General response function for interacting quantum liquids

Morawetz, Klaus; Fuhrmann, Uwe

doi:10.1103/physreve.61.2272

Cited by 31 publications

(42 citation statements)

References 21 publications

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“…The proposed key to the solution is that the local equilibrium distribution must not only exhibit spatial and temporal variations in µ but also in the drift velocity, v (to conserve momentum), and temperature, T (to conserve energy). This idea 6 has, independently, also been recently introduced, and implemented in the context of generalised quantum liquids 7 .…”

Section: Introductionmentioning

confidence: 99%

Relaxation of an electron system: Conserving approximation

Atwal

Ashcroft

2002

Phys. Rev. B

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The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space-and time-dependent chemical potential, drift velocity and temperature. Both quantum kinetic and semi-classical arguments are given, and we calculate and analyze the corresponding analytical d-dimensional dielectric function. Dynamical correlation, arising from relaxation effects, is shown to soften the plasmon dispersion of both two-and three-dimensional systems. Finally, we consider the consequences for a hydrodynamic theory of a d-dimensional interacting electron gas, and by incorporating the competition between relaxation and inertial effects we derive generalised hydrodynamic equations applicable to arbitrary frequencies.

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Section: Introductionmentioning

confidence: 99%

Relaxation of an electron system: Conserving approximation

Atwal

Ashcroft

2002

Phys. Rev. B

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“…In 42,46 was given the polarization function for an interacting quantum system imposing conservation laws on the relaxation time approximation. These polarization functions we have denoted by Π n for density conservation imposed, Π n,j for density and current conservation and Π n,j,E for density, current and energy conservation.…”

Section: Dynamical Response Functionmentioning

confidence: 99%

“…In chapter III we give the dynamical response for quasiparticles which is a special case of the general structure derived earlier 42 . We show that the correct compressibility appears and the third order sum rule can be satisfied if the effective mass and quasiparticle energy is chosen appropriately.…”

Section: Introductionmentioning

confidence: 99%

Dynamical local field, compressibility, and frequency sum rules for quasiparticles

Morawetz

2002

Phys. Rev. B

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The finite temperature dynamical response function including the dynamical local field is derived within a quasiparticle picture for interacting one-, two-and three dimensional Fermi systems. The correlations are assumed to be given by a density dependent effective mass, quasiparticle energy shift and relaxation time. The latter one describes disorder or collisional effects. This parameterization of correlations includes local density functionals as a special case and is therefore applicable for density functional theories. With a single static local field, the third order frequency sum rule can be fulfilled simultaneously with the compressibility sum rule by relating the effective mass and quasiparticle energy shift to the structure function or pair correlation function. Consequently, solely local density functionals without taking into account effective masses cannot fulfill both sum rules simultaneously with a static local field. The comparison to the Monte-Carlo data seems to support such quasiparticle picture. 05.30.Fk,21.60.Ev, 24.30.Cz, 24.60.Ky

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“…The local deviation δµ from the global chemical potential is selected so that the density of particles is conserved at each point and time instant. Momentum and energy conservations can be included, too, leading to slightly more complicated formulas [13,14].Let us now specify δµ from the condition of density conservation which requires that the local equilibrium distribution yields the same density as the actual distribution, n = p f = p f l.e. .…”

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confidence: 99%

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Femtosecond formation of collective modes due to mean-field fluctuations

2005

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Starting from a quantum kinetic equation including the mean field and a conserving relaxationtime approximation we derive an analytic formula which describes the time dependence of the dielectric function in a plasma created by a short intense laser pulse. This formula reproduces universal features of the formation of collective modes seen in recent experimental data of femtosecond spectroscopy. The presented formula offers a tremendous simplification for the description of the formation of quasiparticle features in interacting systems. Numerical demanding treatments can now be focused on effects beyond these gross features found here to be describable analytically.PACS numbers: 71.45. Gm, 78.47.+p, 42.65.Re, 82.53.Mj The last ten years have been characterized by an enormous activity about ultrafast excitations in semiconductors, clusters, or plasmas by ultrashort laser pulses. The femtosecond spectroscopy has opened the exciting possibility to observe directly the formation of collective modes and quasiparticles in interacting many-body systems. This formation is reflected in the time dependence of the dielectric function [1, 2, 3] or terahertz emission [4]. For an overview over theoretical and experimental work see [5,6]. Such ultrafast excitations in semiconductors have been satisfactorily described by calculating nonequilibrium Green's functions [7,8]. This approach allows one to describe the formation of collective modes [3,9] and even exciton population inversions [10].The experimental data in semiconductors like GaAs [2] or InP [3] reveal similar features. These features are explained by several numerically demanding calculations. Since some common features are robust, i.e., independent of the actual used material parameters, it should be possible to describe them by a simple theory. The origin of such robust features likely rests in the short-or transienttime behavior itself. At short times higher-order correlations have no time yet to develop, therefore the dynamics is controlled exclusively by mean-field forces.Based on the mean-field character of the short-time evolution we intend to derive a time-dependent response function from the mean-field linear response. We will start from a conserving relaxation-time approximation which dates back to an idea of Mermin [11,12]. Our aim is a simple analytic formula suitable for fits of experimental data.The electron motion is controlled by the kinetic energŷ E, the external perturbationV ext and the induced meanfield potentialV ind . The corresponding kinetic equation for the one-particle reduced density matrixρ readṡwith the relaxation time τ and a local equilibrium density matrixρ l.e. determined in the following. We will calculate the response in the momentum representationwhere |p is an eigenstate of momentum p. For interpretations it is more convenient to transform the reduced density matrix to the Wigner distribution in phase spacewhere R is the spatial coordinate. The relaxation process in Eq.(1) tends to establish a local equilibrium. Following Mermin...

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General response function for interacting quantum liquids

Cited by 31 publications

References 21 publications

Relaxation of an electron system: Conserving approximation

Relaxation of an electron system: Conserving approximation

Dynamical local field, compressibility, and frequency sum rules for quasiparticles

Femtosecond formation of collective modes due to mean-field fluctuations

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