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Impact of time-correlated noise on zero-noise extrapolation

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Physical Review A 2022年第5期106卷 052406-052406页

作者： Kevin Schultz Ryan LaRose Andrea Mari Gregory Quiroz Nathan Shammah B. David Clader William J. Zeng Johns Hopkins University Applied Physics Laboratory Laurel Maryland 20723 USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48823 USA Unitary Fund Walnut California 91789 USA Goldman Sachs & Co New York New York 10282 USA

Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time correlated. In this paper, we investigate the feasibility and performance of zero-noise extrapolation in the presence of time-correlated noise. We show that, in contrast to white noise, time-correlated noise is harder to mitigate via zero-noise extrapolation because it is difficult to scale the noise level without also modifying its spectral distribution. This limitation is particularly strong if “local” gate-level methods are applied for noise scaling. However, we find that “global” noise-scaling methods, e.g., global unitary folding, can be sufficiently reliable even in the presence of time-correlated noise.

关键词： Quantum algorithms Quantum benchmarking Quantum control

Breakdown of Boltzmann-type Models for the Alignment of Self-propelled Rods

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arXiv 2023年

作者： Murphy, Patrick Perepelitsa, Misha Timofeyev, Ilya Lieber-Kotz, Matan Islas, Brandon Igoshin, Oleg A. Department of Bioengineering Rice University HoustonTX77005 United States Center for Theoretical Biological Physics Rice University HoustonTX77005 United States Department of Mathematics University of Houston TX77204 United States Department of Computational and Applied Mathematics Rice University HoustonTX77005 United States Department of Chemistry Rice University HoustonTX77005 United States Department of Biosciences Rice University HoustonTX77005 United States

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann’s hypothesis of"molecular chaos", that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems. © 2023, CC BY.

关键词： Boltzmann equation

Complexity for an open quantum system

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Physical Review D 2022年第4期105卷 046011-046011页

作者： Arpan Bhattacharyya Tanvir Hanif S. Shajidul Haque Md. Khaledur Rahman Indian Institute of Technology Gandhinagar Gujarat 382355 India Department of Theoretical Physics University of Dhaka Dhaka-1000 Bangladesh High Energy Physics Cosmology & Astrophysics Theory Group and The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch Cape Town 7700 South Africa National Institute for Theoretical and Computational Sciences (NITheCS) Rondebosch Cape Town 7700 South Africa

We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix by tracing out the bath degrees of freedom for both regular and inverted oscillators and compute the complexity of purification (COP) and complexity by using the operator-state mapping. We find that when the oscillator is regular, the COP saturates quickly for both underdamped and overdamped oscillators. Interestingly, when the oscillator is underdamped, we discover a kink-like behavior for the saturation value of the COP with a varying damping coefficient. For the inverted oscillator, we find a linear growth of the COP with time for all values of the bath-system interaction. However, when the interaction is increased the slope of the linear growth decreases, implying that the unstable nature of the system can be regulated by the bath.

关键词： computational complexity Gauge-gravity dualities Open quantum systems Quantum chaos

Energy-based discontinuous Galerkin difference methods for second-order wave equations

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arXiv 2021年

作者： Zhang, Lu Appelö, Daniel Hagstrom, Thomas Department of Applied Physics and Applied Mathematics Columbia University New YorkNY United States Department of Computational Mathematics Science & Engineering Department of Mathematics Michigan State University East LansingMI United States Department of Mathematics Southern Methodist University DallasTX United States

We combine the newly-constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second order form. The approximation properties of the resulting method are excellent and the allowable time steps are large compared to traditional discontinuous Galerkin methods. The one drawback of the combined approach is the cost of inversion of the local mass matrix. We demonstrate that for constant coefficient problems on Cartesian meshes this bottleneck can be removed by the use of a modified Galerkin difference basis. For variable coefficients or non-Cartesian meshes this technique is not possible and we instead use the preconditioned conjugate gradient method to iteratively invert the mass matrices. With a careful choice of preconditioner we can demonstrate optimal complexity, albeit with a larger *** Codes 65M60, 65M06. Copyright © 2021, The Authors. All rights reserved.

关键词： Galerkin methods

Diffusion spreadability as a probe of the microstructure of complex media across length scales

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arXiv 2021年

作者： Torquato, Salvatore Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, S(∞) − S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability

关键词： Microstructure

Finite-thickness effect of the fluids on bubbles and spikes in Richtmyer–Meshkov instability for arbitrary Atwood numbers

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Plasma Science and Technology 2019年第2期21卷 9-15页

作者： Wanhai LIU Changping YU Pei WANG Zheng FU Lili WANG Yulian CHEN Research Center of Computational Physics Mianyang Normal University LHD Institute of MechanicsChinese Academy of Sciences Institute of Applied Physics and Computational Mathematics Mechanical and Electrical Engineering Department Lanzhou Resources and Environment Voc-Tech College

This paper investigates the finite-thickness effect of two superimposed fluids on bubbles and spikes in Richtmyer–Meshkov instability(RMI) for arbitrary Atwood numbers by using the method of the small parameter expansion up to the second order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitude evolution of bubbles and spikes compared with those in classical RMI. Based on the thickness relationship of the two fluids, the thickness effect on bubbles and spikes for four cases is discussed. The thickness encourages(or reduces)the growth of bubbles or spikes, depending on not only Atwood number, but also the relationship of the thickness ratio of the heavy and light fluids, which is explicitly determined in this paper.

关键词： Richtmyer–Meshkov instability bubbles and spikes finite-thickness

SINGULAR LIMITS FOR THE NAVIER-STOKES-POISSON EQUATIONS OF VISCOUS PLASMA WITH STRONG DENSITY BOUNDARY LAYER

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arXiv 2022年

作者： Ju, Qiangchang Luo, Tao Xu, Xin Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Tong Hong Kong School of Mathematical Sciences College of Oceanic and Atmospheric Sciences Ocean University of China Qingdao China

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space R3+ is rigorously proved under a Navier-slip boundary condition for velocity and the Dirichlet boundary condition for electric potential. This is achieved by establishing the nonlinear stability of the approximation solutions involving the strong boundary layer in density and electric potential, which comes from the break-down of the quasi-neutrality near the boundary, and dealing with the difficulty of the interaction of this strong boundary layer with the weak boundary layer of the velocity field. Copyright © 2022, The Authors. All rights reserved.

关键词： Poisson equation

Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

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arXiv 2021年

作者： Gurevich, Daniel R. Golden, Matthew R. Reinbold, Patrick A.K. Grigoriev, Roman O. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Physics Georgia Institute of Technology AtlantaGA30332 United States

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality, and symmetry, a weak formulation of differential equations, and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics—the Navier-Stokes equation, the continuity equation, and the boundary conditions—as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well-suited for analysis of experimental data. Copyright © 2021, The Authors. All rights reserved.

关键词： Navier Stokes equations

Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models

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arXiv 2024年

作者： Maslowski, Tomasz Cheraghi, Hadi Sirker, Jesko Sedlmayr, Nicholas The Faculty of Mathematics and Applied Physics Rzeszów University of Technology al. Powstańców Warszawy 6 Rzeszów35-959 Poland Computational Physics Laboratory Physics Unit Faculty of Engineering and Natural Sciences Tampere University TampereFI-33014 Finland Helsinki Institute of Physics University of Helsinki FI-00014 Finland Department of Physics and Astronomy Manitoba Quantum Institute University of Manitoba WinnipegR3T 2N2 Canada Institute of Physics M. Curie-Sklodowska University Lublin20-031 Poland

Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three dimensions has not yet been fully investigated. In two dimensions, results so far are known only for relatively simple two-band models. Here we study the general two- and three-dimensional cases. We establish the relation between the non-analyticities in different dimensions, and the functional form of the densities of Fisher zeroes. We show, in particular, that entering a critical region where the density of Fisher zeroes is non-zero at the boundary always leads to a cusp in the derivative of the return rate while the return rate itself is smooth. We illustrate our results by obtaining analytical results for exemplary two- and three-dimensional models. © 2024, CC BY.

关键词： Free energy