Constraints on Fluid Dynamics from Equilibrium Partition Functions

We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with the constraints described in this paper.Comment: Typos corrected, References adde

Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions

Following up on recent work in the context of ordinary fluids, we study the equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We argue that this partition function is generated by a 3 dimensional Euclidean effective action for the massless Goldstone field. We parameterize the general form of this action at first order in the derivative expansion. We demonstrate that the constitutive relations of relativistic superfluid hydrodynamics are significantly constrained by the requirement of consistency with such an effective action. At first order in the derivative expansion we demonstrate that the resultant constraints on constitutive relations coincide precisely with the equalities between hydrodynamical transport coefficients recently derived from the second law of thermodynamics.Comment: 46 page

Hydrodynamics in 1+1 dimensions with gravitational anomalies

The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at second derivative order. This partition function is then used to compute the parity-violating part of the covariant energy-momentum tensor and the transport coefficients.Comment: 9 pages, JHEP format.v2; added comments and references, matching published versio

Collective dynamics of two-mode stochastic oscillators

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure

Memory functions and Correlations in Additive Binary Markov Chains

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.Comment: 11 pages, 5 figure

Non-Abelian anomalous (super)fluids in thermal equilibrium from differential geometry

We apply differential geometry methods to the computation of the anomalyinduced hydrodynamic equilibrium partition function. Implementing the imaginary-time prescription on the Chern-Simons effective action on a stationary background, we obtain general closed expressions for both the invariant and anomalous part of the partition function. This is applied to the Wess-Zumino-Witten action for Goldstone modes, giving the equilibrium partition function of superfluids. In all cases, we also study the anomalyinduced gauge currents and energy-momentum tensor, providing explicit expressions for them.This work has been supported by Plan Nacional de Altas Energías Spanish MINECO grants FPA2015-64041-C2-1-P, FPA2015-64041-C2-2-P, and by Basque Government grant IT979-16. The research of E.M. is also supported by Spanish MINEICO and European FEDER funds grant FIS2017-85053-C2-1-P, Junta de Andalucía grant FQM-225, as well as by Universidad del País Vasco UPV/EHU through a Visiting Professor appointment and by Spanish MINEICO Ramón y Cajal Progra

(Non)-Renormalization of the Chiral Vortical Effect Coefficient

We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula $\sum_{n=1}^\infty n=-1/12$. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large $N$ limit.Comment: 11 pages, 3 figures. Version 2 corrects an error and calculates leading radiative correctio

Agent-based modeling of the impact of advertising on the regional economic cluster lifecycle

The aim of the study is the development and testing of an algorithm for modeling the impact of advertising on various stages of the life cycle of economic clusters. It is assumed, that the life cycle of the cluster consists of the stages: a diffuse group, a hidden cluster, an evolving cluster, a mature cluster, a collapsing cluster. Using the agent-based simulation methods, hierarchical clustering and chaos theory, the following results were obtained: a conceptual model of the behavior of cluster members for cluster formation processes at each stage of the cluster life cycle and an imitation model of the influence of advertising on the life cycle of the economic cluster; the patterns of various stages of the life cycle of the economic cluster and the functioning of the cluster without influence and under the influence of advertising were revealed. Advertising reduces the time at the stages of the associated life cycle of the cluster, increases the stage of maturity of the cluster. Companies that do not comply with the principles of clustering are under the influence of advertising and promotional activities. Such enterprises most often arise in the cluster at the stages of its formation

Model of C-Axis Resistivity of High-\Tc Cuprates

We propose a simple model which accounts for the major features and systematics of experiments on the $c$-axis resistivity, $\rho_c$, for \lsco, \ybco and \bsco . We argue that the $c$-axis resistivity can be separated into contributions from in-plane dephasing and the $c$-axis ``barrier'' scattering processes, with the low temperature semiconductor-like behavior of $\rho_c$ arising from the suppression of the in-plane density of states measured by in-plane magnetic Knight shift experiments. We report on predictions for $\rho_c$ in impurity-doped \ybco materials.Comment: 10 pages + figures, also see March Meeting J13.1

Autonomous stochastic resonance in fully frustrated Josephson-junction ladders

We investigate autonomous stochastic resonance in fully frustrated Josephson-junction ladders, which are driven by uniform constant currents. At zero temperature large currents induce oscillations between the two ground states, while for small currents the lattice potential forces the system to remain in one of the two states. At finite temperatures, on the other hand, oscillations between the two states develop even below the critical current; the signal-to-noise ratio is found to display array-enhanced stochastic resonance. It is suggested that such behavior may be observed experimentally through the measurement of the staggered voltage.Comment: 6 pages, 11 figures, to be published in Phys. Rev.