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arXiv2008

Exact results and new insights for models defined over small-world networks. First and second order phase transitions. I: General result

We present, as a very general method, an effective field theory to analyze models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it gives the exact critical behavior and the exact critical surfaces and percolation thresholds, and provide a clear and immediate (also in terms of calculation) insight of the physics. The underlying structure of the non random part of the model, i.e., the set of spins staying in a given lattice L_0 of dimension d_0 and interacting through a fixed coupling J_0, is exactly taken into account. When J_0\geq 0, the small-world effect gives rise to the known fact that a second order phase transition takes place, independently of the dimension d_0 and of the added random connectivity c. However, when J_0<0, a completely different scenario emerges where, besides a spin glass transition, multiple first- and second-order phase transitions may take place.

cond-mat.dis-nn↗
arXiv2008

Strong Localization of Positive Charge in DNA

Microscopic mechanisms of positive charge transfer in DNA remain unclear. A quantum state of electron hole in DNA is determined by the competition of a pi-stacking interaction $b$ smearing a charge between different base pairs and interaction $λ$ with the local environment which attempts to trap charge. To determine which interaction dominates we investigated charge quantum states in various $(GC)_{n}$ sequences choosing DNA parameters satisfying experimental data for the balance of charge transfer rates $G^{+} \leftrightarrow G_{n}^{+}$, $n=2,3$ \cite{FredMain}. We show that experimental data can be consistent with theory only under an assumption $b\ll λ$ meaning that charge is typically localized within a single $G$ site. Consequently any DNA sequence including the one consisting of identical base pairs behaves more like an insulating material than a molecular conductor.

cond-mat.soft↗
arXiv2008

Exact results and new insights for models defined over small world networks. First and second order phase transitions. II: Applications

We apply a novel method (presented in part I) to solve several small-world models for which the method can be applied analytically: the Viana-Bray model (which can be seen as a 0 or infinite dimensional small-world model), the one-dimensional chain small-world model, and the small-world spherical model in generic dimension. In particular, we analyze in detail the one-dimensional chain small-world model with negative short-range coupling showing that in this case, besides a second-order spin glass phase transition, there are two critical temperatures corresponding to first- or second-order phase transitions.

cond-mat.dis-nn↗
arXiv2008

Numerical studies of Casimir interactions

We study numerically the Casimir interaction between dielectrics in both two and three dimensions. We demonstrate how sparse matrix factorizations enable one to study torsional interactions in three dimensions. In two dimensions we study the full cross-over between non-retarded and retarded interactions as a function of separation. We use constrained factorizations in order to measure the interaction of a particle with a rough dielectric surface and compare with a scaling argument.

quant-ph↗
arXiv2008

Critical Exponents from Field Theory: New Evaluation

We present new evaluation of the critical exponents of O(n)- symmetric ϕ^4 theory from the field theoretical renormalization group, based on the new algorithm for summing divergent series. The central values practically coincide with those by Le Guillou and Zinn-Justin (1980) but their uncertainty is essentially smaller.

cond-mat.stat-mech↗
arXiv2008

Time-fractional derivatives in relaxation processes: a tutorial survey

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classical theory of linear viscoelasticity, we contrast these two types of fractional derivatives in their ability to take into account initial conditions in the constitutive equations of fractional order. We also provide historical notes on the origins of the Caputo derivative and on the use of fractional calculus in viscoelasticity.

math-ph↗
arXiv2008

Optimal design of composite granular protectors

We employ an evolutionary algorithm to investigate the optimal design of composite protectors using one-dimensional granular chains composed of beads of various sizes, masses, and stiffnesses. We define a fitness function using the maximum force transmitted from the protector to a "wall" that represents the body to be protected and accordingly optimize the {topology} (arrangement), {size}, and {material} of the chain. We obtain optimally randomized granular protectors characterized by high-energy equipartition and the transformation of incident waves into interacting solitary pulses. We consistently observe that the pulses traveling to the wall combine to form an extended (long-wavelength), small-amplitude pulse.

cond-mat.mtrl-sci↗
arXiv2010

Shear transformation zone analysis of shear reversal during granular flow

Experimental measurements of the onset of granular flow are directly compared to predictions of the "shear transformation zone" (STZ) theory of amorphous plasticity. The STZ equations make it possible, on a coarse grained level, to incorporate the anisotropy of the particle contact network and its dynamic evolution including changes in the contact network direction under shear reversal. The STZ theory and experiment show qualitative agreement in the transient and steady state shear forces and velocity profiles during the start of shear and shear reversal.

cond-mat.stat-mech↗
arXiv2008

Adsorption-Desorption Kinetics: A Review of a Classical Problem

In this work we have analyzed the adsorption-desorption kinetics in the framework of the lattice gas model. We have shown that the coefficients representing the transition probabilities must be carefully chosen even when they fulfill the principle of detailed balance, otherwise the observables arising from the kinetics present anomalous behavior. We have demonstrated that when the adsorption $A_i$ and desorption $D_i$ coefficients are linearly related through a parameter $γ$, there are values of lateral interaction, $V$, that lead to bad behavior in the kinetics. We have shown a phase diagram for the allowed values of $V$ and $γ$, concluding that detailed balance does not guarantee a correct physical behavior of the observables obtained from the rate equations like adsorption isotherms, sticking coefficients and thermal desorption spectra. Alternatively, we have introduced a description of the adsorption-desorption processes based in a simple but consistent energetic argument that leads to a correct behavior of the observables without physical inconsistencies.

cond-mat.stat-mech↗
arXiv2008

Genus Distributions For Extended Matrix Models Of RNA

We construct and study an extended random matrix model of RNA (polymer) folding. A perturbation which acts on all the nucleotides in the chain is added to the action of the RNA partition function. The effect of this perturbation on the partition function and the Genus Distributions is studied. This perturbation distinguishes between the paired and unpaired bases. For example, for $α= 1$ (where $α$ is the ratio of the strengths of the original and perturbed term in the action) the partition function and genus distribution for odd lengths vanish completely. This partition function and the genus distribution is non-zero for even lengths where structures with fully paired bases only remain. This implies that (i). the genus distributions are different and (ii). there is a ``structural transition'' (from an ``unpaired-paired base phase'' to a ``completely paired base phase'') as $α$ approaches 1 in the extended matrix models. We compare the results of the extended RNA model with the results of G. Vernizzi, H. Orland and A. Zee in PRL 94, 168103(2005).

cond-mat.stat-mech↗
arXiv2008

Hole burning in polycrystalline C60: the final answer to the long pseudocoherent tails

New NMR experiments reveal the origin of the "pseudocoherence" that leads to long tails in some Carr-Purcell-Meiboom-Gill (CPMG) sequences in contrast with the decay of a standard Hahn echo. We showed in [M.B Franzoni and P.R. Levstein, Phys. Rev. B 72, 235410 (2005)] that under certain conditions these CPMG sequences become spoiled by stimulated echoes. The presence of these echoes evidences that the long tails arise on the storage of magnetization in the direction of the external magnetic field (z-polarization), involving spin-lattice relaxation times of several seconds. Hole burning experiments confirm the presence of a highly inhomogeneous line and show that the flip-flop processes are able to homogenize the line in times agreeing with those obtained through a Hahn echo sequence. As expected, the decay of the stimulated echoes is not sensitive to the quenching of the dipolar interaction through an MREV16 sequence, while the Hahn echo decay increases by a factor of 20. CPMG sequences with hard pulses and different temporal windows clearly show the relevance of the dipolar interaction in between the pulses for the generation of the long tails. In particular, the more time the flip-flop is effective (longer interpulse separation), the shorter are the characteristic times of the long tails.

cond-mat.stat-mech↗
arXiv2008

Cluster Expansion Method for Evolving Weighted Networks Having Vector-like Nodes

The Cluster Variation Method known in statistical mechanics and condensed matter is revived for weighted bipartite networks. The decomposition of a Hamiltonian through a finite number of components, whence serving to define variable clusters, is recalled. As an illustration the network built from data representing correlations between (4) macro-economic features, i.e. the so called $vector$ $components$, of 15 EU countries, as (function) nodes, is discussed. We show that statistical physics principles, like the maximum entropy criterion points to clusters, here in a (4) variable phase space: Gross Domestic Product (GDP), Final Consumption Expenditure (FCE), Gross Capital Formation (GCF) and Net Exports (NEX). It is observed that the $maximum$ entropy corresponds to a cluster which does $not$ explicitly include the GDP but only the other (3) ''axes'', i.e. consumption, investment and trade components. On the other hand, the $minimal$ entropy clustering scheme is obtained from a coupling necessarily including GDP and FCE. The results confirm intuitive economic theory and practice expectations at least as regards geographical connexions. The technique can of course be applied to many other cases in the physics of socio-economy networks.

physics.soc-ph↗
arXiv2008

Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System

The nonlinear transport properties of the Mott insulator are discussed with focus on the many-body Landau-Zener mechanism. After reviewing basic concepts such as the non-adiabatic geometric phase and the Schwinger mechanism, we study the decay of the insulating groundstate in strong electric fields using the time-dependent density matrix renormalization group. A short comment on the proposed mapping to the quantum walk model is added before discussing the relevance of the theory to experimental results. This article is a draft of a book chapter of the book entitled "Quantum and Semi-classical Percolation & Breakdown" (Lecture Note in Physics, Springer-Verlag), to appear 2008.

cond-mat.str-el↗
arXiv2008

Locality of dynamics in general harmonic quantum systems

The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. In this work, we formulate Lieb-Robinson bounds for general harmonic systems on general lattices, for which the constituents are infinite-dimensional, as systems representing discrete versions of free fields or the harmonic approximation to the Bose-Hubbard model. We consider both local interactions as well as infinite-ranged interactions, showing how corrections to locality are inherited from the locality of the Hamiltonian: Local interactions result in stronger than exponentially suppressed corrections, while non-local algebraic interactions result in algebraic suppression. We derive bounds for canonical operators, Weyl operators and outline generalization to arbitrary operators. As an example, we discuss the Klein-Gordon field, and see how the approximate locality in the lattice model becomes the exact causality in the field limit. We discuss the applicability of these results to quenched lattice systems far from equilibrium, and the dynamics of quantum phase transitions.

quant-ph↗
arXiv2008

First order phase transitions in nanoscopic systems

The problem of first order phase transitions in nanoscopic systems is investigated in the framework of Hill's nanothermodynamics. We obtain the equilibrium conditions and a generalized version of the Clapeyron-Clausius equation for a nanoscopic system which contains two phases. Our study is exemplified for the case when one of the phases consists of an ideal gas.

cond-mat.stat-mech↗
arXiv2010

The thermostatistical aspect of Werner-type states and quantum entanglement

A general Werner-type state is studied from two viewpoints: (i) an application of dynamical interaction of the objective system with its environment, represented by a unital positive operator-valued measure (POVM), which ensures increase of entropy, makes the system evolve from an initial pure state to a mixed state of the Werner type, and (ii) the space of the objective system is constrained to have a given value of the fidelity. Then, the maximum entropy principle is shown to yield the Werner-type state as a canonical ensemble with the projector Hamiltonian. This novel observation is illustrated by examples of bipartite systems, the separability criteria on which are given in terms of the values of temperature. The present viewpoint may cast light on relevance of thermostatistics to the physics of quantum entanglement. In addition, the POVM scheme presented here offers a way of experimentally generating the Werner-type thermal states.

cond-mat.stat-mech↗