Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session J13: Systems Far From Equilibrium 
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Sponsoring Units: GSNP Chair: Alan Middleton, Syracuse University Room: B112 
Tuesday, March 16, 2010 11:15AM  11:27AM 
J13.00001: Nearequilibrium measurements of nonequilibrium free energy David Sivak, Gavin Crooks Researchers can, with increasing ease, engineer artificial microscopic machines, structures for the deliberate and efficient manipulation of energy, matter and information on the nanometer scale. Although free energy is of primary importance to thermodynamics, typically we have no good way of measuring this quantity out of thermodynamic equilibrium, impeding our ability to predict the behavior of these microscopic molecular machines, which typically operate far from equilibrium. We herein develop an experimentally tractable approach to measure free energy away from equilibrium. We derive a formally exact expression for the probability distribution of a driven system, involving path ensemble averages of work over trajectories of the timereversed system. From this we find a simple nearequilibrium approximation in terms of a timereversed excess mean work, which can be experimentally measured in real systems. With analysis and computer simulation, we demonstrate that for several simple models, our approximation is accurate a substantial distance from equilibrium. [Preview Abstract] 
Tuesday, March 16, 2010 11:27AM  11:39AM 
J13.00002: Connecting fluctuationdissipation ideas to synchronization in equilibrium and nonequilibrium systems Cadilhe Antonio, Arthur Voter Nonequilibrium systems have both fundamental and technological interest for their unusual behavior, but surprisingly little research effort has been put into diagnosing how far a system is from equilibrium. Here, we show a connection between Langevin synchronization ideas and the position autocorrelation function. We present results for the thermalization timescale of a particle in equilibrium or outofequilibrium while coupled to heat a reservoir. In the outofequilibrium system the particle is driven away from equilibrium by a timedependent potential. [Preview Abstract] 
Tuesday, March 16, 2010 11:39AM  11:51AM 
J13.00003: Rare fluctuations in nonequilibrium systems: onset of singularities in the path distribution Oleg Kogan, Mark Dykman Fluctuations in systems away from thermal equilibrium have features that have no analog in equilibrium systems. One of such features concerns large rare excursions far from the stable state in the space of dynamical variables. For equilibrium systems, the most probable fluctuational trajectory to a given state is related to the fluctuationfree trajectory back to the stable state by time reversal. This is no longer true for nonequilibrium systems, where the pattern of the most probable trajectories generally displays singularities. Here we study how the singularities emerge as the system is driven away from equilibrium, and whether there is a threshold for their onset. Using a resonantly modulated nonlinear oscillator as a model, we show that the singularities can emerge without a threshold if it takes an infinite time for the system to go to infinity along the optimal path in thermal equilibrium. We find the scaling of the location of the singularities as a function of the control parameter. If the system reaches infinity in finite time, there is a threshold for the onset of singularities, which we study for the model. [Preview Abstract] 
Tuesday, March 16, 2010 11:51AM  12:03PM 
J13.00004: Selfconsistent Perturbation Theory for Nonequilibrium Steady State for Nonlinear Drift Force Chulan Kwon, Ping Ao, David Thouless We investigate the properties of nonequilibrium steady state for nonlinear drift force. We find that drift force can be decomposed into three parts. The two parts are also present for linear drift force; one is responsible for local detailed balance with diffusive motion due to noise and the other gives cyclic probability current around equiprobability surface. The new part gives residual probability current and may yield the shift of probability maximum from fixed point, that is a novel effect caused by the combination of highdimensional noise and nonlinear drift force. Since nonlinear case is not exactly solvable, we use the perturbation theory where drift force is expanded up to the quartic order about fixed point. The first order perturbation theory shows the existence of residual current and the shift of probability maximum from fixed point, which also shows a good agreement with simulation. [Preview Abstract] 
Tuesday, March 16, 2010 12:03PM  12:15PM 
J13.00005: The concept of effective temperature in current carrying quantum critical states Stefan Kirchner, Qimiao Si At a quantum critical point, a scaleinvariant fluctuation spectrum implies the absence of intrinsic energy scales. The system is therefore readily driven out of equilibrium. The resulting nonlinear response regime violates the fluctuationdissipation theorem. We study the outof equilibrium phenomena in a single electron transistor with ferromagnetic leads, which can be tuned through a quantum phase transition[1]. We consider the breakdown of the fluctuationdissipation theorem and study the universal behavior of the fluctuation dissipation relation of various correlators in the quantum critical regime[2]. In particular, we explore the concept of effective temperature as a means to extend the fluctuationdissipation theorem into the nonlinear regime[3]. Such effective temperatures were introduced in the context of steady states in chaotic systems, and successfully used for nonstationary states in glassy systems. References: [1] S. Kirchner et al.,PNAS 102, 18824 (2005). [2] S. Kirchner and Q. Si, PRL 103, 206401 (2009). [3] S. Kirchner and Q. Si, arXiv:0909.3925 (2009). [Preview Abstract] 
Tuesday, March 16, 2010 12:15PM  12:27PM 
J13.00006: Thermalization near Integrability in the 1D BoseHubbard model Amy Cassidy, Vanja Dunjko, Maxim Olshanii, Charles W. Clark We discuss how nearness to integrability affects relaxation from an initial nonequillibrium state in the onedimensional (1D) BoseHubbard model (BHM), within the classical field approximation. The 1D BHM has a threshold for chaos, which is govered by two parameters: the nonlinearity and energy per particle [1]. This threshold separates regions of the phase space where the dynamics are regular and regions where they are chaotic. The 1D BHM becomes integrable in both the noninteracting limit and the continum limit. Additionally, the equations of motion are close to that of the completely integrable AblowitzLadik lattice [2]. A completely integrable system is not expected to relax to the usual thermodynamic state due to the extra conservation laws. We investigate thermalization in the 1D BHM and the impact of the nearby integrable models. \\[4pt] [1] A. C. Cassidy, \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{102} 025302 (2009) \\[0pt] [2] M. J. Ablowitz and J. F. Ladik, \textit{J. Math. Phys.} \textbf{16} 598 (1975) [Preview Abstract] 
Tuesday, March 16, 2010 12:27PM  12:39PM 
J13.00007: On the absorbingstate phase transition in the triplet creation model Ronald Dickman, Geza Odor We study the lattice reaction diffusion model $3A\to 4A$, $A\to\emptyset$ (``triplet creation") using numerical simulations and $n$site approximations [1]. The simulation results suggest that the phase transition is discontinuous at high diffusion rates. In this regime the order parameter appears to be a discontinuous function of the creation rate; no evidence of a stable interface between active and absorbing phases is found. Based on an effective mapping to a modified compact directed percolation process, we shall nevertheless argue that the transition is {\it continuous} in one dimension, despite the seemingly discontinuous phase transition suggested by studies of finite systems. We also present preliminary results on the phase diagram of the model on the triangular lattice. \\[4pt] [1] G. \'Odor and R. Dickman, J. Stat. Mech. (2009) P08024. [Preview Abstract] 
Tuesday, March 16, 2010 12:39PM  12:51PM 
J13.00008: Dynamic phase transition in the next nearest neighbor kinetic Ising model William Baez, Trinanjan Datta We investigate the effects of nextnearest neighbor interactions on the dynamic phase transition (DPT) of the two dimensional kinetic Ising model subject to a spatially homogeneous AC field. Using the periodaveraged magnetization as the order parameter for the DPT, we study the crossover from the multidroplet regime to the strongfield regime. We compute the probability densities of the period averaged magnetization to study the nature of the phase transition, the susceptibility, and the correlation between the external field and the system magnetization. We also explore the effect of frustration in this model. [Preview Abstract] 
Tuesday, March 16, 2010 12:51PM  1:03PM 
J13.00009: Repeated and notperiodic quenches in a gas of independent particles Luca D'Alessio, Anatoli Polkovnikov, Yariv Kafri We have studied the evolution of the energy distribution of a gas of independent classical particles inside a cavity whose length is changed repeatedly in time. The protocol we have considered is not periodic and this leads to heating of the system. We have found that the evolution can be described by a generalized diffusion process along the energy axis. The scaling form of the asymptotic distribution has been found in 1D and 2D both analytically and numerically. In 1D the asymptotic distribution is Gibbs while in 2D a different universal distribution appears. This work is a relevant example of a repeated and notperiodic quenches which are attracting much attention lately. [Preview Abstract] 
Tuesday, March 16, 2010 1:03PM  1:15PM 
J13.00010: State selection in the noisy stabilized KuramotoSivashinsky equation Dina Obeid, J. Michael Kosterlitz, Bj\"orn Sandstede We investigate the stability of stationary patterns in out of equilibrium dissipative systems in the presence of stochastic noise, choosing the stabilized KuramotoSivashinsky (SKS) equation with white Gaussian distributed noise. The SKS equation is one of the simplest equations with the essential ingredients of non linearity and having a band of stable periodic states. Numerical simulations indicate that the noise selects one of these states as being the most stable. This is consistent with an analysis of the phasediffusion constants of the periodic states of the deterministic version where one of the states is more stable than the rest. We speculate that this is a mechanism of selecting a unique state by stochastic noise. [Preview Abstract] 
Tuesday, March 16, 2010 1:15PM  1:27PM 
J13.00011: Vortices in the 2D Kuramoto model Tony Lee, Heywood Tam, Gil Refael, Jeffrey Rogers, Michael Cross We study the synchronization of oscillators in 2D lattices with nearest neighbor coupling. The boundaries between synchronized domains are due to the motion of vortices. Since the phase winds by {\$}2$\backslash $pi{\$} around a vortex, it generates {\$}2$\backslash $pi{\$} phase slips between oscillators across its path. Thus, the synchronization behavior of the system can be viewed in terms of the production, movement, and annihilation of vortex pairs. Although the Kuramoto model is nonlinear, we show how to use the steady state solution of the linearized model to predict where the vortices are produced and how they move. We also study vortex density as a function of system size and coupling. This vortex approach may lead to an analytical understanding of why the lower critical dimension for macroscopic entrainment is 2. [Preview Abstract] 
Tuesday, March 16, 2010 1:27PM  1:39PM 
J13.00012: Transient spatiotemporal chaos in reactiondiffusion networks Renate Wackerbauer Complex transient dynamics is reported in various extended systems, including transient turbulence in shear flows, transient spatiotemporal chaos in reaction diffusion models, and nonchaotic irregular transient dynamics in neural networks. The asymptotic stability is difficult to determine since the transient lifetime typically increases exponentially with the system size. Our studies show that transient spatiotemporal chaos is extensive in various reaction diffusion systems; the Lyapunov dimension increases linearly with the network size. A master stability analysis provides insight into the asymptotic stability in the Baer Eiswirth and the GrayScott systems. The asymptotic state is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime depends on the number of transverse directions that are unstable along a typical excitation cycle. [Preview Abstract] 
Tuesday, March 16, 2010 1:39PM  1:51PM 
J13.00013: Spontaneous current induced by symmetry breaking in a system of random frequency oscillators Hyunggyu Park, Jaegon Um, Hyunsuk Hong, Fabio Marchesoni We investigate the onset of Isingtype symmetry breaking in a system of random frequency oscillators under a bistable pinning potential. In particular, we demonstrate the emergence of spontaneous current induced by symmetry breaking. As the potential barrier increases, the reentrant phase transition is found along with a drastic change of the phase transition nature at the turning point. Various other interesting features including negative mobility are also discussed. [Preview Abstract] 
Tuesday, March 16, 2010 1:51PM  2:03PM 
J13.00014: Fluctuation theorem in dynamical systems with quenched disorder Jeffrey Drocco, Cynthia Olson Reichhardt, Charles Reichhardt We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropydestroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models. [Preview Abstract] 

J13.00015: ABSTRACT WITHDRAWN 
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