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

Morawetz, Klaus

doi:10.1103/physrevb.66.075125

Cited by 10 publications

(12 citation statements)

References 54 publications

(140 reference statements)

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“…with the last equality valid for zero temperature [83]. The static limit of the latter one is nonzero, which is no contradiction since the long-wave length expansion is performed while the small-frequency limit is written in the first line.…”

Section: Local Field Correctionmentioning

confidence: 99%

“…In the previous paper [83] the situation had been investigated where no currents are present and therefore B = 0 or m = m * and = 0 . Please note that the difference in the two masses has been recognized in the Fermi liquid theory [30] and obviously reflects the properties of the running frame.…”

Section: Galilean Invariancementioning

confidence: 99%

“…The last term describes the dragging of particles due to the frame velocity v and reads explicitly (83) δJ n v = J n δ ln n m * .…”

Section: Backflowsmentioning

confidence: 99%

“…Unfortunately, even the dynamic quantum version of the Singwi-Tosi-Land-Sjölander local field cannot fulfill the compressibility sum rule [82]. The reason is that a single degree of freedom like the self-energy cannot provide this demand and in a previous paper it was shown that one can fulfill both sum rules by introducing two degrees of freedom: the self-energy and the effective mass [83]. While this is impossible with static local field corrections [60,79], the inclusion of the effective mass besides the self-energy makes it possible to adapt these two quantities to complete both sum rules.…”

Section: Introductionmentioning

confidence: 99%

“…The other line of improvements includes collisional correlations in the response [93][94][95][96][97], mostly in relaxation time approximation and imposes conservation laws [83,[98][99][100][101]. The extensions of this dielectric function first published by Mermin [93] has been applied to stopping power problems [98,102].…”

Section: Introductionmentioning

confidence: 99%

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Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

Morawetz

2013

Phys. Rev. E

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The general possible form of mean-field parametrization in a running frame in terms of current, energy, and density functionals is examined under the restrictions of Galilean invariance. It is found that only two density-dependent parameters remain which are usually condensed in a position-dependent effective mass and the self-energy formed by current and mass. The position-dependent mass induces a position-dependent local current, which is identified for different nonlinear frames. In a second step the response to an external perturbation and relaxation towards a local equilibrium is investigated. The response function is found to be universal in the sense that the actual parametrization of the local equilibrium does not matter and is eliminated from the theory due to the conservation laws. The explicit form of the response with respect to density, momentum, and energy is derived. The compressibility sum rule as well as the sum rule by first- and third-order frequency moments are proved analytically to be fulfilled simultaneously. The results are presented for Bose or Fermi systems in one, two, and three dimensions.

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Section: Local Field Correctionmentioning

confidence: 99%

Section: Galilean Invariancementioning

confidence: 99%

“…The last term describes the dragging of particles due to the frame velocity v and reads explicitly (83) δJ n v = J n δ ln n m * .…”

Section: Backflowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

Morawetz

2013

Phys. Rev. E

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Variational solution of theT-matrix integral equation

Nechaev

Chulkov

2005

Phys. Rev. B

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We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and frequency. By examining the ladder diagrams for irreducible polarizability, a connection between this interaction and the local-field factor is established. Based on the obtained solution, a form for the T-matrix contribution to the electron self-energy in addition to the GW term is proposed. In the case of the electron-hole multiple scattering, this form allows one to avoid double counting.

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

Cited by 10 publications

References 54 publications

Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

Variational solution of theT-matrix integral equation

Femtosecond formation of collective modes due to mean-field fluctuations

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