Stochastic equation of motion approach to fermionic dissipative dynamics. II. Numerical implementation

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S2(ππ*)–S1(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system–bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system–bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system–bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S2) is very efficiently quenched by the system–bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode–mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system–bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system–bath coupling as well as the field-matter coupling.

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Epitaxial Growth and Recovery: an Analytic Approach

MRS Proceedings ◽

10.1557/proc-237-189 ◽

1991 ◽

Vol 237 ◽

Cited By ~ 2

Author(s):

A. Zangwillt ◽

C. N. Luset ◽

D. D. Vvedensky ◽

M. R. Wilby

Keyword(s):

Epitaxial Growth ◽

Stochastic Equation ◽

Morphological Evolution ◽

Surface Profile ◽

Equation Of Motion ◽

Analytic Approach ◽

Deposition Flux ◽

Simulation Techniques ◽

Continuum Equation ◽

Computer Based

ABSTRACTMost detailed studies of morphological evolution during epitaxial growth and recovery make use of computer-based simulation techniques. In this paper, we discuss an alternative, analytic approach to this problem which takes explicit account of the atomistically random processes of deposition and surface diffusion. Beginning with a master equation representation of the dynamics of a solid-on-solid model of epitaxial growth, we derive a discrete, stochastic equation of motion for the surface profile. This Langevin equation is appropriate for growth studies. In particular, we are able to provide a microscopic justification for a non-linear continuum equation of motion proposed for this problem by others on the basis of heuristic arguments. During recovery, the deposition flux and its associated shot noise are absent. We analyze this process with a completely deterministic equation of motion obtained by performing a statistical average of the original stochastic equation. Results using the latter compare favorably with full Monte Carlo simulations of the original model for the case of the decay of sinusoidally modulated initial surfaces.

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Catching drifting pebbles

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732562 ◽

2018 ◽

Vol 615 ◽

pp. A178 ◽

Cited By ~ 28

Author(s):

Chris W Ormel ◽

Beibei Liu

Keyword(s):

Strong Coupling ◽

Turbulent Diffusion ◽

Stochastic Equation ◽

Equation Of Motion ◽

Parameter Study ◽

Particle Inertia ◽

Low Mass Stars ◽

Outer Disk ◽

Low Mass ◽

Three Body

Turbulence plays a key role in the transport of pebble-sized particles. It also affects the ability of pebbles to be accreted by protoplanets because it stirs pebbles out of the disk midplane. In addition, turbulence suppresses pebble accretion once the relative velocities become too high for the settling mechanism to be viable. Following Paper I, we aim to quantify these effects by calculating the pebble accretion efficiency ε using three-body simulations. To model the effect of turbulence on the pebbles, we derive a stochastic equation of motion (SEOM) applicable to stratified disk configurations. In the strong coupling limit (ignoring particle inertia) the limiting form of this equation agrees with previous works. We conduct a parameter study and calculate ε in 3D, varying pebble and gas turbulence properties and accounting for the planet inclination. We find that strong turbulence suppresses pebble accretion through turbulent diffusion, agreeing closely with previous works. Another reduction of ε occurs when the turbulent rms motions are high and the settling mechanism fails. In terms of efficiency, the outer disk regions are more affected by turbulence than the inner regions. At the location of the H2O iceline, planets around low-mass stars achieve much higher efficiencies. Including the results from Paper I, we present a framework to obtain ε under general circumstances.

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Coherent-state path integral versus coarse-grained effective stochastic equation of motion: From reaction diffusion to stochastic sandpiles

Physical Review E ◽

10.1103/physreve.93.042117 ◽

2016 ◽

Vol 93 (4) ◽

Cited By ~ 18

Author(s):

Kay Jörg Wiese

Keyword(s):

Coherent State ◽

Path Integral ◽

Stochastic Equation ◽

Reaction Diffusion ◽

Equation Of Motion ◽

Coarse Grained ◽

State Path

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REVISED EQUATION OF MOTION METHOD, SEMI-CLASSICAL LIMIT, AND MATHEMATICALLY CLOSED THEORY OF LARGE AMPLITUDE COLLECTIVE MOTION

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1984613 ◽

1984 ◽

Vol 45 (C6) ◽

pp. C6-111-C6-119

Author(s):

A. Klein

Keyword(s):

Large Amplitude ◽

Classical Limit ◽

Collective Motion ◽

Equation Of Motion ◽

Closed Theory ◽

Motion Method

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Particle motion with air resistance

Progress in Agricultural Engineering Sciences ◽

10.1556/progress.8.2012.1 ◽

2012 ◽

Vol 8 (1) ◽

pp. 1-15

Author(s):

Gy. Sitkei

Keyword(s):

Basic Equation ◽

Initial Conditions ◽

Equation Of Motion ◽

Terminal Velocity ◽

Dimensionless Form ◽

Wood Industry ◽

Acceptable Error ◽

General Validity ◽

Practical Applications ◽

Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

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Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i1.6950 ◽

2015 ◽

Vol 11 (1) ◽

pp. 2960-2971

Author(s):

M.Abdel Wahab

Keyword(s):

Velocity Field ◽

Angular Velocity ◽

Finite Difference ◽

Numerical Study ◽

Outer Sphere ◽

Equation Of Motion ◽

Annular Region ◽

Surface Traction ◽

Angular Velocities ◽

Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1 ï— and the outer sphererotate with angular velocity 2 ï— about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (ï¡,ï¢ ,ïª) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

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On the Harmonic Oscillations for the Motion of a Dynamical System

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v13i2.5754 ◽

2017 ◽

Vol 13 (2) ◽

pp. 4657-4670

Author(s):

W. S. Amer

Keyword(s):

Dynamical System ◽

Numerical Solutions ◽

Equation Of Motion ◽

Parameter Method ◽

Kutta Method ◽

Small Parameter Method ◽

Harmonic Oscillations ◽

Pivot Point ◽

Runge Kutta Method ◽

High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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A Multi-Layer Approach to the Equation of Motion Coupled-Cluster Method for the Electron Affinity

10.26434/chemrxiv.11853399 ◽

2020 ◽

Author(s):

Soumi Haldar ◽

Achintya Kumar Dutta

Keyword(s):

Electron Affinity ◽

Electron Attachment ◽

Equation Of Motion ◽

Cluster Method ◽

Coupled Cluster ◽

Coupled Cluster Method ◽

Large Molecules ◽

Layer Method ◽

Speed Up ◽

Attachment Process

We have presented a multi-layer implementation of the equation of motion coupled-cluster method for the electron affinity, based on local and pair natural orbitals. The method gives consistent accuracy for both localized and delocalized anionic states. It results in many fold speedup in computational timing as compared to the canonical and DLPNO based implementation of the EA-EOM-CCSD method. We have also developed an explicit fragment-based approach which can lead to even higher speed-up with little loss in accuracy. The multi-layer method can be used to treat the environmental effect of both bonded and non-bonded nature on the electron attachment process in large molecules.<br>

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