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 Y16: Trapping, Escape, Dissipation and TransitionsLive
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Sponsoring Units: GSNP Chair: Eric Corwin, University of Oregon |
Friday, March 19, 2021 11:30AM - 11:42AM Live |
Y16.00001: An effective one dimensional approach to calculating mean first passage time in multi-dimensional potentials Thomas Gray, Ee Hou Yong Thermally-activated escape processes in multi-dimensional potentials are of interest to a variety of fields, so being able to calculate the rate of escape -- or the mean first-passage time (MFPT) -- is important. Unlike in one dimension, there is no general, exact formula for the MFPT. Langer's formula, a multi-dimensional generalization of Kramers' one-dimensional formula, provides an approximate result when the barrier to escape is large. Kramers' and Langer's formulae are related to one another by the potential of mean force (PMF). We build on this result by using the PMF in the exact, one-dimensional expression for the MFPT. Our model offers better agreement with Brownian dynamics simulations than Langer's formula, though discrepancies arise when the potential becomes less confining along the direction of escape. When the energy barrier is small our model offers significant improvements upon Langer's theory. Finally, the optimal direction along which to evaluate the PMF no longer corresponds to the unstable mode at the saddle point. |
Friday, March 19, 2021 11:42AM - 11:54AM Live |
Y16.00002: Fractional Brownian Motion in Confined Geometries Samuel Halladay, Thomas Vojta Fractional Brownian motion (FBM) is a Gaussian stochastic process with memory: the increments (steps) are long-range correlated or anticorrelated in time. When allowed to propagate in a confined geometry with reflecting walls, particles exhibiting FBM tend to accumulate at the domain’s boundaries (if the steps are positively correlated) or near the center of the domain (if the steps are negatively correlated). It has been conjectured that, in a confined geometry, the probability density at the boundary will vary as P(x) ~ xκ, where x is the distance from the wall. We confirm this prediction by performing large-scale numerical simulations of reflected FBM in confined geometries of one, two, and three dimensions. In addition, we measure the exponent κ for each geometry and determine its dependence on the anomalous diffusion coefficient α [1]. |
Friday, March 19, 2021 11:54AM - 12:06PM Live |
Y16.00003: Directed Percolation and Numerical Stability of Simulations of Digital MemComputing Machines Yuan-Hang Zhang, Massimiliano Di Ventra Digital MemComputing Machines (DMMs) are a novel, non-Turing class of machines designed to solve combinatorial optimization problems. They can be physically realized with continuous-time, non-quantum dynamical systems with memory, whose ordinary differential equations (ODEs) can be numerically integrated on modern computers. Solutions of many hard problems have been reported by numerically integrating the ODEs of DMMs, showing substantial advantages over state-of-the-art solvers. Using 3-SAT with planted solutions as an explicit example, we show that, despite the stiffness of these ODEs, our simulations are robust as long as the integration scheme preserves the critical points of the ODEs, and an "unsolvable-solvable transition" is observed when decreasing the integration time step Δt near a critical Δtc. To explain these results, we model the dynamical behavior of DMMs as a directed percolation of the state trajectory in the phase space in the presence of noise. This point of view clarifies the reasons behind their numerical robustness and provides an analytical understanding of the unsolvable-solvable transition. These results land further support to the usefulness of DMMs in the solution of hard combinatorial optimization problems. |
Friday, March 19, 2021 12:06PM - 12:18PM Live |
Y16.00004: Dynamics of an impurity in a finite temperature Bose-Einstein condensate Jonas Rønning, Audun Skaugen, Emilio Hernández-García, Cristóbal López, Luiza Angheluta Superfluidity of zero-temperature BECs is the exotic property of dissipationless flows below a critical velocity, also known as the Landau criterion. This implies that any flow obstacle or impurity will experience vanishing drag below this critical velocity. Energy dissipation kicks in at velocities above the critical one, due to the formation of elementary excitations. In this talk we consider the dissipation mechanism and inertial effects of a 2D BEC at finite temperature in the present of an impurity. Analytical expressions are obtained for the forces on the impurity in the limit of a weakly-coupling. These expressions are compared to the analogues classical hydrodynamical forces and verified by numerical simulations. For non-steady flows the force is time dependent and dominated by inertial effects, which is analogues to the inertial force that acts on solid particles in a classical fluid. For steady flows the force is dominated by a self-induced drag, which doesn’t vanish below a critical velocity. At low velocities this is caused by the energy dissipation through interactions of the condensate with the thermal cloud, and it is analogous to the classical Stokes’ drag. There still exists a critical velocity for which the drag is dominated by the acoustic excitations. |
Friday, March 19, 2021 12:18PM - 12:30PM Live |
Y16.00005: Calculation of the configurational energy density of states for Li0.5La0.5TiO3 utilizing first principles optimizations and a new Wang and Landau algorithm variant. Jason Howard In this work a new variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is presented and applied to the 2d Ising model and to density functional theory simulations of the disordered solid state lithium ion conductor Li0.5La0.5TiO3. Tests reveal that the algorithm has good performance and in particular at short iteration. The application of the algorithm to the Li0.5La0.5TiO3 system is an exploration into the disordered nature of the material along with a benchmark into what level of configurational sampling is currently feasible with density functional theory methods. Along with the detailed computational results some mathematical arguments are presented that the algorithm is convergent. The algorithm developed is naturally parallel and is referrred to as BLENDER for BLend Each New Density Each Round. |
Friday, March 19, 2021 12:30PM - 12:42PM Live |
Y16.00006: Minimizing Losses in a Classical Nonlinear Oscillator Nik Gjonbalaj, Anatoli S Polkovnikov, David Campbell Shortcuts to adiabaticity (STAs) have been used to make quick changes to a system while eliminating or minimizing disturbances to the system’s state. Especially in quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, counter-diabatic (CD) driving, and numerically compare its performance in both the quantum and classical versions of a quartic nonlinear oscillator. More specifically, we choose a classical figure of merit, which quantifies the disturbances to the system’s state, and a classical variational technique, which optimizes our driving to minimize disturbances. We then quickly change the strength of the nonlinearity in both systems and compare the classical figure of merit and variational technique to their well-established quantum versions. A reliable method for CD driving in classical oscillators could have many applications, from minimizing heating in bosonic gases to investigating classical nonlinear systems with many degrees of freedom, such as the Fermi-Pasta-Ulam-Tsingou lattice. |
Friday, March 19, 2021 12:42PM - 12:54PM Live |
Y16.00007: Study of phase transitions in Ising systems by exact microcanonical analysis Kedkanok Sitarachu, Michael Bachmann Ising chains and lattices have been studied excessively by canonical statistical analysis. Whereas there is no transition for 1D Ising chains, a ferromagnetic/paramagnetic phase transition occurs in 2D. In our study, we analyzed Ising chains, strips, and squares from the microcanonical perspective. The recently developed least-sensitive inflection-point method [1] was employed to identify potential transition signals in these systems [2, 3]. Our analysis confirms that there is no transition signal for 1D Ising chains as expected, but we find higher-order transitions in addition to the known second-order transition in the 2D Ising systems. A detailed cluster analysis lends insight into the nature of a third-order transition in the paramagnetic phase, which can be understood as a precursor of the continuous transition in the disordered phase. |
Friday, March 19, 2021 12:54PM - 1:06PM Live |
Y16.00008: Predicting phase transitions in nonequilibrium systems Ruben Zakine, Jasna Brujic, Eric Vanden-Eijnden Predicting phase transitions in thermal systems is one of the major achievements of equilibrium statistical mechanics. The situation is more difficult for nonequilibrium systems, in which energy or momentum is continuously injected, and there is a lack of a unifying theory that would give the phase transitions in that context. Here, we will show how a deterministic numerical method based on large deviation theory allows us to infer the nontrivial phase diagrams of nonequilibrium systems that display metastability. Our method proves useful to analyze bistability in reaction-diffusion systems, or to predict the collective behavior of active particles, for which a meanfield description pinpoints the accessible phases of the system. In particular, we are able to find the critical nucleus that drives the system from one metastable phase to another. Controlled experiments, involving swimming droplets which undergo short-range interactions while experiencing tunable birth-death dynamics (injection and dissolution), therefore represent a playground in which to test our approach. |
Friday, March 19, 2021 1:06PM - 1:18PM Live |
Y16.00009: Activity-induced quantum phase transitions Kyosuke Adachi, Kazuaki Takasan, Kyogo Kawaguchi Unique phase transitions such as flocking and motility-induced phase separation (MIPS) have been intensely studied in classical active matter systems. It is interesting to ask how we can extend the concept of active matter to quantum systems. In this talk, we propose a quantum model that undergoes activity-induced phase transitions [1]. By using the correspondence between a classical stochastic model and a quantum Hamiltonian, we show that activity appears as non-Hermiticity in the quantum model, and describe how it can induce quantum analogues of flocking, MIPS, and microphase separation. We also find that such quantum phase transitions are equivalent to dynamical phase transitions in a biased classical stochastic system, which have recently been studied in classical models (e.g., [2]). Our results bridge the gap between two fast-developing areas: active matter and non-Hermitian quantum physics. |
Friday, March 19, 2021 1:18PM - 1:30PM Live |
Y16.00010: Nonlinear diffusion and hydrodynamic fluctuations in kinetically constrained models. Abhishek Raj, Vadim Oganesyan, Sarang Gopalakrishnan We study particle diffusion in interacting lattice gas models with kinetic constraints chosen to enhance density dependence of the diffusion process. We document nonlinear diffusion and hydrodynamic long-time tails and explore the "diffusion cascade" recently discussed by L. Delacretaz. |
Friday, March 19, 2021 1:30PM - 1:42PM Live |
Y16.00011: Dynamics and escape of active particles in a harmonic trap Golan Bel, Dan Wexler, Nir Schachna Gov, Kim Ø. Rasmussen The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an effective temperature. This kind of description is tempting due to the similarities (or lack thereof) to systems in or near thermal equilibrium. However, the generality and validity of the effective temperature is not yet fully understood. We study the dynamics of trapped, undersamped particles subjected to both thermal and active forces. Expressions for the effective temperature due to the potential and kinetic energies are derived, and they differ from each other. A third possible effective temperature can be derived from the Kramers-like expression for the mean escape time of the particle from the trap. We find that over a large fraction of the parameter space, the potential energy effective temperature is in agreement with the escape temperature, while the kinetic effective temperature only agrees with the former two in the overdamped limit. Moreover, we show that the specific implementation of the random active force, and not only its first two moments and the two point autocorrelation function, affects the escape-time distribution. |
Friday, March 19, 2021 1:42PM - 1:54PM Live |
Y16.00012: Comparisons of diagonal and off-diagonal Anderson localization using a random matrix model Arash Mafi, Sandesh Timilsina We conduct a detailed study of Anderson localization in 1D and 2D disordered networks in a random matrix framework. Additionally, we analyze 2D networks with randomly broken links, which we interpret as networks with non-integer dimensions between 1D and 2D. We conduct our extensive numerical analysis for both diagonal and off-diagonal disorder. In particular, we compute the localization length's probability density function using two different metrics, one using the standard deviation and another using the inverse participation ratio. Both methods gauge the spread of eigenvectors over the matrix's element space. The probability density function provides the maximum amount of information regarding the localization, quite more than just the mean localization length. In particular, it allows us to clearly differentiate the localization process for the diagonal versus the off-diagonal disorder. It also allows us to compare the behavior of the two metrics. |
Friday, March 19, 2021 1:54PM - 2:06PM Not Participating |
Y16.00013: Study of localized modes in steelpans via a vector landscape function Petur Bryde, L. Mahadevan The steelpan is a pitched percussion instrument in the form of a concave shell with several regions of lower curvature, called notes. Each note can be made to vibrate independently, an example of mode localization in an elastic shell. We investigate how the strength of localization in steelpans depends on the geometry, and find that it is determined by the change in curvature at the boundary of the note regions. In our analysis, we use a new generalization of the localization landscape theory which can be used to predict localized modes in general shells. The landscape allows us to estimate the localization regions by solving a Poisson problem instead of the full eigenvalue problem. |
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