Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session S57: Noise-driven Dynamics in Far-from-equilibrium Systems III |
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Sponsoring Units: GSNP DBIO Chair: Luis Bonilla Room: BCEC 256 |
Thursday, March 7, 2019 11:15AM - 11:27AM |
S57.00001: Probing noisy dynamics at the nanometer scale David Haviland, Shan Jolin, Riccardo Borgani When driven by a strong pump, a nonlinear oscillator creates correlations in the frequency domain between signal and idler pairs symmetrically placed about the pump frequency. These correlations result in two-mode squeezing and phase-insensitive amplification of the signal. Not only signals but also noise can be squeezed, leading to measurement sensitivity below the standard limits imposed by thermal or quantum fluctuations. There is currently great interest in demonstrating these effects at the quantum limit, but less attention is paid to the squeezing of thermal noise where there is great potential for practical application. We demonstrate two-mode squeezing in dynamic Atomic Force Microscopy (AFM), where the limiting noise at room temperature is the thermal Brownian motion of the cantilever. Unlike previous work on the mechanical amplification of force, we do not use an 'external' nonlinearity to realize gain. Rather the sample itself is the 'gain medium' which causes a widening of the measurement bandwidth over which dynamic AFM is limited by thermal noise. |
Thursday, March 7, 2019 11:27AM - 11:39AM |
S57.00002: Characterizing Activity in Driven Elastic Networks from the Non-equilibrium Scaling Behaviour Grzegorz Gradziuk, Federica Mura, Chase P. Broedersz Detecting and quantifying non-equilibrium activity is essential for studying complex living systems such as cells. We present a non-invasive approach of measuring activity in a system based on the breaking of time-reversal symmetry. We focus on "cycling frequencies" - the frequencies with which the trajectories of pairs of degrees of freedom circle around in phase space, which is related to the entropy production rate. We test our approach on simple toy-models comprised of elastic networks immersed in a viscous fluid with spatially-varying internal driving. We prove both numerically and analytically that the cycling frequencies obey a power law as a function of distance between the selected degrees of freedom. Moreover, the behavior of the cycling frequencies contains information about the dimensionality of the system and the amplitude of active noise. Finally, we aim to find a mapping between the microscopic properties of a non-equilibrium system and macroscopic observables such as the cycling frequencies by including features such as the active force moments or spatial and temporal correlations of the active noise. |
Thursday, March 7, 2019 11:39AM - 11:51AM |
S57.00003: Electrical autonomous Brownian gyrator Kuan-Hsun Chiang, Chi-Lun Lee, Pik-Yin Lai, Yung-Fu Chen We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the resistors are subject to distinct thermal baths, is identical to that of a Brownian gyrator, as first proposed by Filliger and Reimann [1]. The average gyrating dynamics is originated from the absence of detailed balance due to unequal thermal baths. We look into the details of this stochastic gyrating dynamics, its dependences on the temperature difference and coupling strength, and the mechanism of heat transfer through this simple electronic circuit. Our work affirms the general principle and the possibility of a Brownian ratchet working near room temperature scale. |
Thursday, March 7, 2019 11:51AM - 12:03PM |
S57.00004: Experimental observation of fluctuation loops John Neu, Juan Pablo Gonzalez, Stephen Teitsworth Fluctuation loops arise in the large deviation theory of stochastic dynamical systems. Displacements from a stable critical point to a small destination box about a point many standard deviations away are rare. When they do occur, they closely follow a most probable outward path. The most probable outcome after reaching the destination box is deterministic relaxation back to the stable critical point. The union of the outward and relaxation paths constitutes a fluctuation loop. For linear stochastic dynamics, fluctuation loops can be constructed by simple averaging. Ensemble averaging over forward histories after reaching the destination box obviously recovers the relaxation segment. Less obviously, averaging over back histories prior to reaching the destination box recovers the outbound segment. The characterization of fluctuation loops by averaging means that they can be recovered from experimentally recorded time series of state variables. We demonstrate this for a simple electrical network of two capacitively coupled, noise driven RC circuits. Even when the destinations boxes are not many standard deviations away from the stable critical point, it is striking that clearly resolved fluctuation loops emerge from very noisy data. |
Thursday, March 7, 2019 12:03PM - 12:15PM |
S57.00005: Hydrodynamic Brownian motion and nanoscale transport efficiency in liquids Sean Seyler, Steve Pressé Recent experiments have motivated a reexamination of Brownian motion, as hydrodynamic memory and colored thermal noise arising on short spatiotemporal scales lead to substantially different dynamical behavior. We revisit the problem of particle transport in liquids at low Reynolds number, where we account for the Basset-Boussinesq force and added mass effect induced by unsteady particle motion while reincorporating thermal fluctuations so as to satisfy fluctuation-dissipation. The resulting fluctuating Basset-Boussinesq-Oseen equation is solved numerically using an efficient method based on Markovian embedding, which can simultaneously capture the algebraic decay of the memory kernel and the colored noise spectrum to an arbitrary level of precision. We apply various driving forces to ensembles of submicron spherical particles in different liquids while holding constant the amount of input work; the resulting particle displacements and velocities are analyzed in terms of the magnitude, duration, and shape of different forcing protocols. For each protocol, we compute efficiencies for particle transport—with and without hydrodynamic effects—using the mean displacement and current density as proxies for output work. Implications for subcellular biology and nanofluidics are discussed. |
Thursday, March 7, 2019 12:15PM - 12:27PM |
S57.00006: Operator dynamics in Brownian quantum circuit Tianci Zhou, Xiao Chen We view the operator spreading in chaotic evolution as a stochastic process of height growth. The height of an operator represents its spatial extent and a master equation governs the transition to higher operators. We derive and solve a master equation in a random N -spin model with all 2-body interactions. The mean height, being proportional to the squared commutator, will grow exponentially within log N scrambling time and saturates in a manner of logistic function. We propose that the chaos bound at finite temperature could be due to initial height biased towards the high operators, which has smaller Lyapunov exponent. |
Thursday, March 7, 2019 12:27PM - 12:39PM |
S57.00007: Operator dynamics in chaotic long-range interaction sytems Xiao Chen, Tianci Zhou We use out-of-time-order correlator (OTOC) to diagnose the propagation of chaos in one dimensional long-range power law interaction system. We consider a model called Brownian quantum circuit, which allows us to derive the master equation governing the operator dynamics and therefore transforms the evolution of OTOC to a classical stochastic dynamics problem. We find that the chaos propagation relies on the number of qubits N on each site and the power law exponent α. We use OTOC to define light cone and find that in the small N limit (N=1), there are three light cone regimes as we vary α: (1) a log light cone regime when 1<α<2, (2) a sublinear power law light cone regime when 2<α<4 and (3) a linear light cone regime when α>4. We further study the scaling behaviors of OTOC in the vicinity of light cone. Moreover, we also study the operator growth in the large N limit and find it to be remarkably different. Our result provides a unified physical picture for chaos dynamics in power law interaction system and can be generalized to higher spatial dimensions. |
Thursday, March 7, 2019 12:39PM - 12:51PM |
S57.00008: Anomalous diffusion, infinite measures, and limit distributions in a class of exactly solvable stochastic processes Guenter Radons, Takuma Akimoto, Eli Barkai We consider stochastic processes, piecewise constant in time, which can be viewed as a gapless sequences of statistically independent box functions of duration τ_{i} and height v_{i}. Lengths and heights of the boxes are deterministically coupled, whereas the areas τ_{i}v_{i} are i.i.d. random variables. These processes are closely related to the velocity process of space-time coupled Levy walks [1,2], but can more generally be viewed as a renewal processes, where the life times τ_{i} are not simply drawn from one given distribution, but are determined via a deterministic law by the values v_{i} of a relevant stochastic variable. Despite its simplicity, these processes can show anomalous diffusion, or, more general, anomalous behavior of its moments. The latter can be related either to invariant densities, which are non-normalizable, or, for other parameters, to certain scaling densities. We obtained exact results for these quantities because we were able to derive the exact form of the propagator analytically. In addition, we were able to derive non-trivial exact limit distributions for time-averaged quantities of interest. |
Thursday, March 7, 2019 12:51PM - 1:03PM |
S57.00009: Optimal Finite Time Erasure: A mass transport perspective James Melbourne, Saurav Talukdar, Harish Doddi, Murti Salapaka Landauer’s principle states that the average heat dissipation in a bit erasure is atleast kBT ln 2. Recent experiments approach this bound in an asymptotic manner with respect to time. Meanwhile, in the experimentally relevant case that a single bit memory is modeled as a Brownian particle in a bistable well, developments in non-equilibrium thermodynamics and stochastic control predict larger heat dissipation for finite time erasure, dependent on the Wasserstein transportation distance between the initial and final configurations. Inspired by these considerations, we propose an experimentally feasible finite time erasure protocol which approximates a Wasserstein geodesic. Monte Carlo simulations are used to demonstrate the efficacy of the proposed erasure protocol, comparing energetics against existing erasure protocols and the theoretically optimal bounds. |
Thursday, March 7, 2019 1:03PM - 1:15PM |
S57.00010: Exact solutions of dissipative quantum spin chains using Majorana fermions Naoyuki Shibata, Hosho Katsura The Lindblad equation is the well-known quantum master equation which describes the evolution of open quantum systems. While Lindblad equations have been used in the past mostly to describe few-particle systems in e.g., quantum optics, recent years have witnessed a growing interest in many-body systems in the Lindblad setting. However, very few exact results are available for many-body systems. The main difficulty is that we often need to deal with effective interactions arising from dissipation [1] even when the Hamiltonian itself is reducible to that of a free-particle system. This prevents us from understanding the full dynamics of the system. |
Thursday, March 7, 2019 1:15PM - 1:27PM |
S57.00011: Degree heterogeneity increases the probability of rare events in population networks Michael Assaf, Jason Hindes There is great interest in predicting rare and extreme events in complex systems, and in particular, |
Thursday, March 7, 2019 1:27PM - 1:39PM |
S57.00012: Using a System’s Equilibrium Behavior to Reduce Its Energy Dissipation in Non-Equilibrium Processes Sara Tafoya, Steven J. Large, Shixin Liu, Carlos Jose Bustamante, David Sivak Cells must operate far from equilibrium, utilizing and dissipating energy continuously to maintain their organization and to avoid stasis and death. However, they must also avoid unnecessary waste of energy. Recent studies have revealed that molecular machines are extremely efficient thermodynamically when compared to their macroscopic counterparts. However, the principles governing the efficient out-of-equilibrium operation of molecular machines remain a mystery. A theoretical framework has been recently formulated in which a generalized friction coefficient quantifies the energetic efficiency in non-equilibrium processes. Moreover, it posits that to minimize energy dissipation, external control should drive the system along the reaction coordinate with a speed inversely proportional to the square root of that friction coefficient. Here, we demonstrate the utility of this theory for designing and understanding energetically efficient non-equilibrium processes through the unfolding and folding of single DNA hairpins. |
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