Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session M08: Chaos and Nonlinear Dynamics II: From Quantum to FluidsLive
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Sponsoring Units: GSNP Chair: Alexey Galda, University of Chicago |
Wednesday, March 17, 2021 11:30AM - 11:42AM Live |
M08.00001: Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems Lei Chen, Yan Fyodorov, Steven M Anlage Wigner time delay has been of great interest to the physics community because of its importance in describing the scattering properties of open quantum systems. Defined as energy derivative of the total scattering phase shift, the Wigner time delay measures how long a particle/wave lingers in an interaction region before leaving the system through scattering channels. The statistics of Wigner time delay in the lossless limit has been well studied by theorists, but relatively little research has been done for the case when loss or decoherence is present. Here we introduce a complex generalization of Wigner time delay by carefully considering the effects of introducing loss into the system. Through a series of experiments on microwave analogs of quantum graphs and billiards in which we have precision control of the loss strength inside the system, we demonstrate the evolution of the complex Wigner time delay spectrum along with the migration of the scattering matrix poles. We demonstrate experimentally and numerically that the complex Wigner time delay can be used as a practical counter of the imaginary parts of the scattering matrix poles. |
Wednesday, March 17, 2021 11:42AM - 11:54AM Live |
M08.00002: Chaos and integrability in non-unitary Kraus quantum circuits Lucas Sá, Pedro Ribeiro, Tankut Can, Tomaz Prosen Local quantum circuits have become an important paradigm of many-body physics, particularly due to the ability to simulate them by emerging quantum computing facilities. While much is already known about unitary and projective-measurement circuits, it is also of interest to extend their study to the discrete-time Kraus map representation of completely positive quantum dynamics. We do this in two complementary settings: we model chaotic circuits by random Kraus circuits [1] and introduce the Trotterizattion of the Hubbard model at imaginary interaction strength as a paradigmatic integrable non-unitary circuit [2]. |
Wednesday, March 17, 2021 11:54AM - 12:06PM Live |
M08.00003: Private free-space communications based on chaos synchronization of mid-infrared quantum cascade laser light Olivier Spitz, Andreas Herdt, Jiagui Wu, Chee Wei Wong, Wolfgang Elsässer, Frédéric Grillot Free Space Optics (FSO) is a growing technology offering higher bandwidth with fast and cost-effective deployment compared to fiber technology. This work demonstrates private free-space communication with quantum cascade lasers (QCLs). The secret message is encoded into a chaotic waveform so that the information is hard for an eavesdropper to extract [1]. Chaos-based transmissions in FSO are fundamentally restricted by atmospheric phenomena (e.g., turbulence, fog or scattering). Thus, the operating wavelength is a key parameter that has to be chosen wisely to reduce the impact of the environmental parameters. In this context, QCLs are relevant semiconductor lasers because their optical wavelength lies within mid-infrared domains where the atmosphere is highly transparent [2]. The simplest way to generate a chaotic optical carrier from a QCL is to feed back part of its emitted light into the device after a certain time delay [3], beyond which chaos synchronization between the drive and the response QCLs occurs. |
Wednesday, March 17, 2021 12:06PM - 12:18PM Live |
M08.00004: Experimental Observation of Chaos and Chimera in rf SQUID Metamaterials Jingnan Cai, Tamin Tai, Steven M Anlage Rf SQUIDs have been established as viable building blocks for microwave frequency metamaterials [1,2]. The nonlinearity and nonlocal coupling of rf SQUID metamaterials in particular endows them with interesting dynamical properties, such as chaos and chimera states, both of which have been studied extensively by theorists in the context of rf SQUID metamaterials [3,4,5]. |
Wednesday, March 17, 2021 12:18PM - 12:30PM Live |
M08.00005: Chimeras on a seesaw Yuanzhao Zhang, Zachary G Nicolaou, Joseph Hart, Rajarshi Roy, Adilson E Motter Chimera states are symmetry-broken states with coexistence of coherence and incoherence. I will describe a class of new chimera states that is both robust and fragile to noise. Such chimeras are robust to noise in the sense of attracting almost all initial conditions, and they are fragile to noise because arbitrarily small noise can qualitatively change the long-term dynamics (by inducing irregular switching between the coherent and incoherent clusters). I will highlight an unexpected power law that emerges from this noise-induced switching, which contrasts with the exponential scaling observed in typical stochastic transitions and points to a fundamentally new switching mechanism. |
Wednesday, March 17, 2021 12:30PM - 12:42PM Live |
M08.00006: Dissipative nonequilibrium synchronization of topological edge states via self-oscillation Christopher Wayne Wächtler, Victor M. Bastidas, Gernot Schaller, William John Munro The interplay of synchronization and topological band structures with symmetry protected midgap states under the influence of driving and dissipation is largely unexplored. Here we consider a trimer chain of electron shuttles, each consisting of a harmonic oscillator coupled to a quantum dot positioned between two electronic leads. Each shuttle is subject to thermal dissipation and undergoes a bifurcation towards self-oscillation with a stable limit cycle if driven by a bias voltage between the leads [1]. By mechanically coupling the oscillators together, we observe synchronized motion at the ends of the chain, which can be explained using a linear stability analysis [2]. Because of the inversion symmetry of the trimer chain, these synchronized states are topologically protected against local disorder. Our results open another avenue to enhance the robustness of synchronized motion by exploiting topology. |
Wednesday, March 17, 2021 12:42PM - 12:54PM Live |
M08.00007: Nonequilibrium System Behavior Associated with Nonchaotic Barrier Yu Qiao, Rui Kou, Zhaoru Shang We report the Monte Carlo simulation result of a Billiard-type model system. Two large ergodic and chaotic areas are separated by a narrow nonchaotic barrier, referred to as the spontaneously nonequilibrium dimension (SND). The large areas have different heights in a gravitational field. In-plane pressure does work to the lower “plain” when the plain area varies, and gravitational force does work to the upper “plateau” when the plateau height changes. Associated with the local nonchaoticity, the particle density ratio across the SND is spontaneously in a non-Boltzmann form, and the cross-influence of the thermally correlated thermodynamic driving forces becomes asymmetric. As a result, in an isothermal cycle, the overall produced work is greater than the overall consumed work, which cannot be described in the conventional framework of statistical mechanics. A similar effect may be achieved without changing the plateau height, if the plateau-plain border is switchable. SND is not Maxwell’s demon. Its operation does not require specific knowledge of system microstate and therefore, the explanation of the system performance should be unrelated to the physical nature of information. |
Wednesday, March 17, 2021 12:54PM - 1:06PM Live |
M08.00008: Spectral Form Factors from EFTs and Hydrodynamics Michael Winer Spectral form factors (SFFs) are an important diagnostic of level repulsion in chaotic systems. Level repulsion can be supressed (and the SFF enhanced) when the system posesses additional symmetries. We investigate how the SFF behaves when these symmetries are broken. We find a result that transitions between the symmetric and nonsymmetric results. We then specifically investigate hydrodynamic systems, which have approximate conservation laws at every point. Our results give rise to novel quantum field theories, as well as reproducing established results in the case of simple diffusion. |
Wednesday, March 17, 2021 1:06PM - 1:18PM Live |
M08.00009: Sloppy Model Analysis near Bifurcations Christian Anderson, Mark Transtrum In dynamical systems, bifurcations occur when a small change in parameter values results in an obvious topological change in system behavior. They are useful for identifying "tipping points" between qualitatively different types of behaviors, such as phase transitions in matter or from regulated to cancerous cellular pathways. Bifurcations are classified by the nature of the topological change in phase space, with classes being typified by one of only a few "normal forms", indicating that only a few parameters are responsible for driving a system through a bifurcation. Sloppy models provide a framework for identifying relevant parameters in a data-driven way. We apply sloppy model analysis to several dynamical systems near their bifurcations. We show that after an appropriate coarse-graining procedure, sloppy model analysis is able to correctly identify the bifurcation parameters. This suggests that sloppy model analysis can be used to identify the relevant control knobs in multi-parameter models of complex dynamical systems in a data-driven way. |
Wednesday, March 17, 2021 1:18PM - 1:30PM Live |
M08.00010: Towards a renormalization group theory of spontaneous stochasticity in fluid turbulence. Gregory Eyink, Dmytro Bandak Spontaneous stochasticity is the phenomenon of intrinsic unpredictability in nearly singular systems with weak noise. Although conjectured to be ubiquitous in Nature, only relatively recently has it been understood in detail for Lagrangian fluid particles in turbulent flows. The phenomenon of spontaneous stochasticity is associated with a breakdown of uniqueness of solutions and underlies many fundamental and universal aspects of turbulence such as unpredictability beyond chaos, enhanced mixing, and anomalous dissipation. As such a renormalization group account of spontaneous stochasticity would be desirable. To this end, based on the analogy with zero-temperature phase transitions, we provide a renormalization group analysis of a minimal model that displays spontaneous stochasticity, characterizing the domains of attraction of each fixed point, and deriving the universal approach to the fixed points as a singular large-deviations scaling. We present numerical simulations that verify our theoretical predictions, and discuss wider applicability of the method to more realistic models of turbulence. |
Wednesday, March 17, 2021 1:30PM - 1:42PM Live |
M08.00011: Rare events in the transition to turbulence in shear flows Sébastien Gomé, Laurette S Tuckerman, Dwight Barkley Transition to turbulence in shear flows is characterized by intermittent laminar-turbulent patterns that statistically proliferate or collapse depending on the Reynolds number. In pipe, channel or plane Couette flow, turbulence either decays to an absorbing state or proliferates via a process known as splitting. Both are effectively memoryless processes associated with large mean first passage times. The lifetimes depend super-exponentially on the Reynolds number and lead to crossing Reynolds number above which proliferation is more likely than decay. We apply a rare event algorithm, adaptative multi-level splitting (AMS), to the deterministic Navier-Stokes equations to study the transition paths and estimate large time scales that are currently out of reach for direct numerical simulations. Trajectories are selected via an importance function that describes the distance of a flow state to the one-band or two-band attractor. Splitting events approach a most-probable pathway or instanton which paves the way for an out-of-equilibrium description of transition to turbulence. Pathways are intrinsically linked with nucleation processes that approach and leave an edge state in the phase space. |
Wednesday, March 17, 2021 1:42PM - 1:54PM Live |
M08.00012: Many-body level statistics of quantum chaos Yunxiang Liao, Amit Vikram, Victor Galitski In classical systems, chaos is usually diagnosed by the strong sensitivity of trajectories to the initial conditions, whereas in quantum systems, such an indicator is served by the energy level statistics instead. While there has been a large number of studies about the level statistics of single-particle chaotic models, much remains unknown for many-body quantum chaos. We first consider a system of noninteracting fermions populating levels of a random matrix ensemble, and find that, apart from an early time slope, its spectral form factor also exhibits an exponential ramp and a plateau which reflect the repulsion between two distant many-body levels. Using a field theoretical approach, we show that this ramp originates from Goldstone modes caused by the spontaneous breakdown of a SU(2) symmetry. In the presence of interactions, these Goldstone modes acquire a mass, leading to the suppression of the exponential ramp. |
Wednesday, March 17, 2021 1:54PM - 2:06PM Live |
M08.00013: Ground state and elementary excitations of disordered Gross-Pitaevskii lattices Yagmur Kati, Mikhail V. Fistul, Alexander Yu. Cherny, Sergej Flach We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of disorder. We obtain analytical expressions for the thermodynamic properties of the ground state, i.e. the chemical potential and the participation number density, and compare them with direct numerical calculations. For small ground state density, we identify a Lifshits regime where disorder dominates over the interactions. For large ground-state density, the interaction dominates and screens the disorder. The fluctuations above the ground state yield Bogoliubov modes (BM). We compute their localization properties by measuring participation numbers and localization length. The localization length diverges at zero energy. In the strong interaction regime, a novel finite energy BM anomaly develops with a strong increase of localization length. |
Wednesday, March 17, 2021 2:06PM - 2:18PM Live |
M08.00014: Emergent universal statistics in nonequilibrium systems with scale selection Vili Heinonen, Pedro Saenz, Jonasz Slomka, Keaton Burns, Jorn Dunkel Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their dynamics poses major conceptual and practical challenges due to the violation of energy conservation laws. Here, we investigate experimentally and theoretically the statistics of prototypical nonequilibrium systems in which inherent length-scale selection mechanisms confine the dynamics near a known hypersurface. Guided by the spectral analysis of field energies, we discovered generic conditions under which symmetry arguments predict emergent universal statistics even far from equilibrium. We confirmed this prediction in experimental observations of Faraday surface waves on water, and in quantum chaos and active turbulence simulations. Our results indicate that pattern dynamics and transport in driven physical and biological matter can often be described through monochromatic random fields, thus pointing a path to a unified statistical field theory of nonequilibrium systems with length-scale selection. |
Wednesday, March 17, 2021 2:18PM - 2:30PM Live |
M08.00015: Multiscale differential analysis and modeling of one-dimensional fast acoustic streaming Jeremy Orosco, James R Friend Classical modeling of acoustically-driven flows relies almost exclusively on formal expansions about the smallness of the resulting streaming flow in relation to the driving particle velocity---a condition commonly referred to as ``slow streaming.'' This renders tractable the highly nonlinear governing equations in numerical and analytical settings. In contrast, the direction of modern microacoustofluidics research dictates that this order of magnitude separation assumption is not generally valid---in extremal systems, traditional perturbation approaches may fail to properly extract the dynamics of interest. We describe a theoretical approach that affords the user greater generality through its articulation and direct exploitation of the concomitant spatiotemporal scale disparities via multiscale differential operations. The method is applied to a one-dimensional problem of semiinfinite extent defined by particle and streaming velocities possessing similar magnitudes---the ``fast streaming'' condition. The compressible Navier-Stokes equations are solved in an approximate successive manner and the acoustic and streaming field equations are obtained. The steady state of the latter is solved analytically and a comparative analysis is undertaken with respect to the classical theory. |
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