Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session U23: Statistical Physics and Disordered Nonlinear Systems 
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Sponsoring Units: GSNP Chair: William Klein, Boston U Room: LACC 410 
Thursday, March 24, 2005 8:00AM  8:12AM 
U23.00001: Bethe Ansatz for the 1D Hubbard model: from the finite lattice to the thermodynamic limit Pedro Goldbaum We prove that the norm of the Bethe Ansatz wavefunction for the onedimensional Hubbard model does not vanish for all but finitely many values of the interaction U, concluding the proof that it does indeed give the correct ground state of the model. For the finitely many values where the wavefunction could in principle vanish, we propose a method to determine the genuine ground state. We also show the existence of a thermodynamic limit to the distribution function of the parameters of the Bethe Ansatz states, establishing the connection between our previous work on the existence of solution to the Bethe Ansatz equations and the exact solution of the model at half filling in the thermodynamic limit, by E. H. Lieb and F. Y. Wu. [Preview Abstract] 
Thursday, March 24, 2005 8:12AM  8:24AM 
U23.00002: The Chemical Potential Thomas Kaplan The definition of the fundamental quantity, the chemical potential (c.p.), is confused in the literature, there being at least three distinct definitions in various books and papers. Major differences among them can occur for finite systems. We resolve the situation by arguing that the chemical potential defined by the symbol $\mu$ conventionally appearing in the grand canonical density operator is the uniquely correct definition, the grand canonical ensemble being the only one of the various ensembles usually discussed (microcanonical, canonical, Gibbs, grand canonical) that is appropriate for statistical thermodynamics, whenever the c.p. is physically relevant. The derivation of the zerotemperature limit of this $\mu$ for rather general interactingelectron systems by Perdew et. al.,[1] is discussed and extended. The enormous finitesize corrections (in systems $>>$ a cm$^3$) for one rather common definition of the c.p., found by Shegelski [2] within the standard effective mass model of an ideal intrinsic semiconductor, are discussed. The quantum dot is mentioned as a smallsystem application. \newline 1. J. F. Perdew et. al., Phys. Rev. Lett. \textbf{23}, 1691 (1982); J. F. Perdew, in \emph{Densityfunctional methods in Physics}, edited by R. M. Dreizler and J. da Providencia, Plenum Press, 1985. \newline 2. M. R. A. Shegelski, Solid State Commun. \textbf{38}, 351 (1986); Am. J. Phys. \textbf{72}, 676 (2004). [Preview Abstract] 
Thursday, March 24, 2005 8:24AM  8:36AM 
U23.00003: The thermodynamics of reversible thermoelectric nanomaterials Tammy Humphrey, Heiner Linke Irreversible effects in thermoelectric materials limit their efficiency and economy for applications in power generation and refrigeration. While electron transport is unavoidably irreversible in bulk materials, here we derive conditions under which reversible diffusive electron transport can be achieved in nanostructured thermoelectric materials via the same physical mechanism utilized in the threelevel amplifier (thermally pumped laser) and idealized thermophotovoltaic and thermionic devices. From a broader physical perspective, the most interesting aspect of this work is that it suggests that all of the abovementioned solidstate devices may be unified as a single `type' of heat engine which achieves reversibility when heat transfer via particle exchange between reservoirs is isentropic (but nonisothermal), in contrast to heat engines such as Carnot, Otto or Brayton cycles, which achieve reversibility when heat transfer between the working gas and heat reservoirs is isothermal. [Preview Abstract] 
Thursday, March 24, 2005 8:36AM  8:48AM 
U23.00004: Single Particle Jumps in a Glass: Statistics and History Dependence Katharina VollmayrLee We study a binary LennardJones mixture below the glass transition via molecular dynamics simulations. To investigate the dynamics of the system we define single particle jumps via their single particle trajectories. We find two kinds of jumps: ``reversible jumps'' where a particle jumps back and forth between two or more average positions and ``irreversible jumps'' where a particle does not return to any of its former average positions. For both the irreversible and reversible jumps we present as a function of temperature the number of jumps, jump size and waiting time between jumps. With increasing temperature $T$ particles undergo both more jumps, and the percentage of irreversible jumps versus reversible jumps increases. Similarly the jump size increases with increasing $T$. The distributions of jump lengths and waiting times are in accordance with subdiffusive behavior. Whereas the number of jumping particles is dependent on the history of the system, the jump size and waiting times are independent of the history of the glass. [Preview Abstract] 
Thursday, March 24, 2005 8:48AM  9:00AM 
U23.00005: Step Strains in a Disordered Foam Michael Twardos, Michael Dennin Foams consisting of gas bubbles separated by liquid walls are a unique material system that can exhibit solid like properties under small strains and interesting fluid properties under larger strains including stress fluctuations and intermittent flow. Their nonlinear flow behavior is characterized by a viscosity dependence on shear rate and the emergence of a ``yield stress.'' Foams are also interesting as part of a more general class of materials that can be referred to as ``complex fluids'' (granular systems, emulsions) that have been considered in the theoretical framework of jamming. One question raised in studying foams in particular and complex fluids more generally is what is the fundamental feature (including a length scale and time scale) that most prominently describes the flow behavior of these systems near the jamming transition. What properties are universal? To help answer some of these questions, we will discuss an experiment to probe the mechanical properties of a bubble raft (two dimensional foam) by considering step strains applied to this system and focusing on the system's response (stress drops). [Preview Abstract] 
Thursday, March 24, 2005 9:00AM  9:12AM 
U23.00006: Diffusion in a Rough Energy Landscape Ulrich Zurcher We reexamine Zwanzig's model of diffusion in a rough energy landscape [PNAS (USA) 85, 2029 (1988)]. We interpret the one dimensional coordinate as a mesoscopic degree of freedom of the system. It is shown that the fluctuating potential corresponds to a broken symmetry. The corresponding order parameter is associated with long range elastic stress in the system. We derive a Landautype expression for the free energy of the system from which the activation energy for barrier crossings can be obtained. [Preview Abstract] 
Thursday, March 24, 2005 9:12AM  9:24AM 
U23.00007: Dielectric Susceptibility Studies of the Glass Transition of Glycerol at High Pressure Kyaw Win, Narayanan Menon We have measured the dielectric susceptibility of glycerol as a function of frequency (0.01Hz10kHz), temperature (190K250K) and pressure (09kB). The glass transition temperature $T_g$ increases with increasing pressure, however, the thermal fragility, which measures the rate of approach to $T_g$, is independent of pressure. This result is in contrast to studies based on viscosity measurements which probe a higher frequency range, where it was found that fragility increases with pressure. We have also found that the width of relaxation when plotted as a function of the relaxation frequency is only weakly dependent on pressure within this range. [Preview Abstract] 
Thursday, March 24, 2005 9:24AM  9:36AM 
U23.00008: Glassy Behavior of Interface States in AlAlOxAl Tunnel Junctions Jeremy Nesbitt, Arthur Hebard The complex impedance of a tunnel junction can be modeled as the parallel combination of a resistance, which is exponentially sensitive to barrier parameters, and a frequencydependent complex capacitance, which is dominated by the presence of charge traps at the electrode interfaces. We present a study of the time evolution of these interface states by measuring in vacuum the \textit{insitu }complex impedance of AlAlO$_{x}$Al trilayer structures as a function of age $t$. After a sampledependent settling time, both the resistance and capacitance simultaneously exhibit irreversible logarithmic aging. Application of a dc bias voltage at $t$~=~$t_{0}$ gives rise to a resistance transition (with powerlaw dependence on $t$~~$t_{0})$ to a new aging trajectory with a smaller logarithmic slope. This behavior is correlated with barrier parameters determined from the dependence of the resistance on ``witness'' bias sweeps. By examining the dependence of barrier asymmetry on the sign of the voltage bias, we demonstrate that this glassy system retains memory of the state associated with previously applied bias voltages. * This work is supported by NSF under contract DMR 0404962 [Preview Abstract] 
Thursday, March 24, 2005 9:36AM  9:48AM 
U23.00009: Nanoscopic studies of ferroelectric domain walls in epitaxial perovskite thin films Patrycja Paruch, Thierry Giamarchi, Thomas Tybell, JeanMarc Triscone Understanding the behavior of ferroelectric domain walls (DW) is important for applications using multidomain structures. Microscopic studies of these systems are needed to discriminate between periodic lattice and disorder pinning. Epitaxial perovskite films are an excellent model systems for such studies. Using atomic force microscopy on PbZr$_{0.2}$Ti$_{0.8}$O$_3$ thin films we have investigated the static configuration and subcritical dynamics of ferroelectric DW. Measurements of individual nanoscopic domains showed initial nucleation at the AFM tip, followed by radial DW motion. We have demonstrated this motion to be a creep process with a nonlinear velocity response to electric fields: $v\sim \exp [C/E^\mu]$. The dynamical exponent $\mu$ ranged between 0.51 [1,2]. Independent measurements of DW roughness in these films revealed a power law growth of the relative displacements correlation function $B(L)\sim L^{2\zeta}$ at short length scales L, with a wandering exponent $\zeta \sim 0.26$. Together, these results give an effective DW dimensionality of 2.5. These results cannot be explained by lattice pinning, but agree with calculations for twodimensional elastic interfaces in the presence of randombond disorder and dipolar interactions.\\ 1. Tybell, PRL {\bf 89}, 097601 \\ 2. Paruch, condmat/0411178 [Preview Abstract] 
Thursday, March 24, 2005 9:48AM  10:00AM 
U23.00010: The stochastic dynamics of micron and submicron scale mechanical oscillators Mark Paul, Matthew Clark The stochastic response of micron and submicron scale oscillators of arbitrary geometry immersed in a viscous fluid will be discussed. It will be shown that by using the fluctuationdissipation theorem it is possible to calculate, in a straight forward manner, the stochastic dynamics that would be measured in experiment through deterministic calculations of the fluid and solid equations. This approach is used to investigate the motion of single and multiple oscillators for a variety of experimentally realistic geometries. [Preview Abstract] 

U23.00011: Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet Malcolm Kennett, Claudio Chamon, Leticia Cugliandolo We introduce a lattice model for a classical doped two dimensional antiferromagnet which has no quenched disorder, yet displays slow dynamics similar to those observed in supercooled liquids. We calculate twotime spatial and spin correlations via Monte Carlo simulations and find that for sufficiently low temperatures, there is anomalous diffusion and stretchedexponential relaxation of spin correlations. The relaxation times associated with spin correlations and diffusion both diverge at low temperatures in a subArrhenius fashion if the fit is done over a large temperaturewindow or an Arrhenius fashion if only low temperatures are considered. We find evidence of spatially heterogeneous dynamics, in which vacancies created by changes in occupation facilitate spin flips on neighbouring sites. We find violations of the StokesEinstein relation and DebyeStokesEinstein relation and show that the probability distributions of local spatial correlations indicate fast and slow populations of sites, and local spin correlations indicate a wide distribution of relaxation times, similar to observations in other glassy systems with and without quenched disorder. [Preview Abstract] 
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