Correlated adaptation of agents in a simple market: a statistical physics perspective

We discuss recent work in the study of a simple model for the collective behaviour of diverse speculative agents in an idealized stockmarket, considered from the perspective of the statistical physics of many-body systems. The only information about other agents available to any one is the total trade at time steps. Evidence is presented for correlated adaptation and phase transitions/crossovers in the global volatility of the system as a function of appropriate information scaling dimension. Stochastically controlled irrationally of individual agents is shown to be globally advantageous. We describe the derivation of the underlying effective stochastic differential equations which govern the dynamics, and make an interpretation of the results from the point of view of the statistical physics of disordered systems.Comment: 15 Pages. 5 figure

Collective Dynamics of Solitons and Inequivalent Quantizations

The collective dynamics of solitons with a coset space G/H as moduli space is studied. It is shown that the collective band for a vibrational state is given by the inequivalent coset space quantization corresponding to the representation of H carried by the vibration.Comment: 6 pages, revte

Finite-temperature critical point of a glass transition

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition, similar to those observed with hard constraints. In addition, we find that the first-order phase boundary in this softened model ends in a finite-temperature dynamical critical point, which we expect to be present in natural systems. We discuss links between this critical point and quantum phase transitions, showing that dynamical phase transitions in $d$ dimensions map to quantum transitions in the same dimension, and hence to classical thermodynamic phase transitions in $d+1$ dimensions. We make these links explicit through exact mappings between master operators, transfer matrices, and Hamiltonians for quantum spin chains.Comment: 10 pages, 5 figure

Space-time Thermodynamics of the Glass Transition

We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called "glass transition" is a manifestation of low action tails in these distributions where the entropy of trajectory space is sub-extensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature T_g which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models, and note how these ideas apply more generally.Comment: 5 pages, 4 figure

Coarse-grained microscopic model of glass formers

We introduce a coarse-grained model for atomic glass formers. Its elements are physically motivated local microscopic dynamical rules parameterized by observables. Results of the model are established and used to interpret the measured behaviors of supercooled fluids approaching glass transitions. The model predicts the presence of a crossover from hierarchical super-Arrhenius dynamics at short length scales to diffusive Arrhenius dynamics at large length scales. This prediction distinguishes our model from other theories of glass formers and can be tested by experiment.Comment: 5 pages, 5 figure

Thermodynamics of trajectories of the one-dimensional Ising model

We present a numerical study of the dynamics of the one-dimensional Ising model by applying the large-deviation method to describe ensembles of dynamical trajectories. In this approach trajectories are classified according to a dynamical order parameter and the structure of ensembles of trajectories can be understood from the properties of large-deviation functions, which play the role of dynamical free-energies. We consider both Glauber and Kawasaki dynamics, and also the presence of a magnetic field. For Glauber dynamics in the absence of a field we confirm the analytic predictions of Jack and Sollich about the existence of critical dynamical, or space-time, phase transitions at critical values of the "counting" field $s$. In the presence of a magnetic field the dynamical phase diagram also displays first order transition surfaces. We discuss how these non-equilibrium transitions in the 1$d$ Ising model relate to the equilibrium ones of the 2$d$ Ising model. For Kawasaki dynamics we find a much simple dynamical phase structure, with transitions reminiscent of those seen in kinetically constrained models.Comment: 23 pages, 10 figure

Relationship between vibrations and dynamical heterogeneity in a model glass former: extended soft modes but local relaxation

We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of the low (high) frequency vibrational modes and regions of high (low) propensity for motion. This is similar to what was observed in continuous force systems, but our interpretation is different: in our case relaxation is due to localised excitations which propagate through the system; these localised excitations act as background disorder for the elastic network, giving rise to anomalous vibrational modes. Our results show that a correlation between spatially extended low frequency modes and high propensity regions does not imply that relaxational dynamics originates in extended soft modes. We consider other measures of elastic heterogeneity, such as non-affine displacement fields and mode localisation lengths, and discuss implications of our results to interpretations of dynamic heterogeneity more generally.Comment: 5 pages, 5 figure