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arXiv2013

Orbital caloritronic transport in strongly interacting quantum dots

We discuss out-of-equilibrium population imbalances between different orbital states due to applied thermal gradients. This purely thermoelectric orbital effect appears quite generically in nanostructures with a pseudospin degree of freedom. We establish an orbital Seebeck coefficient that characterizes the induced orbital bias in response to a temperature difference between reservoirs coupled to a quantum conductor. We analyze a two-terminal strongly interacting quantum dot with two orbital states and find that the orbital thermopower acts as an excellent tool to describe the transition between SU(4) and SU(2) Kondo physics. Our conclusions are reinforced from a detailed comparison with the charge thermopower using numerical renormalization group calculations.

cond-mat.mes-hall↗
arXiv2018

Statistical Equilibrium in Quantum Gravity: Gibbs states in Group Field Theory

Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental discrete degrees of freedom. However, due to the absence of well-defined concepts of time and energy in background independent settings, formulating statistical equilibrium in such cases is an open issue. This is even more so in a quantum gravity context that is not based on any of the usual spacetime structures, but on non-spatiotemporal degrees of freedom. In this paper, after having clarified general notions of statistical equilibrium, on which two different construction procedures for Gibbs states can be based, we focus on the group field theory formalism for quantum gravity, whose technical features prove advantageous to the task. We use the operator formulation of group field theory to define its statistical mechanical framework, based on which we construct three concrete examples of Gibbs states. The first is a Gibbs state with respect to a geometric volume operator, which is shown to support condensation to a low-spin phase. This state is not based on a pre-defined symmetry of the system and its construction is via Jaynes' entropy maximisation principle. The second are Gibbs states encoding structural equilibrium with respect to internal translations on the GFT base manifold, and defined via the KMS condition. The third are Gibbs states encoding relational equilibrium with respect to a clock Hamiltonian, obtained by deparametrization with respect to coupled scalar matter fields.

gr-qc↗
arXiv2013

CMB and Random Flights: temperature and polarization in position space

The fluctuations in the temperature and polarization of the cosmic microwave background are described by a hierarchy of Boltzmann equations. In its integral form, this Boltzmann hierarchy can be converted from the usual Fourier-space base into a position-space and causal description. We show that probability densities for random flights play a key role in this description. The integral system can be treated as a perturbative series in the number of steps of the random flights, and the properties of random flight probabilities impose constraints on the domains of dependence. We show that, as a result of these domains, a Fourier-Bessel decomposition can be employed in order to calculate the random flight probability densities. We also illustrate how the H-theorem applies to the cosmic microwave background: by using analytical formulae for the asymptotic limits of these probability densities, we show that, as the photon distribution approaches a state of equilibrium, both the temperature anisotropies and the net polarization must vanish.

astro-ph.CO↗
arXiv2011

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.

cond-mat.stat-mech↗
arXiv2012

Next nearest neighbour Ising models on random graphs

This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several applications such as the colour diversity problem and graphical games. We demonstrate ensembles of random graphs, including regular connectivity graphs, that have a periodic variation of free energy, with either the ratio of nearest to next nearest couplings, or the mean number of nearest neighbours. When the coupling ratio is integer paramagnetic phases can be found at zero temperature. This is shown to be related to the locked or unlocked nature of the interactions. For anti-ferromagnetic couplings, spin glass phases are demonstrated at low temperature. The interaction structure is formulated as a factor graph, the solution on a tree is developed. The replica symmetric and energetic one-step replica symmetry breaking solution is developed using the cavity method. We calculate within these frameworks the phase diagram and demonstrate the existence of dynamical transitions at zero temperature for cases of anti-ferromagnetic coupling on regular and inhomogeneous random graphs.

cond-mat.stat-mech↗
arXiv2013

Modeling interacting dynamic networks: I. Preferred degree networks and their characteristics

We study a simple model of dynamic networks, characterized by a set preferred degree, $κ$. Each node with degree $k$ attempts to maintain its $κ$ and will add (cut) a link with probability $w(k;κ)$ ($1-w(k;κ)$). As a starting point, we consider a homogeneous population, where each node has the same $κ$, and examine several forms of $w(k;κ)$, inspired by Fermi-Dirac functions. Using Monte Carlo simulations, we find the degree distribution in steady state. In contrast to the well-known Erdős-Rényi network, our degree distribution is not a Poisson distribution; yet its behavior can be understood by an approximate theory. Next, we introduce a second preferred degree network and couple it to the first by establishing a controllable fraction of inter-group links. For this model, we find both understandable and puzzling features. Generalizing the prediction for the homogeneous population, we are able to explain the total degree distributions well, but not the intra- or inter-group degree distributions. When monitoring the total number of inter-group links, $X$, we find very surprising behavior. $X$ explores almost the full range between its maximum and minimum allowed values, resulting in a flat steady-state distribution, reminiscent of a simple random walk confined between two walls. Both simulation results and analytic approaches will be discussed.

physics.soc-ph↗
arXiv2012

Bethe ansatz for the Temperley-Lieb spin-chain with integrable open boundaries

In this paper we study the spectrum of the spin-1 Temperley-Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe ansatz. These equations provide the complete description of the spectrum of the model.

nlin.SI↗
arXiv2013

Sublinear but Never Superlinear Preferential Attachment by Local Network Growth

We investigate a class of network growth rules that are based on a redirection algorithm wherein new nodes are added to a network by linking to a randomly chosen target node with some probability 1-r or linking to the parent node of the target node with probability r. For fixed 0<r<1, the redirection algorithm is equivalent to linear preferential attachment. We show that when r is a decaying function of the degree of the parent of the initial target, the redirection algorithm produces sublinear preferential attachment network growth. We also argue that no local redirection algorithm can produce superlinear preferential attachment.

cond-mat.stat-mech↗
arXiv2013

The effect of quenched disorder in neutral theories

We study systems with two symmetric absorbing states, such as the voter model and variations of it, which have been broadly used as minimal neutral models in genetics, population ecology, sociology, etc. We analyze the effects of a key ingredient ineluctably present in most real applications: random-field-like quenched disorder. In accord with simulations and previous findings, coexistence between the two competing states/opinions turns out to be strongly favored by disorder in the standard voter model; actually, a disorder-induced phase transition is generated for any finite system size in the presence of an arbitrary small spontaneous-inversion rate (preventing absorbing states from being stable). For non-linear versions of the voter model a general theory (by AlHammal et al.) explains that the spontaneous breaking of the up/down symmetry and an absorbing state phase transition can occur either together or separately, giving raise to two different scenarios. Here, we show that he presence of quenched disorder in non-linear voter models does not allow the separation of the up-down (Ising-like) symmetry breaking from the active-to-absorbing phase transition in low-dimensional systems: both phenomena can occur only simultaneously, as a consequence of the well-known Imry-Ma argument generalized to these non-equilibrium problems. When the two phenomena occur at unison, resulting into a genuinely non-equilibrium ("Generalized Voter") transition, the Imry-Ma argument is violated and the symmetry can be spontaneously broken even in low dimensions.

cond-mat.stat-mech↗
arXiv2013

Entanglement negativity and conformal field theory: a Monte Carlo study

We investigate the behavior of the moments of the partially transposed reduced density matrix ρ^{T_2}_A in critical quantum spin chains. Given subsystem A as union of two blocks, this is the (matrix) transposed of ρ_A with respect to the degrees of freedom of one of the two. This is also the main ingredient for constructing the logarithmic negativity. We provide a new numerical scheme for calculating efficiently all the moments of ρ_A^{T_2} using classical Monte Carlo simulations. In particular we study several combinations of the moments which are scale invariant at a critical point. Their behavior is fully characterized in both the critical Ising and the anisotropic Heisenberg XXZ chains. For two adjacent blocks we find, in both models, full agreement with recent CFT calculations. For disjoint ones, in the Ising chain finite size corrections are non negligible. We demonstrate that their exponent is the same governing the unusual scaling corrections of the mutual information between the two blocks. Monte Carlo data fully match the theoretical CFT prediction only in the asymptotic limit of infinite intervals. Oppositely, in the Heisenberg chain scaling corrections are smaller and, already at finite (moderately large) block sizes, Monte Carlo data are in excellent agreement with the asymptotic CFT result.

cond-mat.stat-mech↗
arXiv2013

Two-time free energy distribution function in (1+1) directed polymers

The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the $N$-particle quantum boson system with attractive interactions.

cond-mat.stat-mech↗
arXiv2013

Role of noise and agents' convictions on opinion spreading in a three-state voter-like model

In this work we study the opinion formation in a voter-like model defined on a square lattice of linear size $L$. The agents may be in three different states, representing any public debate with three choices (yes, no, undecided). We consider heterogeneous agents that have different convictions about their opinions. These convictions limit the capacity of persuasion of the individuals during the interactions. Moreover, there is a noise $p$ that represents the probability of an individual spontaneously change his opinion to the undecided state. Our simulations suggest that the system reaches stationary states for all values of $p$, with consensus states occurring only for the noiseless case $p=0$. In this case, the relaxation times are distributed according to a log-normal function, with the average value $τ$ growing with the lattice size as $τ\sim L^α$, where $α\approx$ 0.9. We found a threshold value $p^{*}\approx$ 0.9 above which the stationary fraction of undecided agents is greater than the fraction of decided ones. We also study the consequences of the presence of external effects in the system, which models the influence of mass media on opinion formation.

physics.soc-ph↗
arXiv2013

About an H-theorem for systems with non-conservative interactions

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the evolution of the single particle probability $P_i(t)$ of being in state $i$ at time $t$, is a suitable model for granular gases and is indicated here as Boltzmann-Fokker-Planck (BFP) equation. The conjectured H-functional, which appears to be non-increasing, is $H_C(t)=\sum_i P_i(t) \ln P_i(t)/Π_i$ with $Π_i = \lim_{t \to \infty} P_i(t)$, in analogy with the H-functional of Markov processes. The extension to continuous states is straightforward. A simple proof can be given for the elastic BFP equation. A semi-analytical proof is also offered for the BFP equation for so-called inelastic Maxwell molecules. Other evidence is obtained by solving particular BFP cases through numerical integration or through "particle schemes" such as the Direct Simulation Monte Carlo.

cond-mat.stat-mech↗
arXiv2013

Numerical estimate of infinite invariant densities: application to Pesin-type identity

Weakly chaotic maps with unstable fixed points are investigated in the regime where the invariant density is non-normalizable. We propose that the infinite invariant density of these maps can be estimated using as the long time limit of t^(1-alpha) rho(x, t), in agreement with earlier work of Thaler. Here rho(x, t) is the normalizable density of particles. This definition uniquely determines the infinite density and is a valuable tool for numerical estimations. We use this density to estimate the subexponential separation lambda_alpha of nearby trajectories. For a particular map introduced by Thaler we use an analytical expression for the infinite invariant density to calculate lambda_alpha exactly, which perfectly matches simulations without fitting. Misunderstanding which recently appeared in the literature is removed.

cond-mat.stat-mech↗
arXiv2013

Quantum Entanglement and Thermal Reduced Density Matrices in Fermion and Spin Systems on Ladders

Numerical studies of the reduced density matrix of a gapped spin-1/2 Heisenberg antiferromagnet on a two-leg ladder find that it has the same form as the Gibbs density matrix of a gapless spin-1/2 Heisenberg antiferromagnetic chain at a finite temperature determined by the spin gap of the ladder. We investigate this interesting result by considering a model of free fermions on a two-leg ladder (gapped by the inter-chain tunneling operator) and in spin systems on a ladder with a gapped ground state using exact solutions and several controlled approximations. We calculate the reduced density matrix and the entanglement entropy for a leg of the ladder (i.e. cut made between the chains). In the fermionic system we find the exact form of the reduced density matrix for one of the chains and determine the entanglement spectrum explicitly. Here we find that in the weak tunneling limit of the ladder the entanglement entropy of one chain of the gapped ladder has a simple and universal form dictated by conformal invariance. In the case of the spin system, we consider the strong coupling limit by using perturbation theory and get the reduced density matrix by the Schmidt decomposition. The entanglement entropies of a general gapped system of two coupled conformal field theories (in 1+1 dimensions) is discussed using the replica trick and scaling arguments. We show that 1) for a system with a bulk gap the reduced density matrix has the form of a thermal density matrix, 2) the long-wavelength modes of one subsystem (a chain) of a gapped coupled system are always thermal, 3) the von Neumann entropy equals to the thermodynamic entropy of one chain, and 4) the bulk gap plays the role of effective temperature.

cond-mat.str-el↗
arXiv2013

Transport-induced correlations in weakly interacting systems

We study spatial correlations in the transport of energy between two baths at different temperatures. To do this, we introduce a minimal model in which energy flows from one bath to another through two subsystems. We show that the transport-induced energy correlations between the two subsystems are of the same order as the energy fluctuations within each subsystem. The correlations can be either positive or negative and we give bounds on their values which are associated with a dynamic energy scale. The different signs originate as a competition between fluctuations generated near the baths, and fluctuations of the current between the two subsystems. This interpretation sheds light on known results for spatially-dependent heat and particle conduction models.

cond-mat.stat-mech↗
arXiv2013

On sampling and modeling complex systems

The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically under sample the space of possible states. We study a generic framework where a complex system is seen as a system of many interacting degrees of freedom, which are known only in part, that optimize a given function. We show that the underlying distribution with respect to the known variables has the Boltzmann form, with a temperature that depends on the number of unknown variables. In particular, when the unknown part of the objective function decays faster than exponential, the temperature decreases as the number of variables increases. We show in the representative case of the Gaussian distribution, that models are predictable only when the number of relevant variables is less than a critical threshold. As a further consequence, we show that the information that a sample contains on the behavior of the system is quantified by the entropy of the frequency with which different states occur. This allows us to characterize the properties of maximally informative samples: in the under-sampling regime, the most informative frequency size distributions have power law behavior and Zipf's law emerges at the crossover between the under sampled regime and the regime where the sample contains enough statistics to make inference on the behavior of the system. These ideas are illustrated in some applications, showing that they can be used to identify relevant variables or to select most informative representations of data, e.g. in data clustering.

physics.data-an↗