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arXiv2009

Entropic origin of stress correlations in granular materials

We study the response of granular materials to external stress using experiment, simulation, and theory. We derive an entropic, Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively.

cond-mat.stat-mech↗

arXiv2009

General formalism of non-equilibrium statistical mechanics, a path approach

In this paper we develop a general formalism of a path approach for non-equilibrium statistical mechanics. Firstly, we consider the classical Gibbs approach for states and find that this formalism is ineffective for non-equilibrium phenomena because it is based on a distribution of probabilities indirectly. Secondly, we develop a path formalism which is directly based on the distribution of probabilities and therefore significantly simplifies the analytical approach. The new formalism requires generalizing the 'static', state quantities of a system, like entropy or free energy potential, to their path analogues. Also we obtain a path balance equation and an equation of equilibrium path. For the distribution of probabilities we obtain a functional dependence similar to the Feynman's path integral formalism of action, only now the role of a Hamiltonian is played by the state entropy. For the production of the state free energy we illustrate a significant dependence on the type of system's connectivity.

cond-mat.stat-mech↗

arXiv2009

Manipulation of double-dot spin qubit by continuous noisy measurement

We consider evolution of a double quantum dot (DQD) two-electron spin qubit which is continuously weakly measured with a linear charge detector (quantum point contact). Since the interaction between the spins of two electrons depends on their charge state, the charge measurement affects the state of two spins, and induces non-trivial spin dynamics. We consider the regimes of strong and weak coupling to the detector, and investigate the measurement-induced spin dynamics both analytically and numerically. We observe emergence of the negative-result evolution and the system stabilization due to an analog of quantum Zeno effect. Moreover, unitary evolution between the triplet and a singlet state is induced by the negative-result measurement. We demonstrate that these effects exist for both strong and weak coupling between the detector and the DQD system.

cond-mat.mes-hall↗

arXiv2010

Generalized q-Onsager algebras and boundary affine Toda field theories

Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q=1, the algebra reduces to the one proposed by Uglov-Ivanov. In the general case and $q\neq 1$, an explicit algebra homomorphism associated with coideal subalgebras of quantum affine Lie algebras (simply and non-simply laced) is exhibited. Boundary (soliton non-preserving) integrable quantum Toda field theories are then considered in light of these results. For the first time, all defining relations for the underlying non-Abelian symmetry algebra are explicitely obtained. As a consequence, based on purely algebraic arguments all integrable (fixed or dynamical) boundary conditions are classified.

math-ph↗

arXiv2009

On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics

This paper describes the development and analysis of finite-volume methods for the Landau-Lifshitz Navier-Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white-noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for non-equilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected non-equilibrium flows. In this paper, we introduce a more systematic approach based on studying discrete equilibrium structure factors for a broad class of explicit linear finite-volume schemes. This new approach provides a better characterization of the accuracy of a spatio-temporal discretization as a function of wavenumber and frequency, allowing us to distinguish between behavior at long wavelengths, where accuracy is a prime concern, and short wavelengths, where stability concerns are of greater importance. We use this analysis to develop a specialized third-order Runge Kutta scheme that minimizes the temporal integration error in the discrete structure factor at long wavelengths for the one-dimensional linearized LLNS equations. Together with a novel method for discretizing the stochastic stress tensor in dimension larger than one, our improved temporal integrator yields a scheme for the three-dimensional equations that satisfies a discrete fluctuation-dissipation balance for small time steps and is also sufficiently accurate even for time steps close to the stability limit.

physics.flu-dyn↗

arXiv2009

Reduced Thermal Conductivity of Nanowires and Nanoribbons with Dynamically Rough Surfaces and the "Problem of One-Dimensional Heat Conductors"

We present analytical model and molecular dynamics simulations of phonon heat transport in nanowires and nanoribbons with anharmonic lattices and dynamically rough surfaces and edges. In agreement with recent experiments on heat transport in single-crystalline silicon nanowires with rough surfaces, our model and simulations predict finite and length-independent phonon thermal conductivity in such quasi-one-dimensional systems, in contrast to anomalous phonon thermal conductivity of corresponding momentum-conserving systems with atomically smooth surfaces, divergent with the system length. Within our model, the main cause of thermal conductivity reduction is momentum-nonconserving scattering of longitudinal acoustic phonons by anharmonic side phonon leads in quasi-one-dimensional phonon waveguide with dynamically rough surface or edge layers.

cond-mat.stat-mech↗

arXiv2009

Nonequilibrium steady state fluctuations in actively cooled resonators

We analyze heat and work fluctuations in the gravitational wave detector AURIGA, modeled as a macroscopic electromechanical oscillator in contact with a thermostat and cooled by an active feedback system. The oscillator is driven to a steady state by the feedback cooling, equivalent to a viscous force. The experimentally measured fluctuations are in agreement with our theoretical analysis based on a stochastically driven Langevin system. The asymmetry of the fluctuations of the absorbed heat characterizes the oscillator's nonequilibrium steady state and reveals the extent to which a feedback cooled system departs from equilibrium in a statistical mechanics perspective.

cond-mat.stat-mech↗

arXiv2009

On the critical behavior of two-dimensional liquid crystals

The Lebwohl-Lasher (LL) model is the traditional model used to describe the nematic-isotropic transition of real liquid crystals. In this paper, we develop a numerical study of the temperature behaviour and of finite-size scaling of the two-dimensional (2D) LL-model. We discuss two possible scenarios. In the first one, the 2D LL-model presents a phase transition similar to the topological transition appearing in the 2D XY-model. In the second one, the 2D LL-model does not exhibit any critical transition, but its low temperature behaviour is rather characterized by a crossover from a disordered phase to an ordered phase at zero temperature. We realize and discuss various comparisons with the 2D XY-model and the 2D Heisenberg model. Adding to previous studies of finite-size scaling behaviour of the order parameter and conformal mapping of order parameter profile, we analyze the critical scaling of the probability distribution function, hyperscaling relations and stiffness order parameter and conclude that the second scenario (no critical transition) is the most plausible.

cond-mat.stat-mech↗

arXiv2009

Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs

We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except $\mathcal{E}_4^{(12)}$ proposed by di Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be computed for the corresponding integrable statistical mechanical models and provide the framework for studying corresponding braided subfactors to realise all the SU(3) modular invariants as well as a framework for a new SU(3) planar algebra theory.

math.OA↗

arXiv2009

The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain

Toeplitz matrices have applications to different problems of statistical mechanics. Recently they were used for calculation of entanglement entropy in spin chains. We use the Fisher-Hartwig formula to calculate entanglement entropy of large block of spins in the ground state of XY spin chain. We also calculate Renyi entropy and prove that the spectrum of the density matrix of a block of spins is exact geometric sequence [also different eigenvalues are degenerated differently].

math-ph↗

arXiv2010

The inclusion process: duality and correlation inequalities

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other -- a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction, -- the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.

math.PR↗

arXiv2009

Variational principle of counting statistics in master equations

We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral formulation without the assumption of mesoscopic systems. It has been clarified that the saddle point method for the path integral is not an approximation, but a valid procedure in the present derivation. Hence, a variational principle in the counting statistics is naturally derived. In order to obtain the variational principle, we employ many independent replicas of the same system. In addition, the Euler-Maclaurin formula is used in order to connect the discrete and continuous properties of the system.

cond-mat.stat-mech↗

arXiv2009

Effect of platy- and leptokurtic distributions in the random-field Ising model: Mean field approach

The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter $τ< 3$ to each site. For $τ< 5/3$, such distributions, which are basically Student-$t$ and $r$-distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a $α$-stable Lévy distribution with $α= (3 - τ)/(τ- 1)$. For every value of $τ$, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz ($τ= 2$) which is accompanied with a divergent free energy per spin (at zero temperature).

cond-mat.stat-mech↗

arXiv2009

Inhomogeneous Fermi mixtures at Unitarity: Bogoliubov-de Gennes vs. Landau-Ginzburg

We present an inhomogeneous theory for the low-temperature properties of a resonantly interacting Fermi mixture in a trap that goes beyond the local-density approximation. We compare the Bogoliubov-de Gennes and a Landau-Ginzburg approach and conclude that the latter is more appropriate when dealing with a first-order phase transition. Our approach incorporates the state-of-the-art knowledge on the homogeneous mixture with a population imbalance exactly and gives good agreement with the experimental density profiles of Shin {\it et al}. [Nature {\bf 451}, 689 (2008)]. We calculate the universal surface tension due to the observed interface between the equal-density superfluid and the partially polarized normal state of the mixture. We find that the exotic and gapless superfluid Sarma phase can be stabilized at this interface, even when this phase is unstable in the bulk of the gas.

cond-mat.stat-mech↗

arXiv2009

Gravity, Entropy, and Cosmology: In Search of Clarity

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity \emph{in} entropy calculations must be distinguished from the entropy \emph{of} gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself increases in entropy, and that (iii) the Second Law of Thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse.

cond-mat.stat-mech↗

arXiv2009

Competitive nucleation in metastable systems

Metastability is observed when a physical system is close to a first order phase transition. In this paper the metastable behavior of a two state reversible probabilistic cellular automaton with self-interaction is discussed. Depending on the self-interaction, competing metastable states arise and a behavior very similar to that of the three state Blume-Capel spin model is found.

cond-mat.stat-mech↗

arXiv2009

Scaling Relations for Contour Lines of Rough Surfaces

Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of underlying phenomena. Here, we analyze scaling properties of the cumulative distribution of iso-height loops (i.e., contour lines) of rough self-affine surfaces in terms of loop area and system size. Inspired by the Coulomb gas methods, we find the generating function of the area of the loops. Interestingly, we find that, after sorting loops with respect to their perimeters, Zipf-like scaling relations hold for ranked loops. Numerical simulations are also provided in order to demonstrate the proposed scaling relations.

cond-mat.stat-mech↗

arXiv2009

Classical and quantum anisotropic Heisenberg antiferromagnets

We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and cubic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding, in the quantum lattice gas description, to supersolid) phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.

cond-mat.stat-mech↗