A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients Dμν. The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the Dμν are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation. Relations to other methods are discussed, like "dissipative tunneling", RPA at finite temperature and generalizations of the "Static Path Approximation".

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Linear response theory, fluctuation–dissipation theorem

Series on Advances in Statistical Mechanics - An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics ◽

10.1142/9789814374798_0006 ◽

2012 ◽

pp. 123-150

Keyword(s):

Linear Response ◽

Linear Response Theory ◽

Response Theory ◽

Fluctuation Dissipation ◽

Fluctuation Dissipation Theorem

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Scrutinizing GW-Based Methods Using the Hubbard Dimer

Frontiers in Chemistry ◽

10.3389/fchem.2021.751054 ◽

2021 ◽

Vol 9 ◽

Author(s):

S. Di Sabatino ◽

P.-F. Loos ◽

P. Romaniello

Keyword(s):

Excitation Spectrum ◽

Trace Formula ◽

Electron Interaction ◽

Excitation Energies ◽

Fluctuation Dissipation ◽

Fluctuation Dissipation Theorem ◽

Wide Range ◽

Self Consistent ◽

Approximate Nature ◽

Self Consistency

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.

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Linear-Response Theory and Fluctuation Dissipation Theorem Including the Spatial Dependence

Spectroscopy of Condensed Media ◽

10.1016/b978-0-12-734780-6.50011-x ◽

1985 ◽

pp. 333-347

Keyword(s):

Spatial Dependence ◽

Linear Response ◽

Linear Response Theory ◽

Response Theory ◽

Fluctuation Dissipation ◽

Fluctuation Dissipation Theorem

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LINEAR RESPONSE THEORY, FLUCTUATION-DISSIPATION THEOREM

An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics ◽

10.1142/9789814350280_0004 ◽

1994 ◽

pp. 111-140

Keyword(s):

Linear Response ◽

Linear Response Theory ◽

Response Theory ◽

Fluctuation Dissipation ◽

Fluctuation Dissipation Theorem

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Remark on memory function approach and linear response theory

Canadian Journal of Physics ◽

10.1139/p70-206 ◽

1970 ◽

Vol 48 (13) ◽

pp. 1631-1633 ◽

Cited By ~ 1

Author(s):

T. H. Cheung ◽

E. Tong ◽

K. P. Wang

Keyword(s):

Correlation Function ◽

Linear Response ◽

Spin Diffusion ◽

Memory Function ◽

Linear Response Theory ◽

Function Approach ◽

Response Theory ◽

Fluctuation Dissipation ◽

Fluctuation Dissipation Theorem ◽

General Connection

It is generally understood (Kubo) that the linearized version of the memory function approach of Mori and Zwanzig is equivalent, through the application of the fluctuation–dissipation theorem, to the corresponding linear response theory of correlation function calculations developed in the work of Kadanoff and Martin. We give here a simple example of spin diffusion to show this explicitly, which reflects the general connection between these two approaches.

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