorptions involving three distinct valence-bands labeled: A, B, and C. Theoretical results based on “ab initio” calculation gives corresponding valence-band energy separations of 50 meV and 200 meV, respectively, which are in good agreement with the experimental results.

In the study of cellular automata (CA) there is often the problem of understanding if the observed spatio-temporal behaviour may be significant from a physical point of view. In this contribution we compare the behaviour of an experimental system — a fluid in an annular cell heated from below — with that of suitably chosen probabilistic CA rules. This has been made possible by the reduction of the space-time evolution of the experimental system to a symbolic dynamics.

RIASSUNTO Vengono descritte due nuove specie di Anfipodi (Crustacea) provenienti dalle acque freatiche di due diverse localita africane. Afridiella messanai n. sp., raccolta in un pozzo a Uebhao (Somalia meridionale) si differenzia dalle altre due specie sinora note, soprattutto nel palpo mandibolare, nella forma dei gnatopodi e nella diversa spinulazione degli uropodi III. Il ritrovamento di questa specie ci costringe a ridimensionare le differenze tra Afridiella e Bogidiella. In particolare perdono importanza il palpo mandibolare, il callo laterale delle mandibole ed i gnatopodi. Maghrebidiella maroccana n. gen. n. sp., raccolta in Marocco, in un pozzo situato a poca distanza da Marrakech, si distingue dagli altri generi noti di Bogidiellidi per i seguenti caratteri: forma dell'epistoma e del palpo mandibolare, processo molare non triturativo, assenza di setole sul lobo interno delle mascelle I, pleopodi con esopodite allungato e presenza di 3 spine sulla faccia esterna del peduncolo degli uropodi I. Ma...

We argue that it is possible to use an alternative resummation technique of QCD perturbative expansion, introducing a physically sensible infrared parameter. The application of this procedure to large p ⊥ distribution for the process pp→π 0 X is studied.

We study the distribution of the resistance fluctuations of biased resistor networks in nonequilibrium steady states. The stationary conditions arise from the competition between two stochastic and biased processes of breaking and recovery of the elementary resistors. The fluctuations of the network resistance are calculated by Monte Carlo simulations which are performed for different values of the applied current, for networks of different size and shape and by considering different levels of intrinsic disorder. The distribution of the resistance fluctuations generally exhibits relevant deviations from Gaussianity, in particular when the current approaches the threshold of electrical breakdown. For two-dimensional systems we have shown that this non-Gaussianity is in general related to finite size effects, thus it vanishes in the thermodynamic limit, with the remarkable exception of highly disordered networks. For these systems, close to the critical point of the conductor-insulator transition, non-Gaussianity persists in the large size limit and it is well described by the universal Bramwell-Holdsworth-Pinton distribution. In particular, here we analyze the role of the shape of the network on the distribution of the resistance fluctuations. Precisely, we consider quasi-one-dimensional networks elongated along the direction of the applied current or trasversal to it. A significant anisotropy is found for the properties of the distribution. These results apply to conducting thin films or wires with granular structure stressed by high current densities., 8 pages, 4 figures. Invited talk at the 18-th International Conference on Noise and Fluctuations, 19-23 September 2005, Salamanca

We study the distribution of resistance fluctuations of conducting thin films with different levels of internal disorder. The film is modeled as a resistor network in a steady state determined by the competition between two biased processes, breaking and recovery of the elementary resistors. The fluctuations of the film resistance are calculated by Monte Carlo simulations which are performed under different bias conditions, from the linear regime up to the threshold for electrical breakdown. Depending on the value of the external current, on the level of disorder and on the size of the system, the distribution of the resistance fluctuations can exhibit significant deviations from Gaussianity. As a general trend, a size dependent, non universal distribution is found for systems with low and intermediate disorder. However, for strongly disordered systems, close to the critical point of the conductor-insulator transition, the non-Gaussianity persists when the size is increased and the distribution of resistance fluctuations is well described by the universal Bramwell-Holdsworth-Pinton distribution., Comment: 6 pages, 7 figures, 2th. Int. SPIE Symp. on Fluctuations and Noise, Maspalomas (Spain) 25-28 May, 2004

This corrects the article DOI: 10.1103/PhysRevE.100.052135.