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arXiv2008

On the Quantum Instability of Attractive Bose Systems

We explore the zero-temperature behavior of an assembly of bosons interacting through a zero-range, attractive potential. Because the two-body interaction admits a bound state, the many-body model is best described by a Hamiltonian that includes the coupling between atomic and molecular components. Due to the positive scattering length, the low-density collection is expected to remain stable against collapse despite the attraction between particles. Although a variational many-body analysis indicates a collapsing solution with only a molecular component to its condensate at low density, the expected atomic condensate solution can be obtained if the chemical potential is allowed to be complex valued. In addition to revealing two discrete eigenfrequencies associated with the molecular case, an expansion in small oscillations quantifies the imaginary part of the chemical potential as proportional to a coherent decay rate of the atomic condensate into a continuum of collective phonon excitations about the collapsing lower state.

cond-mat.other↗

arXiv2007

Diffusion-limited unbinding of small peptides from PDZ domains

PDZ domains are typical examples of binding motifs mediating the formation of protein-protein assemblies in many different cells. A quantitative characterization of the mechanisms intertwining structure, chemistry and dynamics with the PDZ function represent a challenge in molecular biology. Here we investigated the influence of native state topology on the thermodynamics and the dissociation kinetics for a complex PDZ-peptide via Molecular Dynamics simulations based on a coarse-grained description of PDZ domains. Our native-centric approach neglects chemical details but incorporates the basic structural information to reproduce the protein functional dynamics as it couples to the binding. We found that at physiological temperatures the unbinding of a peptide from the PDZ domain becomes increasingly diffusive rather than thermally activated, as a consequence of the significant reduction of the free energy barrier with temperature. In turn, this results in a significant slowing down of the process of two orders of magnitude with respect to the conventional Arrhenius extrapolation from low temperature calculations. Finally, a detailed analysis of a typical unbinding event based on the rupture times of single peptide-PDZ contacts allows to shed further light on the dissociation mechanism and to elaborate a coherent picture of the relation between function and dynamics in PDZ domains.

physics.bio-ph↗

arXiv2007

Locality Estimates for Quantum Spin Systems

We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained Lieb-Robinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasi-locality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multi-dimensional Lieb-Schultz-Mattis Theorem.

math-ph↗

arXiv2008

Random sequential adsorption model of damage and crack accumulation: Exact one-dimensional results

The random sequential adsorption (RSA) model is modified to describe damage and crack accumulation. The exclusion for object deposition (for damaged region formation) is not for the whole object, as in the standard RSA, but only for the initial point (or higher-dimensional defect) from which the damaged region or crack initiates. The one-dimensional variant of the model is solved exactly.

cond-mat.stat-mech↗

arXiv2008

First Column Boundary Operator Product Expansion Coefficients

We calculate boundary operator product expansion coefficients for boundary operators in the first column of the Kac table in conformal field theories. For c=0 we give closed form expressions for all such coefficients. Then we generalize to the augmented minimal models, giving explicit expressions for coefficients valid when ϕ_{1,2} mediates a change from fixed to free boundary conditions. These quantities are determined by computing an arbitrary four-point correlation function of first column operators. Our calculation first determines the appropriate (non-logarithmic) conformal blocks by using standard null-vector methods. The behavior of these blocks under crossing symmetry then provides a general closed form expression for the desired coefficients, as a product of ratios of gamma functions. This calculation was inspired by the need for several of these coefficients in certain correlation function formulas for critical two-dimensional percolation and the augmented q=2 and q=3 state critical Potts models.

cond-mat.stat-mech↗

arXiv2008

Correlation Inequalities for Spin Glass in one Dimension

We prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched disorder. The second inequality has the opposite sign of the GKS inequality of type II. In the non symmetric case with positive average we show that while the direct correlation keeps its sign the truncated one changes sign when crossing a suitable line in the parameter space. That line separates the regions satisfying the GKS second inequality and the one proved here.

math-ph↗

arXiv2008

T. Dauxois' "Non-Gaussian distributions under scrutiny" under scrutiny

A recent paper by T. Dauxois entitled "Non-Gaussian distributions under scrutiny" is submitted to scrutiny. Several comments on its content are made, which constitute, at the same time, a brief state-of-the-art review of nonextensive statistical mechanics, a current generalization of the Boltzmann-Gibbs theory. Some inadvertences and misleading sentences are pointed out as well.

cond-mat.stat-mech↗

arXiv2007

Updating Probabilities: A Complex Agent Based Example

It has been shown that one can accommodate data (Bayes) and constraints (MaxEnt) in one method, the method of Maximum (relative) Entropy (ME) (Giffin 2007). In this paper we show a complex agent based example of inference with two different forms of information; moments and data. In this example, several agents each receive partial information about a system in the form of data. In addition, each agent agrees or is informed that there are certain global constraints on the system that are always true. The agents are then asked to make inferences about the entire system. The system becomes more complex as we add agents and allow them to share information. This system can have a geometrical form, such as a crystal structure. The shape may dictate how the agents are able to share information, such as sharing with nearest neighbors. This method can be used to model many systems where the agents or cells have local or partial information but must adhere to some global rules. This could also illustrate how the agents evolve and could illuminate emergent behavior of the system.

stat.ME↗

arXiv2009

Fractal structure of a solvable lattice model

Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer matrix method and the $n$-equivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can be generalized for the models suitable to the transfer matrix treatment, and hence this gives general relation between solvable lattice models and fractal geometry.

cond-mat.stat-mech↗

arXiv2008

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: The case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter $q=Q^{*4} /T^*$, $Q^*$ is the reduced quadrupole moment of the molecule and $T^*$ the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of Perturbation Theory (PT) in the Mean Spherical Approximation (MSA). As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.

cond-mat.stat-mech↗

arXiv2008

Path Integral Ground State study of 2D solid 4He

We have studied a two-dimensional triangular commensurate crystal of 4He with the exact T=0 K Path Integral Ground State (PIGS) Monte Carlo method. We have projected onto the true ground state both a Jastrow-Nosanow wave function, in which equilibrium positions are explicitly given and no Bose-Einstein (BEC) is present, and a translationally invariant shadow wave function, in which the solid phase emerges through a spontaneously broken symmetry process and it has BEC. We find a remarkable convergence to the same properties, both the diagonal ones as well as the off-diagonal one-body density matrix rho_1. This supplies a strong evidence that no variational bias are present in the PIGS method. We find no BEC in the commensurate 2D 4He crystal at T=0 K, rho_1 shows an exponential decay in the large distance range. The structure found in rho_1 is due to virtual vacancy--interstitial pairs and this shows up in the momentum distribution.

cond-mat.other↗

arXiv2008

Density functional methods for polymers: a coil-globule transition case study

We consider a free energy functional on the monomer density function that is suitable for the study of coil-globule transition. We demonstrate, with explicitly stated assumptions, why the entropic contribution is in the form of the Kullback-Leibler distance, and that the energy contribution is given by two-body and three-body terms. We then solve for the free energy analytically on a set of trial density functions, and reproduce de Gennes' classical theory on polymer coil-globule transition. We then discuss how our formalism can be applied to study polymer dynamics from the perspective of dynamical density function theory.

cond-mat.soft↗

arXiv2008

Discontinuous Jamming Transitions in Soft Materials

Many systems in nature exhibit transitions between fluid-like states and solid-like states, or "jamming transitions". There is a strong theoretical foundation for understanding equilibrium phase transitions that involve solidification, or jamming. Other jamming transitions, such as the glass transition, are less well-understood. The jamming phase diagram has been proposed to unify the description of equilibrium phase transitions, the glass transitions, and other non-equilibrium jamming transitions. As with equilibrium phase transitions, which can either be first order (discontinuous in a relevant order parameter) or second order (continuous), one would expect that generalized jamming transitions can be continuous or discontinuous. In studies of flow in complex fluids, there is a wide range of evidence for discontinuous transitions, mostly in the context of shear localization, or shear banding. In this paper, I review the experimental evidence for discontinuous transitions. I focus on systems in which there is a discontinuity in the rate of strain between two, coexisting states: one in which the material is flowing and the other in which it is solid-like.

cond-mat.soft↗

arXiv2008

Overcharging and charge reversal in the electrical double layer near the point of zero charge

The ionic adsorption around a weakly charged spherical colloid, immersed in size-asymmetric 1:1 and 2:2 salts, is studied. We use the primitive model of an electrolyte to perform Monte Carlo simulations as well as theoretical calculations by means of the hypernetted chain/mean spherical approximation (HNC/MSA) and the unequal-radius modified Gouy-Chapman (URMGC) integral equations. Structural quantities such as the radial distribution functions, the integrated charge, and the mean electrostatic potential are reported. Our Monte Carlo "experiments" evidence that near the point of zero charge the smallest ionic species is preferentially adsorbed onto the macroparticle, independently of the sign of the charge carried by this tiniest electrolytic component, giving rise to the appearance of the phenomena of charge reversal and overcharging. Accordingly, charge reversal is observed when the macroion is slightly charged and the coions are larger than the counterions. In the opposite situation, i.e. if the counterions are larger than the coions, overcharging occurs. In other words, in this paper we present the first simulational data on overcharging, showing that this novel effect surges close to the point of zero charge as a consequence of the ionic size asymmetry. Further, it is seen that the inclusion of hard-core correlations in HNC/MSA leads to spatial regions near the macroion's surface in which the integrated charge and/or the mean electrostatic potential can decrease when the colloidal charge is augmented and vice versa. These observations aware about the interpretation of electrophoretic mobility measurements using the standard Poisson-Boltzmann approximation beyond its validity region.

cond-mat.soft↗

arXiv2008

Asymptotics for the survival probability of a Rouse chain monomer

We study the long-time asymptotical behavior of the survival probability P_t of a tagged monomer of an infinitely long Rouse chain in presence of two fixed absorbing boundaries, placed at x = \pm L. Mean-square displacement of a tagged monomer obeys \bar{X^2(t)} \sim t^{1/2} at all times, which signifies that its dynamics is an anomalous diffusion process. Constructing lower and upper bounds on P_t, which have the same time-dependence but slightly differ by numerical factors in the definition of the characteristic relaxation time, we show that P_t is a stretched-exponential function of time, \ln(P_t) \sim - t^{1/2}/L^2. This implies that the distribution function of the first exit time from a fixed interval [-L,L] for such an anomalous diffusion has all moments.

cond-mat.stat-mech↗

arXiv2008

A vortex dynamics approach to the Nernst effect in fluctuating superconductors

We present a new method to study the Nernst effect and diamagetism of an extreme type-II superconductor dominated by phase fluctuations. We work directly with vortex variables and our method allows us to tune vortex parameters (e.g., core energy and number of vortex species). We find that diamagnetic response and transverse thermoelectric conductivity ($α_{xy}$) persist well above the Kosterlitz-Thouless transition temperature, and become more pronounced as the vortex core energy is increased. However, they \textit{weaken} as the number of internal vortex states are increased. We find that $α_{xy}$ closely tracks the magnetization $(-M/T)$ over a wide range of parameters.

cond-mat.supr-con↗

arXiv2008

Transmission Eigenvalue Densities and Moments in Chaotic Cavities from Random Matrix Theory

We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads $(N_1,N_2)$ are analytically known from the Jacobi ensemble of Random Matrix Theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form $<λ_1^m>$ for $m>-|N_1-N_2|-1$ and $β=2$, thus improving the existing results in the literature. Secondly, we offer an independent derivation of the average density and higher order correlation functions for $β=2,4$ which does not make use of the orthogonal polynomials technique. This result may be relevant for an efficient numerical implementation avoiding determinants.

cond-mat.mes-hall↗

arXiv2008

From short to fat tails in financial markets: A unified description

In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to embrace both regimes. By means of Kramers-Moyal (KM) coefficients evaluated from empirical time series, we obtain the evolution equation for the probability density function (PDF) of price returns. We also present consistent asymptotic solutions for the timescale dependent equation that emerges from the empirical analysis. From these solutions, new relationships connecting PDF characteristics, such as tail exponents, to parameters of KM coefficients arise. The results reveal a dynamical path that leads from Gaussian to fat-tailed statistics, furnishing insights on other complex systems where akin crossover is observed.

q-fin.ST↗