Latest Research Papers In Condensed Matter Physics | (Cond-Mat.Stat-Mech) 2019-04-19
Statistical Mechanics
Typical entropy of a subsystem: Page curve and its variance (1904.08370v1)
Eugenio Bianchi, Pietro Dona
2019-04-17
When an isolated quantum system is in a random pure state, the average entropy of a subsystem is close to maximal. The exact formula for the average
was conjectured by Page in 1995 and later proved. Here we compute the exact formula for the variance
and show that, in a large system, any subsystem has
. Therefore, the average entropy of a subsystem is also its typical entropy. The methods introduced here allow us to compute also the exact formula for the skewness and, in principle, the higher order moments of the probability distribution
. We compare exact and numerical results to the normal distribution with given mean and variance, and comment on the relation to previous results on concentration of measure. We discuss the application to physical systems with Hilbert space given by a direct sum of tensor products, such as the space of eigenstates of a given energy. In particular, we show how the thermal entropy of a gas of photons arises as the typical entanglement entropy of a subsystem.
Crystallization in Three-Dimensions: Defect-Driven Topological Ordering and the Role of Geometrical Frustration (1812.11265v2)
Carline S. Gorham, David E. Laughlin
2018-12-29
Herein, fundamentals of topology and symmetry breaking are used to understand crystallization and geometrical frustration in topologically close-packed structures. This frames solidification from a new perspective that is unique from thermodynamic discussions. Crystallization is considered as developing from undercooled liquids, in which orientational order is characterized by a surface of a sphere in four-dimensions (quaternion) with the binary polyhedral representation of the preferred orientational order of atomic clustering inscribed on its surface. As a consequence of the dimensionality of the quaternion orientational order parameter, crystallization is seen as occurring in "restricted dimensions." Homotopy theory is used to classify all topologically stable defects, and third homotopy group defect elements are considered to be generalized vortices that are available in superfluid ordered systems. This topological perspective approaches the liquid-to-crystalline solid transition in three-dimensions from fundamental concepts of: Bose-Einstein condensation, the Mermin-Wagner theorem and Berezinskii-Kosterlitz-Thouless (BKT) topological-ordering transitions. In doing so, in this article, concepts that apply to superfluidity in "restricted dimensions" are generalized in order to consider the solidification of crystalline solid states.
A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle (1812.07819v2)
Giacomo Gradenigo, Satya N. Majumdar
2018-12-19
We study the probability distribution
of the total displacement
of an
-step run and tumble particle on a line, in presence of a constant nonzero drive
. While the central limit theorem predicts a standard Gaussian form for
near its peak, we show that for large positive and negative
, the distribution exhibits anomalous large deviation forms. For large positive
fluid' phase to acondensed' phase that is dominated by a single large run. A similar first-order transition occurs for negative large fluctuations as well. Numerical simulations are in excellent agreement with our analytical predictions.
Ordering dynamics in the voter model with aging (1904.07128v2)
Antonio F. Peralta, Nagi Khalil, Raul Toral
2019-04-15
The voter model with memory-dependent dynamics is theoretically and numerically studied at the mean-field level. The `internal age', or time an individual spends holding the same state, is added to the set of binary states of the population, such that the probability of changing state (or activation probability
) depends on this age. A closed set of integro-differential equations describing the time evolution of the fraction of individuals with a given state and age is derived, and from it analytical results are obtained characterizing the behavior of the system close to the absorbing states. In general, different age-dependent activation probabilities have different effects on the dynamics. When the activation probability
, the system reaches a steady state with coexistence of opinions. In the case of aging, with
(zero or not) and the velocity of
) or power-law like (
). Exact conditions for having one or another behavior, together with the equations and explicit expressions for the exponents, are provided.
Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability (1904.08326v1)
Andrea Cairoli, Chiu Fan Lee
2019-04-17
Anomalous diffusion, manifest as a nonlinear relationship between the position mean square displacement and the temporal duration, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behaviour is often observed to emerge spontaneously from the mutual interactions between constituent motile units in biological systems. Examples where these phenomena can be observed simultaneously have been identified in recent experiments on bird flocks, fish schools and bacterial swarms. These results pose an intriguing question, which cannot be resolved by existing theories of active matter: How is the collective motion of these systems affected by the anomalous diffusion of constituent units? Here, we answer this question for a microscopic model of active L'evy matter -- a collection of interacting superdiffusive active particles, in which the superdiffusion is modeled as L'evy flight and the interactions promote polar alignment of the particle directions. We present in details the derivation of the hydrodynamic equations of motion of the model, obtain from these equations the spatially homogeneous states, and study the stability of these states against linear perturbations. Our analysis indicates that the disorder-order phase transition can be critical, in contrast to ordinary active fluids where the phase transition is first-order. These results suggest the existence of potentially novel universal properties of active systems.
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