High frequency dielectric function of metals taking into account Umklapp processes

Application of the Non-Equilibrium Statistical Operator Method to the Dynamical Conductivity of Metallic and Classical Plasmas

“…The most essential feature of the dependence of the effective collision frequency on electron temperature, for the case of ordered ion lattice with electron-phonon interactions and Umklapp processes, is that for T e > E F (E F ≈ 11.6 eV for solid-density aluminum) the real part ν is decreasing as ν ∼ T −4 e according to the asymptotic behavior of Expressions (52), see [14]. This is much faster than the scaling ν ∼ T −3/2 e for the case of electron-ion interaction in a high-temperature plasma [12].…”

“…In this paper, we present briefly the NSO method and its application to the permittivity of metallic plasmas, which is described by a Hamiltonian accounting for electron-phonon interactions and Umklapp processes, as well as the application to the permittivity of plasmas without a long-range order of ions, which is described by a Hamiltonian accounting for electron-ion and electron-electron interactions. We continue our previous investigations to work out a systematic quantum statistical approach to the response properties of WDM [10][11][12][13][14] with an application to aluminum, considering additional processes of interaction in the strongly coupled Coulomb system. We derive analytical expressions for the dynamical collision frequency and related quantities, in particular the absorption coefficient.…”

“…ν 1 (ω) is the complex effective collision frequency of electrons for Drude-like transitions (within the conduction band) and in single-moment approximation, while r ω (18) is the so-called renormalization factor, which takes into account the influence of higher moments of the density operator [8,12,22] and, in the case considered here, the influence of transitions between different bands. Inserting the solution of the system of Equations (14) for F m into Expressions (18), we obtain the complex effective collision frequency in terms of the correlation functions N nm and C nm . In our further considerations we look at the two following cases:…”

“…It was shown that this leads to an accuracy of a few % for the calculation of the renormalization factor. Therefore, restricting our approximation to only two bands or two moments of the density matrix in Cases (a) and (b), respectively, and using the solution of Equation (14), the renormalization factor can be written in terms of respective correlation functions:…”

A new algorithm for investigating strongly correlated systems using Hubbard model

“…Despite the simple appearance of the Hubbard model, it has an exact solution in only one dimension [6]. In larger than one-dimensional systems, the model is not solved exactly and various approximation methods have been used to study it, including mean field theory (MFT) [7], Green function decoupling schemes [8], functional integral formulations [9], and various other approximations [10].…”