Thermodynamic Green's Functions Research Articles

Electrical Conductivity of Charged Particle Systems and Zubarev’s Nonequilibrium Statistical Operator Method

One of the fundamental problems in physics which are not rigorously solved yet is the statistical mechanics of nonequilibrium processes. An important contribution to describe irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev who invented the method of the nonequilibrium statistical operator (NSO). We discuss this approach, in particular the extended von Neumann equation, and consider as example the electrical conductivity of a charged particle system. The selection of the set of relevant observables is considered. The relation between kinetic theory and linear response theory is shown. Using thermodynamic Green functions, a systematic treatment of correlation functions is given, but convergence has to be investigated. Different expressions for the conductivity are compared, and open questions are identified.

Influence of phonon-phonon coupling on superconducting state in honeycomb-type crystal lattice

We have taken into account the superconducting state inducing in the crystal lattice of the honeycomb-type. In the framework of the Eliashberg theory, we have determined the thermodynamic properties of the system. The phonon spectral function, which is the input parameter in the Eliashberg equations, has been calculated by using the thermodynamic Green functions. We have considered the model of the coupled Einstein oscillators with frequency ω0=100 meV. We have shown that the increasing inter-phonon coupling constant (f) causes the rapid growth of the critical temperature ([TC]max=36.2 K) just below the maximum value of f equal to 0.25ω0. Simultaneously, the order parameter and the thermodynamic critical field take the values increasingly distant from the predictions of the BCS theory, which results from the strong-coupling and the retardation effects.

Corrections to the Electrical Conductivity of the Fully Ionized Plasma at Moderate Values of the Degeneracy Parameter

AbstractThe influence of the electronic degeneration on the electrical conductivity of the fully ionized low‐density hightemperature plasma is investigated. The consideration basis is the following: the linear response theory in the formulation of Zubarev, Lenard‐Balescu‐type collision integrals with dynamical screening of the Coulomb interaction, the first Born approximation in the thermodynamic Green's functions technique. Asymptotic expansions for correlation functions for electron‐ion and electron‐electron scattering as functions of the degeneracy parameter Θ = kBT/EF in the range from Θ » 1 to Θ → 1 are obtained. The results presented are improved approximation formulas for the correlation functions and the electrical conductivity. The Spitzer factors for the electrical conductivity are slightly corrected. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy

We studied the lattice vibrations of two inter-penetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential, using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. In addition, as the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of the FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a non-zero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitionsmore » are continuous ones and that the phase transition may exhibit a “devil's staircase” behavior at a finite temperature.« less

Spectral Line Shapes of He I Line 3889 Å

Spectral line shapes of neutral helium 3889 Å(23S–33P) transition line are calculated by using several theoretical methods. The electronic contribution to the line broadening is calculated from quantum statistical many-particle theory by using thermodynamic Green's function, including dynamic screening of the electron-atom interaction. The ionic contribution is taken into account in a quasistatic approximation, where a static microfield distribution function is presented. Strong electron collisions are consistently considered with an effective two-particle T-matrix approach, where Convergent Close Coupling method gives scattering amplitudes including Debye screening for neutral helium. Then the static profiles converted to dynamic profiles by using the Frequency Fluctuation Model. Furthermore, Molecular Dynamics simulations for interacting and independent particles are used where the dynamic sequence of microfield is taken into account. Plasma parameters are diagnosed and good agreements are shown by comparing our theoretical results with the recent experimental result of Jovićević et al. (J. Phys. B: At. Mol. Opt. Phys. 2005, 38, 1249). Additionally, comparison with various experimental data in a wide range of electron density ne ≈ (1022− 1024)m−3 and temperature T ≈ (2−6) × 104 K are presented.

EFFECTS OF DEFECTS AND ANHARMONICITY ON dx2-y2 WAVE PAIRING SYMMETRY IN CUPRATES

In this paper, the renormalized frequency spectrum and one-particle spectral function of a high temperature superconductor (HTS) is studied using double time thermodynamic Green's function approach via a newly formulated Hamiltonian (without considering BCS type Hamiltonian) which includes the effects of electron–phonon interactions, anharmonicities and that of isotopic impurities. It is investigated that the renormalized frequency further invokes the appearance of energy gap and functional dependence of dx2-y2 wave pairing in the superconducting state in cuprates. The salient feature of the present theory is the electron–phonon interaction in the vicinity of the impurity atoms reveals four-fold symmetric quasiparticle "cloud" aligned with the nodes of d-wave superconducting gap, which is believed to characterize superconductivity in high temperature superconducting materials. It has been further inferred that, a modest contribution of anharmonicity can also induce superconductivity.

Renormalization effects and phonon density of states in high temperature superconductors

Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS) are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian) that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS) and agreements with experimental observations.

Quantum-statistical line shape calculation for Lyman-α lines in dense H plasmas

We present results for the Lyman-α line of hydrogen in dense plasmas. Full line profiles are calculated within a quantum-statistical method, based on thermodynamic Green's functions. The contributions of plasma ions and electrons are considered separately. Linear and quadratic Stark effect as well as quadrupole effects are taken into account for ions. The model microfield method is used to include ion dynamics. The focus of this work lies on the contribution to broadening and shift by free electrons beyond the Born approximation. The effect of strong collisions can be identified as ladder-like diagrams of the electron-emitter propagator. In an effective two-particle approximation, the electronic self-energy is given in terms of scattering amplitudes, analogous to Baranger's expressions [Baranger, M 1958 Phys. Rev. 112 855]. We obtained scattering amplitudes from convergent close-coupling calculations including medium effects via Debye screening. Additionally, the electronic coupling between initial and final states is taken care of by a vertex correction. In our examples, the free electron density ranges between 1023 and 1025 m−3 at a plasma temperature of 1 and 2 eV, respectively.

Spectral Line Broadening in Dense Plasmas

Spectral line broadening is calculated based on a microscopic quantum statistical approach. By using thermodynamic Green's function, plasma correlation effect, electrostatic and dynamic screening, and perturber-radiator interaction are taken into account. Ions are treated in quasistatic approximation due to Stark effect. The line broadening for 6678 Å (21P-31D) and 5016 Å (21S-31P) transitions of neutral helium is calculated in the electron density range ne=(0.25–50)×1022 m-3 and temperature range T=(0.5–4)×104 K, and the density and temperature dependence of the line width are investigated. A good agreement is shown by comparing the calculated values with the existing experimental and theoretical data.

Perturbation theory for the Matsubara green function with the Hamiltonian of the one-impurity problem: The Dyson equation

A technique for computing the thermodynamic (Matsubara) Green function for the Hubbard Hamiltonian as applied to the one-impurity problem is proposed. There are only four states in this problem, which makes it solvable.

Quantum Theory of Solid State Plasma Dielectric Response

AbstractWe review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired “second quantized” creation and annhilation field operators of interacting quantum many‐body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron‐hole pair excitations and plasmons (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T c mediated by the antiferromagnetic exchange and spin fluctuations.

Dynamic mean field in the Hubbard model

In the framework of the one-impurity problem formulated for the nondegenerate Hubbard Hamiltonian, general expressions are derived for all its principal correlation functions, as well as its retarded and advanced thermodynamic (Matsubara) Green functions. These results are analyzed for the case of zero temperature.

Dynamic Local Field Corrections for Two‐Component Plasmas

AbstractTwo approaches to the dynamic local field correction for two‐component plasmas are combined with each other. In the first one, we start from the Zubarev approach to linear response theory and use perturbative techniques such as thermodynamic Green's functions. Via this approach, we obtain an approximation for the dynamical collision frequency. In a second approach, we extend the Mermin ansatz to allow for local‐field corrections besides electron‐ion collisions. These are implemented using the recurrence relation technique for electronelectron correlations making use of up‐to‐date results for the interacting electron gas. Exploratory calculations are performed for impurity scattering in an electron gas at T = 0. Static local field corrections due to Farid et al. are employed in describing the interacting electron gas in the static limit. The influence of collisions and correlations on the plasmon dispersion is investigated. Implications for plasma diagnostics are discussed (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Pressure Broadening of Some He I Lines

Quantum statistical approach is adopted for calculating the spectral line shapes of neutral helium in dense plasmas. Stark broadening of isolated He I lines 5048 Å (), 3889 Å (), and 3188Å () is presented. Based on thermodynamic Green's function, the electronic contribution to the shift and width is considered. The participation of ions to the line broadening is treated in a quasistatic approximation, by taking both quadratic Stark effect and quadrupole interaction into account. The calculated shifts and widths are compared with existing data.

Refraction Indices of Non-Uniform Systems from the First Principles

ABSTRACTA novel, first-principle theoretical approach and synergetic computational methods designed to predict electronic and magnetic transport properties of strongly spatially inhomogeneous systems, including small quantum dots and wires (QDs and QWs, respectively), and molecules, have been developed recently. This approach is based on a many-body quantum theoretical formalism - a projection operator method due to Zubarev and Tserkovnikov (ZT) - formulated in terms of the equilibrium, two-time temperature Green functions (or TTGFs). There are several significant advantages of this approach, as compared to traditional non-equilibrium two-time thermodynamic and field-theoretical Green's function (NGF) methods that are currently used to study electronic and magnetic transport properties of strongly spatially inhomogeneous systems. In particular, the TTGFs are directly related to experimentally assessable microscopic charge, spin and microcurrent densities.In the work reported here the TTGF-based approach has been used to derive a fundamental, yet tractable expression for the space-time Fourier transform of the tensor of quasi-local refraction indices (TRI) from the first principles. The TTGFs necessary to predict TRI can be calculated using quantum statistical mechanical means, modeling and simulations, and experimental data. Applications of the theoretical predictions for TRI open new prospects in materials design. In particular, the derived theoretical expression for TRI can be used to guide experimental synthesis of structured materials and systems with both direction- and position-dependent indices of refraction in desirable frequency ranges.

Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.

Analysing brilliance spectra of a laser-induced carbon plasma

Brilliance spectra of a carbon plasma generated by subpicosecond high intensity laser pulses are analysed (Wilhein et al 1998 J. Opt. Soc. Am. 15 1235). The plasma parameters such as electron density and temperature are determined using a plasma slab model. Synthetic carbon He-α and He-β line profiles are calculated for the inferred plasma parameters by using thermodynamic Green's function, based on a microscopic quantum statistical approach assuming local thermal equilibrium. Self-absorption is taken into account considering one-dimensional radiation transport equation. The comparison between the measured spectrum and our calculated synthetic profile is good for He-α line (C V 1s2–1s2p), while discrepancies are found in the case of He-β line (C V 1s2–1s3p).

Thermodynamic Green functions in theory of superconductivity

A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models. A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function. By applying the noncrossing approximation for the self-energy, a closed selfconsistent system of equations is obtained, similar to the conventional Eliashberg equations. A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.

Shift and broadening of neutral helium spectral lines in dense plasmas

Shift and broadening of isolated neutral helium lines 7281Å (21P − 31S), 6678 Å (21P − 31D), and 4713 Å (23P − 43S) in a dense plasma are investigated. Based on a quantum statistical theory using thermodynamic Green's functions, where the electronic contributions to the shift and width are considered. Dynamical screening of the electron-atom interactions are included. Compared to the width, the electronic shift is more affected by dynamical screening. This effect is increased at high density. A cut-off procedure for strong collisions is used. The effect of the ions are taken into account in a quasi-static approximation, with both the quadratic Stark effect and the quadrapole interaction. The results for shift and width agree well with theoretical calculations and experimental data.