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Search Results: 1 - 10 of 144441 matches for " F. Borgonovi "
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Classical statistical mechanics of a few-body interacting spin model
F. Borgonovi,F. M. Izrailev
Physics , 1999, DOI: 10.1103/PhysRevE.62.6475
Abstract: We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction is very strong. Specific attention is paid to classical analogs of the average shape of quantum eigenstates and "local density of states", which are very important in quantum chaology. Analytical predictions are then compared with numerical data.
Particle propagation in a random and quasiperiodic potential
F. Borgonovi,D. L. Shepelyansky
Physics , 1996, DOI: 10.1016/S0167-2789(97)00155-3
Abstract: We numerically investigate the Anderson transition in an effective dimension $d$ ($3 \leq d \leq 11$) for one particle propagation in a model random and quasiperiodic potential. The found critical exponents are different from the standard scaling picture. We discuss possible reasons for this difference.
Enhancement of magnetic anisotropy barrier in long range interacting spin systems
F. Borgonovi,G. L. Celardo
Physics , 2011, DOI: 10.1088/0953-8984/25/10/106006
Abstract: Magnetic materials are usually characterized by anisotropy energy barriers which dictate the time scale of the magnetization decay and consequently the magnetic stability of the sample. Here we present a unified description, which includes coherent rotation and nucleation, for the magnetization decay in generic anisotropic spin systems. In particular, we show that, in presence of long range exchange interaction, the anisotropy energy barrier grows as the volume of the particle for on site anisotropy, while it grows even faster than the volume for exchange anisotropy, with an anisotropy energy barrier proportional to $V^{2-\alpha/d}$, where $V$ is the particle volume, $\alpha \leq d $ is the range of interaction and $d$ is the embedding dimension. These results shows a relevant enhancement of the anisotropy energy barrier w.r.t. the short range case, where the anisotropy energy barrier grows as the particle cross sectional area for large particle size or large particle aspect ratio.
Dynamics of random dipoles : chaos {\it vs} ferromagnetism
F. Borgonovi,G. L. Celardo
Statistics , 2010, DOI: 10.1088/1742-5468/2010/05/P05013
Abstract: The microcanonical dynamics of an ensemble of random magnetic dipoles in a needle has been investigated. Analyzing magnetic reversal times, a transition between a chaotic paramagnetic phase and an integrable ferromagnetic phase has been numerically found. In particular, a simple criterium for transition has been formulated. Close to the transition point the statistics of average magnetic reversal times and fluctuations have been studied and critical exponents numerically given.
Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model
L. Spadafora,G. P. Berman,F. Borgonovi
Quantitative Finance , 2010, DOI: 10.1140/epjb/e2010-10305-8
Abstract: Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes (BS) expression with volatility in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile.
Do your volatility smiles take care of extreme events?
L. Spadafora,G. P. Berman,F. Borgonovi
Quantitative Finance , 2010,
Abstract: In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is possible to get a new fitting procedure of the volatility smile that considers also the exponential decay of the real PDF of returns observed in the financial markets. Our study finds application in the Risk Management activities where the tails characterization of financial returns PDF has a central role for the risk estimation.
Chaos and statistical relaxation in quantum systems of interacting particles
L. F. Santos,F. Borgonovi,F. M. Izrailev
Physics , 2011, DOI: 10.1103/PhysRevLett.108.094102
Abstract: We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength function. We show that although the fluctuations of energy levels in integrable and non-integrable systems are principally different, global properties of the eigenstates may be quite similar, provided the interaction between particles exceeds some critical value. In this case the quench dynamics can be described analytically, demonstrating the universal statistical relaxation of the systems irrespectively of whether they are integrable or not.
Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
L. F. Santos,F. Borgonovi,F. M. Izrailev
Physics , 2011, DOI: 10.1103/PhysRevE.85.036209
Abstract: We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins-1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasi-particles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation process following a quench is very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and non-integrable systems.
Irregular Dynamics in a One-Dimensional Bose System
G. P. Berman,F. Borgonovi,F. M. Izrailev,A. Smerzi
Physics , 2003, DOI: 10.1103/PhysRevLett.92.030404
Abstract: We study many-body quantum dynamics of $\delta$-interacting bosons confined in a one-dimensional ring. Main attention is payed to the transition from the mean-field to Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wavefunction and the momentum distribution depend on time for a weak and strong interactions. We show that the transition from regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.
Chaos and Thermalization in a Dynamical Model of Two Interacting Particles
F. Borgonovi,I. Guarneri,F. M. Izrailev,G. Casati
Physics , 1997, DOI: 10.1016/S0375-9601(98)00545-3
Abstract: A quantum dynamical model of two interacting spins, with chaotic and regular components, is investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close agreement with the Bose-Einstein distribution despite the small number of particles ($n=2$). However, the corresponding temperature differs from that derived from the standard Canonical Ensemble. On the other side, an acceptable agreement with the latter is restored by artificially randomizing the model. Different definitions of temperature are then discussed and compared .
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