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Results for “generalized Langevin equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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29 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Mass Changes the Diffusion Coefficient of Particles with Ligand-Receptor Contacts in the Overdamped Limit

Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands that bind reversibly to surface receptors: heavy particles diffuse more slowly than light ones of the same size. We show this by simulation and by deriving an analytic formula for the mass-dependent diffusion coefficient in the overdamped limit. We estimate the magnitude of this effect for a range of biophysical ligand-receptor systems, and find it is potentially observable for tailored micronscale DNA-coated colloids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum Gravity and Laser Interferometry: Towards Observable Predictions

Understanding quantum gravity remains one of the deepest challenges in modern physics, as direct experimental access to Planck-scale effects is beyond current technological reach. However, recent theoretical advances indicate that quantum fluctuations of spacetime may produce measurable effects in precision experiments, particularly near causal horizons. This opens new avenues for testing quantum gravity phenomena through high-precision measurement techniques. This dissertation develops multiple theoretical models to characterize these effects and examines their potential observational signatures in future gravitational wave interferometers. We begin by investigating the role of quantum fluctuations in near-horizon geometries through the lens of the AdS/CFT correspondence, which provides a powerful framework for understanding the interplay between quantum field theory and general relativity via holographic principles. By modeling stochastic energy-momentum sources in Rindler-AdS spacetime, we demonstrate that vacuum fluctuations transform the Einstein equations into a Langevin-type stochastic differential equation, leading to potentially observable fluctuations in photon traversal times. Extending this approach to Minkowski spacetime, we establish a correspondence between gravitational shockwaves and fluid dynamics, showing that near-horizon perturbations satisfy an equation analogous to that governing incompressible fluids, thereby reinforcing the membrane paradigm and hydrodynamic analogies in the context of the fluid/gravity duality. Furthermore, we construct the covariant phase space of a spherically symmetric causal diamond in Minkowski spacetime, identifying two fundamental charges that govern its evolution. These results provide a foundation for quantizing causal horizons and understanding their microscopic degrees of freedom. Building upon these theoretical developments, we further examine a related stochastic phenomenon: the gravitational wave memory background arising from the cumulative memory steps produced by supermassive black hole mergers. After reviewing the standard stochastic gravitational wave background, gravitational memory effects, and BMS symmetries, we model the stochastic memory background using a Brownian motion framework. We show that while the cumulative memory background initially appears above the sensitivity curve of space-based interferometers like LISA, the realistic subtraction of individually resolvable merger events substantially suppresses the residual signal, making its detection more challenging. This highlights the critical importance of source subtraction when evaluating the detectability of gravitational memory effects. By bridging fundamental theory with experimental prospects, this dissertation contributes to the ongoing effort to uncover the quantum nature of spacetime through precision measurement techniques. Whether through detecting quantum spacetime fluctuations, gravitational memory backgrounds, or probing the symmetries of causal horizons, the pursuit of observable quantum gravity phenomena continues to expand the frontiers of both theory and experiment.

Zhang, Yiwen [Caltech] (ORCID:0000000323559416)↗
NASA NTRS1975

Langevin equation with stochastic damping - Possible application to critical binary fluid

We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.

Jasnow, D.↗
NASA NTRS1994

Decoherence and dissipation for a quantum system coupled to a local environment

Decoherence and dissipation in quantum systems has been studied extensively in the context of Quantum Brownian Motion. Effective decoherence in coarse grained quantum systems has been a central issue in recent efforts by Zurek and by Hartle and Gell-Mann to address the Quantum Measurement Problem. Although these models can yield very general classical phenomenology, they are incapable of reproducing relevant characteristics expected of a local environment on a quantum system, such as the characteristic dependence of decoherence on environment spatial correlations. I discuss the characteristics of Quantum Brownian Motion in a local environment by examining aspects of first principle calculations and by the construction of phenomenological models. Effective quantum Langevin equations and master equations are presented in a variety of representations. Comparisons are made with standard results such as the Caldeira-Leggett master equation.

Gallis, Michael R.↗
DOE OSTI2021

Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations

We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. Furthermore, the physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, Z 2 symmetry breaking, PT symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. In this work, we derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Lastly, potential applications and caveats to the usage of LD are included as a summary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Modeling nanoparticle charge distribution in the afterglow of non-thermal plasmas and comparison with measurements

Particle charging in the afterglows of non-thermal plasmas typically take place in a non-neutral space charge environment. We model the same by incorporating particle-ion collision rate constant models, developed in prior work by analyzing particle-ion trajectories calculated using Langevin Dynamics simulations, into species transport equations for ions, electrons and charged particles in the afterglow. A scaling analysis of particle charging and additional Langevin Dynamics calculations of the particle-ion collision rate constant are presented to extend the range of applicability to ion electrostatic to thermal energy ratios of 300 and diffusive Knudsen number (that scales inversely with gas pressure) up to 2000. The developed collision rate constant models are first validated by comparing predictions of particle charge against measured values in a stationary, non-thermal DC plasma from past PK-4 campaigns published in Phys. Rev. Lett. 93(8): 085001 and Phys. Rev. E 72(1): 016406). The comparisons reveal excellent agreement within ±35% for particles of radius 0.6,1.0,1.3 μm in the gas pressure range of ~20-150 Pa. The experiments to probe particle charge distributions by Sharma et al. (J. Physics D: Appl. Phys. 53(24): 245204) are modeled using the validated particle-ion collision rate constant models and the calculated charge fractions are compared with measurements. The comparisons reveal that the ion/electron concentration and gas temperature in the afterglow critically influence the particle charge and the predictions are generally in qualitative agreement with the measurements. Along with critical assessment of the modeling assumptions, several recommendations are presented for future experimental design to probe charging in afterglows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗