Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions

Forster, Dieter

doi:10.1201/9780429493683

Cited by 549 publications

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“…The idea here is that we replace the unknown actual density operator of the system by one that only depends on the mean values of relevant variables, gives the correct values for them, and maximizes the informational entropy. This relevant density is then used to calculate mean values and correlation functions [3,11,34].…”

Section: B Mori Theorymentioning

confidence: 99%

Projection operators in statistical mechanics: a pedagogical approach

Vrugt

Wittkowski

2020

Eur. J. Phys.

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The Mori-Zwanzig projection operator formalism is one of the central tools of nonequilibrium statistical mechanics, allowing to derive macroscopic equations of motion from the microscopic dynamics through a systematic coarse-graining procedure. It is important as a method in physical research and gives many insights into the general structure of nonequilibrium transport equations and the general procedure of microscopic derivations. Therefore, it is a valuable ingredient of basic and advanced courses in statistical mechanics. However, accessible introductions to this methodin particular in its more advanced forms -are extremely rare. In this article, we give a simple and systematic introduction to the Mori-Zwanzig formalism, which allows students to understand the methodology in the form it is used in current research. This includes both basic and modern versions of the theory. Moreover, we relate the formalism to more general aspects of statistical mechanics and quantum mechanics. Thereby, we explain how this method can be incorporated into a lecture course on statistical mechanics as a way to give a general introduction to the study of nonequilibrium systems. Applications, in particular to spin relaxation and dynamical density functional theory, are also discussed. * Corresponding author: raphael.wittkowski@uni-muenster.de 1 Active particles are particles that convert energy into directed motion. A good example are swimming microorganisms [1]. 2 This is not possible for active systems [7].

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Section: B Mori Theorymentioning

confidence: 99%

Projection operators in statistical mechanics: a pedagogical approach

Vrugt

Wittkowski

2020

Eur. J. Phys.

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“…V is the area, and let it and the phase angle f vary slowly over the bulk. Their dynamics is then governed by the hydrodynamic Hamiltonian[41,42] H dr…”

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confidence: 99%

Fermi surface pockets in electron-doped iron superconductor by Lifshitz transition

Rodríguez

Melendrez

2018

J. Phys. Commun.

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The wavefunction renormalization Z(k′, ω) that appears on the right-hand side of the Eliashberg Equations listed in equation (58) of section 4.2 and in equations (D.1), (D.2) and (D.3) of appendix D must be replaced by Z(k′, ω′), where ω′ = E(k′). It must also be added that the subsequent Eliashberg equations (59a) and (59b) in section 4.3 are achieved under the approximation that the above corrected wavefunction renormalization on the righthand side of equation (58) is replaced by its value at the Fermi level: Z(k′, ω) as ω→0. These corrections and clarifications do not change any of the results and conclusions obtained in the paper. ORCID iDsJose P Rodriguez https:/ /orcid.org/0000-0002-5169-6883

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“…Non-equilibrium systems are arguably the most interesting cases to use the 2-TCF. Equilibrium systems are time translation invariant (Forster, 1995) but time symmetry is not retained in non-equilibrium systems. This symmetry break is reflected in the CCS-1-TCFs, but ACS-1-TCFs keep the symmetry for both equilibrium and non-equilibrium processes.…”

Section: Discussionmentioning

confidence: 99%

On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis

Bikondoa

2017

J Appl Crystallogr

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Multi-time correlation functions are especially well suited to study nonequilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.

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Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions

Cited by 549 publications

References 0 publications

Projection operators in statistical mechanics: a pedagogical approach

Projection operators in statistical mechanics: a pedagogical approach

Fermi surface pockets in electron-doped iron superconductor by Lifshitz transition

On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis

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