Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session D13: Statistical and Nonlinear Physics: General 
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Sponsoring Units: GSNP Chair: James Dufty, University of Florida Room: D225/226 
Monday, March 21, 2011 2:30PM  2:42PM 
D13.00001: Stability and dynamical properties of CooperShepardSodano compactons Andres Cardenas, Bogdan Mihaila, Fred Cooper, Avadh Saxena Extending a Pade approximant method used recently to study the properties of compactons in the RosenauHyman (RH) equation [see B. Mihaila et al. Phys. Rev. E 81, 056708 (2010)], we study the numerical stability of single compactons of the CooperShepardSodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed several approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton solutions and find they are numerically stable. Similar to the collisions between RH compactons, the CSS compactons reemerge with the same coherent shape when scattered. The time evolution of the smallamplitude ripple resulting after scattering depends on the values of the parameters characterizing the corresponding CSS equation. The simulation of the CSS compacton scattering requires a much smaller artificial viscosity to obtain numerical stability than in the case of RH compacton propagation. [Preview Abstract] 
Monday, March 21, 2011 2:42PM  2:54PM 
D13.00002: Pair Correlations for Charges in a Harmonic Trap Jeffrey Wrighton, James Dufty, Hanno K\"{a}hlert, Torben Ott, Patrick Ludwig, Michael Bonitz A classical system of N identical charges in a harmonic trap exhibits both shell structure and orientational ordering due to Coulomb correlations. The shell structure can be reproduced accurately using approximate correlations from the bulk OCP [1]. Here we report additional relationships between correlations in the trap and those for the bulk OCP: 1) pair correlations calculated without reference to their location in the trap agree with those of the bulk OCP, 2) orientational pair correlations among particles within a shell are represented by those of the bulk OCP, when Euclidean distance is replaced by arc length (qualitative agreement using 3D OCP; quantitative agreement using 2D OCP). At stronger coupling, the correlations induce an ordering within the shells (spherical Wigner crystal). It is shown that the orientational correlations for this phase are described by those for the single sphere Thomson problem, i.e. the Thomson sites represent the ``lattice" for the spherical crystal. Finite temperature effects for this phase are described as well. Research supported by DOE award DEFG0207ER54946, and by the Deutsche Forschungsgemeinschaft via SFBTRR24.\\[4pt] [1] J. Wrighton, J. Dufty, H. Kaehlert, and M. Bonitz, Phys. Rev. E \textbf{80}, 038912 (2009); Contrib. Plasma Phys. \textbf{50}, 2630 (2010). [Preview Abstract] 
Monday, March 21, 2011 2:54PM  3:06PM 
D13.00003: Quasibound state lifetimes and classical periodic orbits in HOCl Alex Barr, Kyungsun Na, Linda Reichl We use a discrete variable representation together with reaction matrix theory to calculate the quasibound states of a Chlorine atom scattering off a diatomic molecule of Hydrogen and Oxygen. The lifetimes of these quasibound states are found to vary over six orders of magnitude in a very small energy window. By examining Husimi distributions for various quasibound states we show that the longestlived quasi bound states are anchored by an island of stability surrounding a stable periodic orbit in the otherwise chaotic classical phase space. This stable periodic orbit, which corresponds to Chlorine rotating around the HO molecule, is responsible for the very long lifetimes of these quasibound states. [Preview Abstract] 
Monday, March 21, 2011 3:06PM  3:18PM 
D13.00004: An Infinite Order Phase Transition Pradeep Kumar, Avinash Khare, Avadh Saxena An infinite order phase transition, in the sense envisioned by Ehrenfest, must show no singularity in any finite (thermal or mechanical) derivative of the free energy. By considering the infinite p limit of a free energy that we have derived for a pth order phase transition, we can derive a Landau type free energy. We will discuss the properties of the free energy and identify the features essential for a description of an infinite order phase transition. These include a logarithmic interaction between the fields and a novel dependence on spatial gradients. Contrary to popular belief, since some symmetry is broken at each finite p order, we submit that an infinite order phase transition does not exclude a symmetry being broken. Restricting to one dimension, we solve for domain wall solutions. Finally we show the relationship between an infinite order phase transition and Tachyon condensation. They are both analyzed as the infinite p limit of a class of p enumerated field theories. The mathematical difference being that the free energy for infinite order transition belongs to a potential that is negative (inverted) of the action for tachyon condensation. [Preview Abstract] 
Monday, March 21, 2011 3:18PM  3:30PM 
D13.00005: First Principles Derivation of Fading Models from Wave Chaos Theory JenHao Yeh Wave chaos is the study of solutions to linear wave equations in situations where the ray dynamics recovered in the classical limit is chaotic. Fading is the observation of variations in signal strength measured at a receiver due to timedependent variations in the propagation or multipath scattering and interference. A quantitative statistical theory of wave chaos  random matrix theory (RMT)  can be applied to predict statistical properties of many quantities, such as the scattering matrix, of a wave chaotic system. Here we started from the statistical model of the scattering matrix [1] to establish a general fading model that includes Rayleigh fading and then combine the RMT fading model with our random coupling model that takes account systemspecific features [24] to build a more general fading model that includes Rician fading. In the high loss limit, our model agrees with the Rayleigh/Rice models, however, it shows deviation in the limit of low loss. We have performed experiments [3,4] to verify the RMT fading model. \\[0pt] [1] http://publish.aps.org/search/field/author/Brouwer\_P\_W (P. W. Brouwer) and http://publish.aps.org/search/field/author/Beenakker\_C\_W\_J (C. W. J. Beenakker), Phys. Rev. B 55, 4695 (1997). [2] James A. Hart, \textit{et al.}, Phys. Rev. E~80, 041109 (2009). [3] JenHao Yeh, \textit{et al}.,~Phys. Rev. E 81, 025201(R) (2010). [4] JenHao Yeh, \textit{et al}.,~Phys. Rev. E 82, 041114 (2010). [Preview Abstract] 
Monday, March 21, 2011 3:30PM  3:42PM 
D13.00006: Quantum statistical mechanics on infinitely ramified fractals Joe P. Chen I present the thermodynamics of identical particles confined in infinitely ramified, exactly selfsimilar fractals, such as the Sierpinski carpet (in 2D) and the Menger sponge (in 3D). Recent results from analysis on fractals have established that the heat kernel associated with the Laplacian on such fractals satisfy, in the shorttime regime, a scaling relation with exponent $d_{\rm S}/2$ (where $d_{\rm S}$ is the spectral dimension) modulated by logperiodic oscillations. I explain how such a scaling affects the partition function, and the resultant thermodynamics associated with blackbody radiation [1], Casimir effect, and electrons in the fractal box. [Preview Abstract] 
Monday, March 21, 2011 3:42PM  3:54PM 
D13.00007: Unified Approach to Quantum and Classical Dualities Emilio Cobanera, Gerardo Ortiz, Zohar Nussinov We discuss a new systematic and algebraic approach to searching for dualities in quantum systems. By associating ``bond algebras'' to quantum Hamiltonians we show how dualities can be characterized, recognized as unitary transformations, and mapped to dualities of classical partition functions. Hence our approach unifies classical and quantum dualities and provides a powerful method for determining exact properties of systems of interest. We show how duality transformations can be used always to eliminate gauge symmetries completely, and present a new duality between the Abelian Higgs model and a generalized Kitaev's extended toric code model in {\it three space dimensions} that illustrate this point. We also show new dualities for $Z_p$) gauge models. [Preview Abstract] 
Monday, March 21, 2011 3:54PM  4:06PM 
D13.00008: Fluctuationinduced forces in strongly anisotropic critical systems M. Burgsm\"uller, H.W. Diehl, M.A. Shpot Strongly anisotropic critical systems have two (or more) correlation lengths $\xi_\alpha$ and $\xi_\beta$ that diverge as nontrivial powers $\xi_\alpha\sim \xi_\beta^\theta\to \infty$ upon approaching criticality. We investigate the effective (Casimirlike) forces that are induced between two confining parallel boundary planes at a distance $L$ by fluctuations in such systems at bulk criticality. Two fundamentally distinct orientations of boundary planes must be distinguished: parallel, for which the planes are parallel to all of the available $1\le m < d$ $\alpha$directions, and perpendicular, for which they are perpendicular to an $\alpha$direction, but parallel to all other $\alpha$ and $\beta$directions. Using a RG approach, we show that universal Casimir amplitudes $\Delta^{BC}_{\,\perp}$, depending on both the largescale boundary condition (BC) at both plates and the type of surface plane orientation, can be introduced to characterize the asymptotic $L$dependence of the critical fluctuationinduced force. This varies as $\mathcal{F}\sim (\partial/\partial L)$$\,\Delta^{BC}_{\,\perp}\,L^{\zeta_{\,\perp}}$, where the proportionality constant is nonuniversal. To corroborate these findings, $O(n)$ $\phi^4$ models with $m$axial Lifshitz points are investigated below their upper critical dimension $d=4+m/2$. Explicit one and twoloop results for $\Delta^{BC}_{\,\perp}$ are presented for both orientations and periodic or Dirichletlike boundary conditions, along with large$n$ results. [Preview Abstract] 
Monday, March 21, 2011 4:06PM  4:18PM 
D13.00009: Multifractality of instantaneous normal modes at mobility edges TenMing Wu In terms of the multifractal analysis, we investigate the characteristics of instantaneous normal modes (INMs) at mobility edges (MEs) of a simple fluid, where the locations of two MEs in the INM spectrum were identified in a previous work (Phys. Rev. E 79, 041105 (2009)). The mass exponents and the singularity spectrum of the INMs are obtained by both the boxsize and systemsize scalings under the typical average. The INM eigenvectors at a ME exhibit a multifractal nature and the multifractal INMs at each ME yield the same results in generalized fractal dimensions and singularity spectrum. Our results indicate that the singularity spectrum of the multifractal INMs agrees well with that of the Anderson model at the critical disorder. This good agreement provides a numerical evidence for the universal multifractality at the localizationdelocalization transition. For the multifractal INMs, the probability density function and the spatial correlation function of squared vibrational amplitudes are also calculated. The relation between probability density function and singularity spectrum is examined numerically, so are the relations between the critical exponents of the spatial correlation function and the mass exponents of the multifractal INMs. All results will be appeared in Phys. Rev. E. [Preview Abstract] 
Monday, March 21, 2011 4:18PM  4:30PM 
D13.00010: Experimental study of memory erasure in a doublewell potential Yonggun Jun, John Bechhoefer We have experimentally demonstrated memory erasure in a timedependent, doublewell potential using a protocol suggested by Dillenschneider and Lutz [PRL 102, 210601 (2009)]. The protocol implements the erasure of information by removing the potential barrier, skewing the potential to one side, and then raising the barrier back. In this context, erasure means that no matter which well the particle started the cycle in, it ends up in a designated well. We implement the potential by placing an overdamped, charged Brownian particle in a feedback trap that uses electrophoresis to generate an arbitrary virtual twodimensional potential. In a large system, Landauer's principle gives a lower bound for the heat dissipated in the erasure of a single bit (kT ln2). In a small system such as ours, thermal fluctuations allow for occasional violations. We quantify such violations as a function of barrier size and show that while averages are consistent with Landauer's principle, the tail of the distribution of dissipation per cyclea fraction of trajectoriesviolates it. [Preview Abstract] 
Monday, March 21, 2011 4:30PM  4:42PM 
D13.00011: Cosmology in One Dimension: Fractal Geometry, Power Spectra and Correlation Bruce Miller, JeanLouis Rouet Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and superclusters suggests that a natural scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so,over what range of scales. Onedimensional models demonstrate that the important dynamics for cluster formation occur in the positionvelocity plane. Here the development of scaling behavior and multifractal geometry is investigated for a family of onedimensional models for three different, scalefree, initial conditions. A possible physical mechanism for understanding the selfsimilar evolution is introduced. It is shown that hierarchical cluster formation depends both on the model and the initial power spectrum. Under special circumstances a simple relation between the power spectrum, correlation function, and correlation dimension in the highly nonlinear regime is confirmed. [Preview Abstract] 

D13.00012: ABSTRACT WITHDRAWN 
Monday, March 21, 2011 4:54PM  5:06PM 
D13.00013: Thermodynamics in a complete description of the Landau diamagnetism S. Curilef, F. Olivares, F. Pennini We analyze some consequences that come from semiclassical measures as the Wehrl entropy and the Fisher information for the problem of a particle in a magnetic field starting from a complete description of the Husimi function. We discuss in the most complete form (three dimensions)[1] some results related to measures in contrast with the incomplete form (two dimensions)[2,3]. The formulation in two dimensions is sufficient unto itself to explain the problem whenever the length of the cylindrical geometry of the system is large enough. Our semiclassical description constitutes a useful framework to illustrate problems related to size effects, role of boundaries and other typical anomalies derived from the size of the system, which are refereed to two parameters as area and length and they explicitly appear in the form of the limiting temperature and magnetic field. In addition, we discuss that the zero temperature can be achieved only if the length of the system size is large enough, otherwise physical properties strongly depend on the size of the system. Moreover, from the quantization of the quantum Hall effect, we have obtained a family of quantized Wehrl entropies.\\[4pt] [1] F. Olivares, et al, PRE \textbf{81} 041134 (2010);\\[0pt] [2] D. Herrera, et al, Eur J Phys \textbf{29} 439 (2008);\\[0pt] [3] S, Curilef, et al, PRB \textbf{71} 024420 (2005). [Preview Abstract] 
Monday, March 21, 2011 5:06PM  5:18PM 
D13.00014: Newtonian trajectories as a tool for quantum dynamics in an electromagnetic field Fons Brosens, Wim Magnus In previous studies, we showed that the classical equations of motion provide a solution to quantum dynamics, if appropriately incorporated in the Wigner distribution function, exactly reformulated in a type of Boltzmann equation. However, this earlier work was limited to scalar potentials. In the presence of an electromagnetic field, we now show that this description in terms of classical paths remains valid, despite the fact that the definition of the Wigner distribution function is not gauge invariant. Some analytical results are also presented. [Preview Abstract] 
Monday, March 21, 2011 5:18PM  5:30PM 
D13.00015: The bond problem with an arbitrary percolation radius is solved! Vladimir Udodov, Mariya Bureeva The results of investigations of main characteristics of a onedimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat) are presented for the problem of bonds and sites. It is shown that for a finitesize system the stability condition is fulfilled while the scaling hypothesis is inacceptable for onedimensional bond problem. The correlation length exponent $\nu $ in a onedimensional problem of bonds has been found to exceed the values of $\nu $ in the problem of sites for equallength chains, and, in general, this exponent was found to be extraordinary large compared to the 2D and 3D cases for ordinary phase transitions in macrosystems. The scaling hypothesis is inapplicable to random (disordered) onedimensional nanostructures containing hundreds of structural elements. The results obtained in this work can be used in modeling hopping conduction in semiconductors at low temperatures and polytype transformations in closepacked crystals. For the first time, using the method of computer simulation, we have solved the bond problem for the model of onedimensional percolation in finitesize systems of tens of nanometers with an arbitrary percolation radius. [Preview Abstract] 
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