Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method

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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A NEW EQUATION OF MOTION METHOD FOR MULTIPHONON NUCLEAR SPECTRA

International Journal of Modern Physics E ◽

10.1142/s0218301309013087 ◽

2009 ◽

Vol 18 (04) ◽

pp. 944-950 ◽

Cited By ~ 1

Author(s):

F. ANDREOZZI ◽

F. KNAPP ◽

N. LO IUDICE ◽

A. PORRINO ◽

J. KVASIL

Keyword(s):

Giant Dipole Resonance ◽

Equations Of Motion ◽

Iterative Solution ◽

Equation Of Motion ◽

Negative Parity ◽

Dipole Resonance ◽

New Equation ◽

Motion Method

A method which generates a multiphonon basis through the construction and the iterative solution of a set of equations of motion is adopted to investigate the negative parity spectrum and the structure of the giant dipole resonance in 16 O .

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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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Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

Journal of High Energy Physics ◽

10.1007/jhep06(2021)165 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Haiming Yuan ◽

Xian-Hui Ge

Keyword(s):

Boundary Condition ◽

Green’S Function ◽

Green's Function ◽

Equations Of Motion ◽

Equation Of Motion ◽

Boundary Theory ◽

Hydrodynamic Analysis ◽

Dimensionless Variables ◽

Pass Through ◽

Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

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Exploring the Accuracy of a Low Scaling Similarity Transformed Equation of Motion Method for Vertical Excitation Energies

Journal of Chemical Theory and Computation ◽

10.1021/acs.jctc.7b00802 ◽

2017 ◽

Vol 14 (1) ◽

pp. 72-91 ◽

Cited By ~ 35

Author(s):

Achintya Kumar Dutta ◽

Marcel Nooijen ◽

Frank Neese ◽

Róbert Izsák

Keyword(s):

Equation Of Motion ◽

Excitation Energies ◽

Vertical Excitation ◽

Motion Method ◽

Vertical Excitation Energies

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Quantum dynamics of the photostability of pyrazine

Physical Chemistry Chemical Physics ◽

10.1039/c5cp04605j ◽

2015 ◽

Vol 17 (44) ◽

pp. 29518-29530 ◽

Cited By ~ 16

Author(s):

Matthieu Sala ◽

Stéphane Guérin ◽

Fabien Gatti

Keyword(s):

Electronic State ◽

Ground State ◽

Quantum Dynamics ◽

Ground Electronic State ◽

Conical Intersection ◽

Radiationless Decay

We propose a new mechanism for the radiationless decay of photoexcited pyrazine to its ground electronic state involving a conical intersection between the dark Au(nπ) state and the ground state.

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Dynamic Characteristics of a Hydrostatic Gas Bearing Driven by Oscillating Exhaust Pressure

Journal of Tribology ◽

10.1115/1.3260968 ◽

1984 ◽

Vol 106 (4) ◽

pp. 477-483 ◽

Cited By ~ 1

Author(s):

C. B. Watkins ◽

H. D. Branch ◽

I. E. Eronini

Keyword(s):

Reynolds Equation ◽

Numerical Solutions ◽

Equations Of Motion ◽

Equation Of Motion ◽

Source Model ◽

Regular Perturbation ◽

Response Characteristics ◽

Finite Difference Approximations ◽

Bode Plots ◽

Gas Bearing

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference approximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

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Theoretical study of photoinduced proton coupled electron transfer reaction using the non-perturbative hierarchical equations of motion method

The Journal of Chemical Physics ◽

10.1063/1.4982928 ◽

2017 ◽

Vol 146 (18) ◽

pp. 184108 ◽

Cited By ~ 8

Author(s):

Kai Song ◽

Qiang Shi

Keyword(s):

Electron Transfer ◽

Transfer Reaction ◽

Theoretical Study ◽

Equations Of Motion ◽

Electron Transfer Reaction ◽

Proton Coupled Electron Transfer ◽

Motion Method

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Integrals of the motion and green functions for time-dependent mass harmonic oscillators

Revista Mexicana de Física ◽

10.31349/revmexfis.64.30 ◽

2018 ◽

Vol 64 (1) ◽

pp. 30

Author(s):

Surarit Pepore

Keyword(s):

Harmonic Oscillator ◽

Harmonic Oscillators ◽

Time Dependent ◽

Green Functions ◽

Feynman Path Integral ◽

Feynman Path ◽

Damped Harmonic Oscillator ◽

System Trajectory ◽

Dependent Mass ◽

Motion Method

The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Greenfunction is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phasespace. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsatingmass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between theintegrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.

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