Relaxation of an electron system: Conserving approximation

Atwal, Gurinder S.; Ashcroft, N. W.

doi:10.1103/physrevb.65.115109

Cited by 43 publications

(31 citation statements)

References 23 publications

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“…The selfconsistent choice of diagrams is dictated by the requirement of gauge invariance or, equivalently, by the application of Ward-Pitaevskii identities, 10 thereby ensuring that conservation laws are enforced in the electron dynamics. 11 As previously noted, 8,12,13 the polarizability diagrams in Fig. 1 can all be expressed in terms of the three-point function ⌳ (3) (q ,p ); thus An explicit formula for the three-point function ⌳ (3) (p ,q ) in two dimensions has been given by Neumayr and Metzner.…”

Section: ͑7͒mentioning

confidence: 94%

Dynamical local-field factors and effective interactions in the two-dimensional electron liquid

Atwal¹,

Ashcroft²

2003

Phys. Rev. B

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We present an analytical study of the dynamical local-field factors associated with the response of a homogeneous two-dimensional interacting electron liquid as functions of momentum, frequency, and density. We derive sum rules that constrain their asymptotic forms ͑in momentum and frequency͒ for both the spinsymmetric and spin-antisymmetric cases. Parametrized expressions for the local-field factors are proposed, based on all available sum rules and on many-body perturbation theory, and these are found to be in good agreement with quantum Monte Carlo calculations. Finally, these expressions are used to evaluate the effective electron-electron interaction in a local approximation for two-dimensional systems. It is shown that both the quantitative and qualitative behaviors of the interaction are sensitive to the inclusion of dynamical correlations.

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Section: ͑7͒mentioning

confidence: 94%

Dynamical local-field factors and effective interactions in the two-dimensional electron liquid

Atwal¹,

Ashcroft²

2003

Phys. Rev. B

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“…Furthermore, more advanced number-and energy-conserving BGK as well as number-, momentum-, energy-conserving BGK models have been presented in Refs. [25,26] and [27,28], respectively, which yield analytic expressions for the permittivities in terms of combinations of the plasma dispersion function. However, for a completely ionized plasma, the model permittivity within the BGK approximation and the corresponding Drude model for the transverse permittivity [7,[22][23][24] lead to the significant deviations from the known limiting cases in the range of moderate and strong collisions [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Dielectric function of a collisional plasma for arbitrary ionic charge

et al. 2014

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A simple model for the dielectric function of a completely ionized plasma with an arbitrary ionic charge, that is valid for long-wavelength high-frequency perturbations is derived using an approximate solution of a linearized Fokker-Planck kinetic equation for electrons with a Landau collision integral. The model accounts for both the electron-ion collisions and the collisions of the subthermal (cold) electrons with thermal ones. The relative contribution of the latter collisions to the dielectric function is treated phenomenologically, introducing some parameter κ that is chosen in such a way as to get a well-known expression for stationary electric conductivity in the low-frequency region and fulfill the requirement of a vanishing contribution of electron-electron collisions in the high-frequency region. This procedure ensures the applicability of our model in a wide range of plasma parameters as well as the frequency of the electromagnetic radiation. Unlike the interpolation formula proposed earlier by Brantov et al. [Brantov et al., JETP 106, 983 (2008)

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“…We know that changes in entropy satisfy δS = δQ/T + δS i , where δQ is the generalized heat added to the system, such as heat flowing in through the system boundaries and δS i is the entropy change due to irreversible processes such as relaxation. For a closed system, δQ = 0 and δS = δS i ≥ 0 [5,[25][26][27][28]. As the system is dynamically driven by applied fields, the material relaxes and local fields are formed in the material that differ from the applied fields.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Nanoscale Metrology Based on Entropy Production and Fluctuations

Baker–Jarvis

2008

Entropy

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The goal in this paper is to show how many high-frequency electromagnetic metrology areas can be understood and formulated in terms of entropy evolution, production, and fluctuations. This may be important in nanotechnology where an understanding of fluctuations of thermal and electromagnetic energy and the effects of nonequilibrium are particularly important. The approach used here is based on a new derivation of an entropy evolution equation using an exact Liouville-based statistical-mechanical theory rooted in the Robertson-Zwanzig-Mori formulations. The analysis begins by developing an exact equation for entropy rate in terms of time correlations of the microscopic entropy rate. This equation is an exact fluctuation-dissipation relationship. We then define the entropy and its production for electromagnetic driving, both in the time and frequency domains, and apply this to study dielectric and magnetic material measurements, magnetic relaxation, cavity resonance, noise, measuring Boltzmann's constant, and power measurements.

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Relaxation of an electron system: Conserving approximation

Cited by 43 publications

References 23 publications

Dynamical local-field factors and effective interactions in the two-dimensional electron liquid

Dynamical local-field factors and effective interactions in the two-dimensional electron liquid

Dielectric function of a collisional plasma for arbitrary ionic charge

Electromagnetic Nanoscale Metrology Based on Entropy Production and Fluctuations

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