arXiv subjects

Mauro Bologna

Publications and source records attributed to Mauro Bologna.

33 records · Page 2Linked to original sources

arXiv2013

Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic fluctuations with a given distribution $ψ(τ)$ of residence times in each velocity state. We obtain analytical solutions for the diffusion process in a generic external potential and for a generic statistics of residence times, including the non-ergodic regime in which the mean residence time diverges. We show that these analytical solutions are in agreement with numerical simulations.

cond-mat.dis-nn↗

arXiv2011

Transmission of Information between Complex Networks: 1/f-Resonance

We study the transport of information between two complex networks with similar properties. Both networks generate non-Poisson renewal fluctuations with a power-law spectrum 1/f^(3-μ), the case μ= 2 corresponding to ideal 1/f-noise. We denote by μ_S and μ_P the power-law indexes of the network "system" of interest S and the perturbing network P respectively. By adopting a generalized fluctuation-dissipation theorem (FDT) we show that the ideal condition of 1/f-noise for both networks corresponds to maximal information transport. We prove that to make the network S respond when μ_S < 2 we have to set the condition μ_P < 2. In the latter case, if μ_P < μ_S, the system S inherits the relaxation properties of the perturbing network. In the case where μ_P > 2, no response and no information transmission occurs in the long-time limit. We consider two possible generalizations of the fluctuation-dissipation theorem and show that both lead to maximal information transport in the condition of 1/f-noise.

cond-mat.stat-mech↗

arXiv2010

Asymptotic solution for first and second order integro-differential equations

This paper addresses the problem of finding an asymptotic solution for first and second order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of the paper is to go beyond the tauberian theorem in the case of integral-differential equations which are widely used by the scientific community. The results are applied to the convolute form of the Lindblad equation setting generic conditions on the kernel in such a way as to generate a positive definite density matrix, and show that the structure of the eigenvalues of the correspondent liouvillian operator plays a crucial role in determining the positivity of the density matrix.

cond-mat.stat-mech↗

arXiv2010

Beyond the Death of Linear Response: 1/f optimal information transport

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

cond-mat.stat-mech↗

arXiv2006

Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

The dynamical emergence (and subsequent intermittent breakdown) of collective behavior in complex systems is described as a non-Poisson renewal process, characterized by a waiting-time distribution density $ψ(τ)$ for the time intervals between successively recorded breakdowns. In the intermittent case $ψ(t)\sim t^{-μ}$, with complexity index $μ$. We show that two systems can exchange information through complexity matching and present theoretical and numerical calculations describing a system with complexity index $μ_{S}$ perturbed by a signal with complexity index $μ_{P}$. The analysis focuses on the non-ergodic (non-stationary) case $μ\leq 2$ showing that for $μ_{S}\geq μ_{P}$, the system $S$ statistically inherits the correlation function of the perturbation $P$. The condition $μ_{P}=μ_{S}$ is a resonant maximum for correlation information exchange.

cond-mat.stat-mech↗

arXiv2006

Response of Complex Systems to Complex Perturbations: Complexity Matching

We argue that complex systems, defined as non-Poisson renewal process, with complexity index $μ$, exchange information through complexity matching. We illustrate this property with detailed theoretical and numerical calculations describing a system with complexity index $μ_{S}$ perturbed by a signal with complexity index $μ_{P}$. We focus our attention on the case $1.5 \leq μ_S \leq 2$ and $1 \leq μ_{P} \leq 2$. We show that for $μ_{S} \geq μ_P$, the system S reproduces the perturbation, and the response intensity increases with increasing $μ_P$. The maximum intensity is realized by the matching condition $μ_P = μ_S$. For $μ_{P} > μ_{S}$ the response intensity dies out as $1/t^{μ_P-μ_S}$.

cond-mat.stat-mech↗

arXiv2006

Wavefront solution in extended quantum circuits with charge discreteness

A wavefront solution for quantum (capacitively coupled) transmission lines with charge discreteness (PRB {\bf 64}, 235309 (2001)) is proposed for the first time. The nonlinearity of the system becomes deeply related to charge discreteness. The wavefront velocity is found to depend on a step discontinuity on the (pseudo) flux variable, $f$, displaying allowed and forbidden regions (gaps), as a function of $f$. A preliminary study of the stability of the solutions is presented. The dual transmission line hamiltonian is proposed and finally, we find a connection with the (quantum) Toda lattice.

cond-mat.mes-hall↗

arXiv2006

Renewal aging and linear response

We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier work of other groups, and we find that aging may have the effect of annihilating any sign of coherent response to harmonic perturbation. We also derive the linear response using dynamic arguments and we find a coherent response, although with an intensity dying out very slowly. In the case of a step-like perturbation the dynamic arguments yield in the long-time limit a steady signal whose intensity may be significantly smaller than the phenomenological approach prediction.

cond-mat.stat-mech↗

arXiv2005

Linear response to perturbation of non-exponential renewal processes

We study the linear response of a two-state stochastic process, obeying renewal condition, by means of a stochastic rate equation equivalent to a master equation with infinite memory. We show that the condition of perennial aging makes the response to coherent perturbation vanish in the long-time limit.

cond-mat.stat-mech↗

arXiv2004

Aging and Rejuvenation with Fractional Derivatives

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2 >ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.

cond-mat.stat-mech↗

arXiv2002

Decoherence, wave function collapses and non-ordinary statistical mechanics

We consider a toy model of pointer interacting with a 1/2-spin system, whose $σ_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $σ_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation.

cond-mat.stat-mech↗

arXiv2001

Dynamic versus thermodynamic approach to non-canonical equilibrium

We study the dynamic and thermodynamic origin of non-canonical equilibria, and we discuss their connection with the generalized central limit theorem and the micro-canonical Boltzmann principle. We reach the conclusion that the zeroth law of thermodynamics and the Boltzmann principle are fulfilled thanks to an apparent fault turned into a benefit: the dynamic approach can only produce a truncated form of inverse power law equilibrium.

cond-mat.stat-mech↗

arXiv2000

Trajectory versus probability density entropy

We study the problem of entropy increase of the Bernoulli-shift map without recourse to the concept of trajectory and we discuss whether, and under which conditions if it does, the distribution density entropy coincides with the Kolmogorov-Sinai entropy, namely, with the trajectory entropy.

cond-mat.stat-mech↗

arXiv2000

Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^γ}{\partial x^γ}[P(x,t) ]^ν$. Exact time-dependent solutions are found for $ ν= \frac{2-γ}{1+ γ}$ ($-\infty<γ\leq 2$). By considering the long-distance {\it asymptotic} behavior of these solutions, a connection is established, namely $q=\frac{γ+3}{γ+1}$ ($0<γ\le 2$), with the solutions optimizing the nonextensive entropy characterized by index $q$ . Interestingly enough, this relation coincides with the one already known for Lévy-like superdiffusion (i.e., $ν=1$ and $0<γ\le 2$). Finally, for $(γ,ν)=(2, 0)$ we obtain $q=5/3$ which differs from the value $q=2$ corresponding to the $γ=2$ solutions available in the literature ($ν<1$ porous medium equation), thus exhibiting nonuniform convergence.

cond-mat.stat-mech↗

arXiv1999

The Levy diffusion as an effect of sporadic randomness

The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is present in the corresponding microscopic dynamics and (ii) that the consequent process of memory erasure is properly taken into account by the theoretical treatment.

cond-mat.stat-mech↗