Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session X56: Chaos and Nonlinear Dynamics 
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Sponsoring Units: GSNP Chair: Adolfo Del Campo, University of Massachusetts Boston Room: BCEC 255 
Friday, March 8, 2019 8:00AM  8:12AM 
X56.00001: Renormalization Group for Barrier Escape: Crossover to Intermittency David Hathcock, James Patarasp Sethna We develop a critical theory of barrier crossing in overdamped systems with low barriers. Traditional calculations in reactionrate theory typically assume the energy barrier separating two metastable states is much larger than the thermal energy of particles in the system. When the barrier vanishes, however, there is a qualitative change in behavior as the metastable states merge. Instead of escaping over a barrier, particles now slide down a sloping potential. We formulate a simple renormalization group description of this transition and derive the scaling form for the mean escape time with an arbitrary potential and spatially dependent noise. The renormalization group analysis unifies barrier crossing problems with the theory of intermittency, originally used to describe bursts of chaotic dynamics in discrete maps. This correspondence leads to an exact functional expression for the escape time that, in certain limits, recovers the results predicted by reactionrate theory, intermittency theory, and deterministic dynamics. 
Friday, March 8, 2019 8:12AM  8:24AM 
X56.00002: Operator Scrambling and Fermi's Golden Rule Bin Yan, Lukasz Cincio, Wojciech Zurek The outoftimeorder correlator (OTOC) qualifies the scrambling of local operators over the entire system. It has been argued that at early times the OTOC exhibits an exponential growth with a rate bounded above by 2π/β, where β is the inverse temperature. 
Friday, March 8, 2019 8:24AM  8:36AM 
X56.00003: Universal entanglement spectra in random quantum circuits PoYao Chang, Xiao Chen, Sarang Gopalakrishnan, Jed Pixley We will discuss the time evolution of the entanglement spectra in a spin1/2 chain 
Friday, March 8, 2019 8:36AM  8:48AM 
X56.00004: Extreme Decoherence and Quantum Chaos Zhenyu Xu, Luis Pedro GarciaPintos, Aurelia Chenu, Adolfo del Campo We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating klocal interactions. Our findings suggest the use of quantum chaotic systems as a natural testbed for spontaneous wave function collapse models. We further discuss the implications on the decoherence of AdS/CFT black holes resulting from the unitarity loss associated with energy dephasing. 
Friday, March 8, 2019 8:48AM  9:00AM 
X56.00005: Experimental Study of Quantum Graphs With Symplectic Symmetry Lei Chen, Edward Ott, Thomas M Antonsen, Steven Anlage Quantum graphs had been introduced as a powerful tool to study quantum chaos. Graphs with timereversal symmetry (TRS) and broken timereversal symmetry (BTRS), which correspond to the Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE) respectfully, had been previously explored experimentally. We are introducing a microwave network with special design to study the Gaussian symplectic ensemble (GSE) statistics, which may be useful for research in quantum dots with strong spinorbit scattering and other quantum chaotic systems. Two geometrically identical subgraphs with GUE symmetry are constructed from coaxial cables connected by T junctions. BTRS properties are realized by making nodes with circulators. The two subgraphs are connected with two bonds, along which one has phase shift of π, and the other one has zero phase shift. The phase shift π and 0 are achieved by putting short and open circuit connector caps into the bonds respectfully. This trick ensures the graph has an antiunitary symmetry T which squares to 1. Statistical analysis of both experimental data and simulations based on the Random Coupling Model (RCM) for this GSE graph will be presented. 
Friday, March 8, 2019 9:00AM  9:12AM 
X56.00006: Nonlinear wave chaos in superconducting billiards Min Zhou, Thomas M Antonsen, Edward Ott, Steven Anlage The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly overmoded regime. It is of interest to extend the RCM to strongly nonlinear systems. We have studied the statistics of harmonics generated in a billiard by a nonlinear circuit [1] and the case of a billiard with a single nonlinear port, both of which have a pointlike nonlinearity. In this talk, we discuss measurements of the nonlinear Sparameters in superconducting billiards where the nonlinearity is continuously distributed. By taking advantage of the high power (up to +35 dBm) vector network analyzer (VNA), we observe that the Sparameters are power dependent. One billiard is a cutcircle quasi2D microwave cavity which is made of Pbplated copper. The granular Pb material has a dominant nonlinear resistance that manifests in the Sparameters We find the noise from the measurement setup affects the statistics in such a low loss system. Another billiard is the TiN on Si wafer billiard, where TiN is expected to have a dominant nonlinear reactance. We will present some preliminary results for this system. The goal is to study how the RCM can be extended to apply to nonlinear systems. 
Friday, March 8, 2019 9:12AM  9:24AM 
X56.00007: Enhanced Stability and Exceptional Points in Active Photonic Couplers Vassilios Kovanis, Yertay Zhiyenbayev, Constantinos Valagiannopoulos, Yannis Kominis We consider active photonic couplers consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by paritytime or other types of symmetry, there exist finitepower, constantintensity Nonlinear Supermodes, resulting from the balance between gain, loss, nonlinearity, coupling, and dissimilarity. These Nonlinear Supermodes are characterized by the amplitude ratio and the phase difference of the two electric wave fields, which can be tuned to have almost any desired value, by appropriate parameter selection. The asymmetry of the system is shown to result in nonreciprocal dynamics enabling directed power transport functionality. In turn, we systematically investigate the dynamical response of such asymmetric coupler in the context of a set of singlemode equations with gain/loss saturation included. Additionally, we point and map, in the parameter and in the solution space of this photonic structure, a rich set of Exceptional Points, corresponding to nonHermitian degeneracies where two eigenvalues and eigenvectors coalesce. The importance of the Exceptional Points is crucial for the system response under noisy perturbations or other modulations as well as for sensing applications. 
Friday, March 8, 2019 9:24AM  9:36AM 
X56.00008: Unwinding the model manifold: choosing similarity measures to remove local minima in sloppy dynamical systems Benjamin Francis, Mark Transtrum We consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification based on how sensitivities scale at long observation times. We show that for oscillatory models, sensitivities can become arbitrarily large, which implies a high effectivedimensionality on the model manifold. This translates to multimodal fitting problems and stands in contrast to the low effectivedimensionality previously observed in sloppy models with a single fixed point. We define a measure of curvature on the model manifold which we call the winding frequency that estimates the density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can "unwind" the model manifold and give low winding frequencies. This prescription translates the model manifold from one of high effectivedimensionality into the "hyperribbon" structures observed elsewhere. This translation opens the door for applications of sloppy model analysis and model reduction methods developed for models with low effectivedimensionality. 

X56.00009: ABSTRACT WITHDRAWN

Friday, March 8, 2019 9:48AM  10:00AM 
X56.00010: Nucleation of Defect Turbulence in the Twodimensional Complex GinzburgLandau Equation Weigang Liu, Uwe Claus Tauber We numerically investigate nucleation processes in the transient dynamics of the twodimensional complex GinzburgLandau equation towards its "frozen" state with stationary spiral structures. We are interested in the transition kinetics between a random initial configuration and the latter frozen state with a welldefined low density of quasistationary vortices. Nucleation is monitored using the characteristic length between the emerging shock structures. The average nucleation time for different system sizes is measured over many independent realizations to obtain good statistics. An extrapolation method as well as a phenomenological formula are employed to eliminate finitesize effects.The nonzero barrier for the nucleation of single vortex droplets in the extrapolated infinitesize limit suggests that the transition to the frozen state is discontinuous. We also investigate the nucleation of target waves which emerge if a specific spatial inhomogeneity is introduced. A long "fat" tails exists in the distribution of nucleation times in this case, which suggest that the associated transition may be continuous. 
Friday, March 8, 2019 10:00AM  10:12AM 
X56.00011: Thouless and Relaxation Time Scales in ManyBody Quantum Systems Mauro Schiulaz, E. Jonathan TorresHerrera, Lea Santos We study the time scales involved in the relaxation process of isolated quantum manybody systems. Using experimental observables and a realistic manybody quantum model, we unveil three different time scales: a very short time that characterizes the early fast decay of the initial state, and two much longer times that increase exponentially with system size. These are the Thouless time, t_{Th}, and the relaxation time, t_{R}. The Thouless time refers to the point beyond which the dynamics acquire universal features, and relaxation happens when the evolution reaches a stationary state. We show that in chaotic systems, t_{Th}<<t_{R}, while for systems approaching a manybody localized phase, t_{Th} tends to t_{R}. We also compare these results with those for random matrices, and study how selfaveraging properties depend on time scales. 
Friday, March 8, 2019 10:12AM  10:24AM 
X56.00012: Capture and chaotic scattering of a charged particle by a magnetic monopole under a uniform electric field Kou Misaki, Naoto Nagaosa Motivated by the realization of magnetic monopole of Berry curvature by the energy crossing point, we theoretically study the effect of magnetic monopole under a uniform electric field in the semiclassical dynamics, which is relevant to many physical situations such as relaxation through the diabolic point. We found that the competition between the backward scattering by the monopole magnetic field and the acceleration by the electric field leads to the bound state, i.e., capture of a particle near the monopole. Furthermore, the nonlinearity induced by the magnetic monopole leads to the chaotic behavior in the transient dynamics, i.e., the transient chaos. We computed characteristic quantities of the strange saddle which gives rise to the transient chaos, and verified that the abrupt bifurcation occurs as we tune the system parameter toward the parameter region in which the system is integrable. 
Friday, March 8, 2019 10:24AM  10:36AM 
X56.00013: PULSEDYN: Open source code for dynamical simulations of strongly nonlinear systems Rahul Kashyap, Surajit Sen We present PULSEDYN which is an open source C++ code written with the goal of performing highly accurate and late time simulations on strongly and weakly nonlinear chains while requiring minimal effort on the user’s part. PULSEDYN offers a suite of potentials and solvers and simulations and may be set up using a parameter file and running the code provided as an executable. PULSEDYN is also written with an emphasis on modularity, allowing for easy changes to be made to the code. PULSEDYN is available to download from Github and is accompanied by documentation and a detailed user manual [1]. We show standard results reproduced from literature using PULSEDYN for benchmarking purposes. We then use PULSEDYN to demonstrate how a strongly nonlinear FermiPastaUlamTsingou system transitions from quasiequilibrium to the equipartitioned state and verify our results by correctly predicting the exact equilibrium specific heat of the system from the simulated equipartitioned state. 
Friday, March 8, 2019 10:36AM  10:48AM 
X56.00014: The dynamics of the musical saw Petur Bryde, L Mahadevan The musical saw is played by first being bent into an S–curve before it is bowed  this geometry allows for vibration modes that are localized near the point of inflection. To understand this, we consider how the spectrum of a curved plate or beam is controlled by a spatially varying curvature profile. Using a recent geometric interpretation of Andersonlike localization that links the underlying eigenvalue problem and a closely related elliptic problem allows us to determine the conditions for and extent of mode localization and suggests an explanation for the sweet sound of the saw. 
Friday, March 8, 2019 10:48AM  11:00AM 
X56.00015: Thermodynamics of Turing Machines Artemy Kolchinsky, David Wolpert Turing Machines [TMs] are the canonical model of computation. Using results from thermodynamics of computation, we investigate bounds on the amount of work required to perform calculations using TMs. First, we consider the minimal amount of work required to run a given input program on a TM. We also consider the minimal amount of work required to produce a given string as an output of a TM, in analogy to Kolmogorov complexity (which asks about the length of the shortest program needed to produce a given string on a TM). We analyze two ways of implementing a TM, one of which is shown to require less work than any computable implementation. We also show that unlike the Kolmogorov complexity of a string which can be arbitrarily large, the minimal amount of work required to produce a given string is bounded by a constant. 
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