Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Z16: General Statistical and Nonlinear Physics II |
Hide Abstracts |
Room: 401 |
Friday, March 7, 2014 11:15AM - 11:27AM |
Z16.00001: Non-adiabatic effect on quantum pumping Chikako Uchiyama We study quantum pumping for an anharmonic junction model which interacts with two kinds of bosonic environments. We provide an expression for the quantum pumping under a piecewise modulation of environmental temperatures with including non-adiabatic effect under Markovian approximation. The obtained formula is an extension of the one expressed with the geometrical phase(Phys. Rev. Lett. {\bf 104},170601 (2010)). This extension shows that the quantum pumping depends on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequencies of spectral density other than the conditions of modulation. We clarify that the pumping current including non-adiabatic effect can be larger than that under the adiabatic condition. This means that we can find the optimal condition of the current by adjusting these parameters. (The article has been submitted as http://arxiv.org/submit/848201 and will be appeared soon.) [Preview Abstract] |
Friday, March 7, 2014 11:27AM - 11:39AM |
Z16.00002: Robustness of quantum multifractality Bertrand Georgeot, R\'emy Dubertrand, Ignacio Garcia-Mata, Olivier Giraud, Gabriel Lemari\'e, John Martin Several models where quantum wave functions display multifractal properties have been recently identified. In the quantum chaos field, they correspond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. These multifractality properties lead to particular transport properties and appear in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allow to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with unprecedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of small perturbations. We identify two distinct processes of multifractality destruction according to the type of perturbation, and specify a range of parameters where multifractality could indeed be observed in physical systems in presence of imperfections. [Preview Abstract] |
Friday, March 7, 2014 11:39AM - 11:51AM |
Z16.00003: The ``Quantized Intrinsically Localized Modes" of a three-dimensional Lattice Derya Kanbur, Peter Riseborough The low-energy Intrinsically Localized Modes (ILMs) of a cubic lattice with nearest-neighbor interactions and quartic anharmonicity are examined using the Ladder Approximation.Due to the symmetry of the lattice and the isotropic nature of the anharmonic interaction,the ILMs are characterized by an intrinsic spin corresponding to either $S=0$ or $S=2$ as well as by their spatial symmetries.The lowest energy ILMs form preferentially for center of mass momenta at which several van-Hove singularities coalesce at the upper edge of the (non-interacting) two-phonon continuum.For $T=0$ and interactions larger than the critical value,the ILMs form above the top of the two-phonon continuum near the preferred values of $\underline{q}$,but fall into the continuum as $\underline{q}$ is shifted further away from the optimal value of $\underline{q}$.The critical value of the anharmonic interaction is found to be reduced for non-zero temperatures.The results are compared with experimental results on NaI. [Preview Abstract] |
Friday, March 7, 2014 11:51AM - 12:03PM |
Z16.00004: Elastic wave propagation in the presence of linear and nonlinear dispersive mechanisms Romik Khajehtourian, Mahmoud Hussein The introduction of nonlinear and dispersive effects alters the dispersion of elastic waves in a solid medium. In this work, we derive an exact dispersion relation for longitudinal elastic wave propagation in a one-dimensional homogeneous thin rod in the presence of both linear and nonlinear dispersive mechanisms. Our amplitude- and radius-dependent exact dispersion relation contains the effects of finite strain, specifically Green-Lagrange strain, as well as lateral inertia. In general, the nonlinearity tends to steepen the waveform since large-amplitude waves are able to catch up with slower low-amplitude waves while the dispersion widens the waveform since large-wavelength waves cannot catch up with faster small-wavelength waves. The dispersion relation presented in this work provides information on both these mechanisms which may be used to elucidate the interplay between the waveform narrowing and widening effects due to nonlinearity and dispersion, respectively. A discussion is provided on the implications of the present analysis on elucidating the properties of shock and solitary waves. [Preview Abstract] |
Friday, March 7, 2014 12:03PM - 12:15PM |
Z16.00005: Utilizing nonlinearity of transistors for reconfigurable chaos computation William Ditto, Behnam Kia A VLSI circuit design for chaos computing is presented that exploits the intrinsic nonlinearity of transistors to implement a novel approach for conventional and chaotic computing circuit design. In conventional digital circuit design and implementation, transistors are simply switched on or off. We argue that by using the full range of nonlinear dynamics of transistors, we can design and build more efficient computational elements and logic blocks. Furthermore, the nonlinearity of these transistor circuits can be used to program the logic block to implement different types of computational elements that can be reconfigured. Because the intrinsic nonlinear dynamics of the transistors are utilized the resulting circuits typically require fewer transistors compared to conventional digital circuits as we exploit the intrinsic nonlinearity of the transistors to realize computations. [Preview Abstract] |
Friday, March 7, 2014 12:15PM - 12:27PM |
Z16.00006: Optical Asymmetry Induced by PT-symmetric Nonlinear Fano Resonances Nicholas Bender, Fakroddin Nazari, Hamidreza Ramezani, Mohammad Moravvej-Farshi, Demetrios Christodoulides, Tsampikos Kottos We introduce a new type of Fano resonances, realized in a photonic circuit which consists of two nonlinear PT-symmetric micro-resonators side-coupled to a waveguide, which have line-shape and resonance position that depends on the direction of the incident light. We utilize these features in order to induce asymmetric transport up to 47 dBs in the optical C-window. Our set-up requires low input power and does not compromise the power and frequency characteristics of the output signal. [Preview Abstract] |
Friday, March 7, 2014 12:27PM - 12:39PM |
Z16.00007: Time Reversal Experiments in Chaotic Cavities Bo Xiao, Jen-Hao Yeh, Thomas Antonsen, Edward Ott, Steven Anlage Wave focusing through a strongly scattering medium has been an intriguing topic in the fields of optics, acoustics and electromagnetics. By introducing the time reversal technique, prior knowledge about each transmission channel is no longer needed since the step of sending waves through the medium measures this information. Many approaches have been explored to achieve better focusing quality, which is influenced by several factors, such as the propagation loss. We present a method to focus electromagnetic wave at an arbitrary location in ray-chaotic billiards or cavities using the time reversal technique. First, a ray-tracing algorithm calculates orbit information from knowledge of the cavity geometry. We use this information to generate a synthetic signal, which is then sent into the cavity as if it's the time reversed signal in the traditional time-reversal scheme. This method tries to obtain channel information numerically but has limited accuracy due to the loss, the coupling, the mode density, and the existence of chaotic. We discuss the effects of these factors by presenting experimental results on a low-loss superconducting cavity, changing the ports(to modify coupling) and frequency range(to vary the mode density), and modifying the cavity to obtain smaller Lyapunov exponents and thus longer Ehrenfest times to vary the time over which the semi-classical approximation is valid. [Preview Abstract] |
Friday, March 7, 2014 12:39PM - 12:51PM |
Z16.00008: Matched Bipartite Digraph Representation of Generalized Dynamical System Formed by One-way Barriers John Li, John Mahoney, Kevin Mitchell We studied a dynamical system with stable and unstable manifolds that behave as one-way barriers, instead of separatrices in traditional dynamical system that are two-way barriers. This asymmetry gives rise to a richer dynamical behavior such as the overlapping of basins of attraction. The recently developed \emph{Burning Invariant Manifold} (BIM) theory took a dynamical system approach to understand front propagation in Advection-Reaction-Diffusion systems, which have BIMs as the one-way barriers. Through numerical simulations under BIM theory, we found that although both unstable and stable BIMs are one-way barriers, unstable BIMs are the ones that we can experimentally observe the fronts converging onto, and the stable BIMs act as the basin boundaries. We further hypothesized a duality relation between the stable and unstable BIMs. Under the duality hypothesis, we developed a mechanism of the behavior of the system by reducing it back to a traditional system based on topology, and we found a simplification of the system by to summarize the topological information into a Matched Bipartite directed graph (MB digraph). [Preview Abstract] |
Friday, March 7, 2014 12:51PM - 1:03PM |
Z16.00009: The Elusive Present: Hidden Past and Future Correlation and Why We Build Models Pooneh Mohammadiara Markov models assume that the present encodes all of a process's history. This is almost never the case if one randomly samples structured processes. So, how does this failure come about? How do measurements encode the past? And, how many are needed to capture correlations between the past and future? Here, we show how much information can be extracted from the past without having any information about the present. We show how to quantify this and then draw out the consequences. The most important of which is that when present hides past-future correlation we must build models. [Preview Abstract] |
Friday, March 7, 2014 1:03PM - 1:15PM |
Z16.00010: The Role of Partial Enthalpy in Thermal Conductivity Calculations for Nanofluids Matthew Edwards, John Shelton Over the past decade, reports of significantly enhanced thermal conductivity in solutions of nanoscale particles (nanofluids) have elicited a great deal of interest due to the large number of applications for efficient heat transfer fluids. A common method for calculating the thermal conductivity of a nanofluid uses the autocorrelation of the microscopic heat flux (Green-Kubo formalism), which contains a correction for the net transport of enthalpy due to species diffusion. The partial enthalpy component of the correction term cannot be found from microscopic quantities and is often approximated by the partitioned enthalpy. Using NPT molecular dynamics simulations over a wide range of interaction energies, we show that this approximation leads to spurious enhancements with magnitudes similar to those reported in the literature. The discrepancy arises because the partitioned enthalpy neglects the change in fluid-fluid interaction enthalpy which occurs around solid particles; in systems with strong fluid-solid interactions this can be a substantial portion of the total enthalpy. This work suggests that the standard method for calculating thermal conductivity in nanofluids may be invalid and that actual conductivity enhancements are comparable to those predicted by Maxwell's theory. [Preview Abstract] |
Friday, March 7, 2014 1:15PM - 1:27PM |
Z16.00011: Kramers-Wannier duality applied to the boolean satifiability problem Joe Mitchell, Benjamin Hsu, Victor Galitski Kramers-Wannier duality, first considered in 1941, is an exact technique used in statistical mechanics to relate two models together through an order-disorder transformation, and thereby study their structure and critical phenomena. The boolean satisfiability problem is one of the most important problems in computer science, specifically complexity theory; it is the first proven NP-complete problem. Using a mapping to a multi-spin Ising model in the limit of zero temperature, we present an application of Kramers-Wannier duality to this problem. This results in a novel relationship between solving the boolean satisfiability counting problem and a different computational problem: listing the non-negative solutions to a particular system of linear integer equations. This mapping relates the complexity of the two problems. We discuss the generality of Kramers-Wannier duality and its possible application to other computational problems. [Preview Abstract] |
Friday, March 7, 2014 1:27PM - 1:39PM |
Z16.00012: Full counting statistics and the Edgeworth series for matrix product states Yifei Shi We consider full counting statistics of spin in matrix product states. In particular, we study the approach to gaussian distribution for magnetization. We derive the asymptotic corrections to the central limit theorem for magnetization distribution for finite but large blocks in analogy to the Edgeworth series. We also show how central limit theorem like behavior is modified for certain states with topological characteristics such as the AKLT state. [Preview Abstract] |
Friday, March 7, 2014 1:39PM - 1:51PM |
Z16.00013: Emergent Newtonian dynamics and the geometric origin of mass Luca D'Alessio, Anatoli Polkovnikov We consider an arbitrary many-body system with possibly infinitely many degrees of freedom interacting with few macroscopic parameters which are allowed to slowly change in time. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. By extending the Kubo linear response theory to such setups we derive the dynamics of the macroscopic d.o.f. which takes the form of the emergent Newton's second law (force is equal to the mass times acceleration) with an extra dissipative term. We find the microscopic expression for the mass tensor relating it to the non-equal time correlation functions in equilibrium. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini-Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion and geometry. [Preview Abstract] |
Friday, March 7, 2014 1:51PM - 2:03PM |
Z16.00014: ABSTRACT WITHDRAWN |
Friday, March 7, 2014 2:03PM - 2:15PM |
Z16.00015: News and views in discontinuous phase transitions Jan Nagler Recent progress in the theory of discontinuous percolation allow us to better understand the the sudden emergence of large-scale connectedness both in networked systems and on the lattice. We analytically study mechanisms for the amplification of critical fluctuations at the phase transition point, non-self-averaging and power law fluctuations. A single event analysis allow to establish criteria for discontinuous percolation transitions, even on the high-dimensional lattice. Some applications such as salad bowl percolation, and inverse fragmentation are discussed. [Preview Abstract] |
Friday, March 7, 2014 2:15PM - 2:27PM |
Z16.00016: Topological Properties of Combinational Logic Functions for Very Large Scale Integrated Circuits Elizabeth Hiteshue, Kelsey Irvin, Mary Lanzerotti, Graziano Vernizzi, Joseph Kujawski, Allan Weatherwax This talk presents topological properties of combinational logic functions implemented with basic logic gates. Combinational logic can be implemented in very large scale integrated circuits, including high-performance microprocessors. Prior work has produced an historically-equivalent (HE) interpretation of Mr. E. F. Rent's 1960 memos for today's complex circuitry, an application to modern microprocessors [1-5], and topological constraints for electronic circuits [6]. This talk will examine combinational logic blocks which may exhibit different connectivity and will evaluate their topological properties.\\[4pt] References: [1] B. Landman and R.Russo, IEEE Trans. Comput., vol. C-20, pp. 1469-1478, 1971; [2] M. Lanzerotti, G. Fiorenza, R. Rand, IBM Jnl. Res. and Develop., vol. 49, pp. 777-803, 2005; [3] M. Lanzerotti, G. Fiorenza, and R. Rand, IEEE Trans. VLSI Syst., vol. 12, pp. 1330-1347, 2004; [4] D. Stroobandt, IEEE Solid-State Circuits Mag., vol. 2, issue 1, pp. 21-27, 2010; [5] M. Lanzerotti, G. Fiorenza, R. Rand, 2011 Proc. APS March Mtg, Dallas, TX, 2011; [6] G. Vernizzi, M. Lanzerotti, J. Kujawski, A. Weatherwax, ``Topological Constraints for E. F. Rent's Work on Microminiature Packaging and Circuitry,'' IBM Jnl. Res. and Dev., in press. [Preview Abstract] |
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