Temperature Green Functions Research Articles

Coupled thermoviscoelastodynamic Green's functions for bi‐material half‐space

By virtue of the representations of displacements, stresses, and temperature fields in terms of two scalar potential functions and the use of correspondence principle, an analytical derivation of fundamental Green's functions for bi‐material half‐space composed of a transversely isotropic thermo‐elastic layer and an isotropic thermo‐visco‐elastic half‐space affected by finite surface or interfacial sources is presented. With the aid of the potential function relationships, the coupled equations of motion and energy equation in both the half‐space and the layer are uncoupled and solved with the aid of Fourier series and Hankel integral transforms. Responses of the medium are derived in the form of improper line integrals related to Hankel inversion transforms. To show the effects of anisotropy and viscoelasticity on the propagation of coupled thermoviscoelastic waves, the derived integrals for displacements, stresses, and temperature Green's functions are evaluated by a numerical scheme.

Least square based method for obtaining one-particle spectral functions from temperature Green functions

A least square based fitting scheme is proposed to extract an optimal one-particle spectral function from any one-particle temperature Green function. It uses the existing non-negative least square (NNLS) fit algorithm to do the fit, and Tikhonov regularization to help with possible numerical singular behaviors. By flexibly adding delta peaks to represent very sharp features of the target spectrum, this scheme guarantees a global minimization of the fitted residue. The performance of this scheme is manifested with diverse physical examples. The proposed scheme is shown to be comparable in performance to the standard Padé analytic continuation scheme.

Full density-matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model

Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models (see A. Weichselbaum and J. von Delft) by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller (2005). While these developments prove particularly useful in the calculation of transient response and finite temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to the Anderson impurity model. We compare the results for the susceptibility and specific heat to both the conventional approach within NRG and to exact Bethe ansatz results. We also point out a subtlety in the calculation of the susceptibility (in a uniform field) within the FDM approach. Finally, we show numerically that for the Anderson model, the susceptibilities in response to a local and a uniform magnetic field coincide in the wide-band limit, in accordance with the Clogston-Anderson compensation theorem.

From Hardcore Bosons to Free Fermions with Painlevé V

We calculate zero temperature Green's function, the density--density correlation and expectation values of a one--dimensional quantum particle which interacts with a Fermi--sea via a $\delta$--potential. The eigenfunctions of the Bethe-Ansatz solvable model can be expressed as a determinant. This allows us to obtain a compact expression for the Green's function of the extra particle. In the hardcore limit the resulting expression can be analysed further using Painlev{\'e} V transcendents. It is found that depending on the extra particles momentum its Green's function undergoes a transition of that for hardcore Bosons to that of free Fermions.

Frequency and wave number dependence of the shear correlator in strongly coupled hot Yang-Mills theory

We use AdS/QCD duality to compute the finite temperature Green's function G(omega,k;T) of the shear operator T_12 for all omega,k in hot Yang-Mills theory. The goal is to assess how the existence of scales like the transition temperature and glueball masses affects the correlator computed in the scalefree conformal N=4 supersymmetric Yang-Mills theory. We observe sizeable effects for T close to T_c which rapidly disappear with increasing T. Quantitative agreement of these predictions with future lattice Monte Carlo data would suggest that QCD matter in this temperature range is strongly interacting.

A general method for testing validity of one-particle spectral functions

Based on the fact that the one-particle spectral function is uniquely extracted from a temperature Green function, a scheme is proposed to test the validity of a one-particle spectral function derived from any temperature Green function of any interacting system under thermal equilibrium. The physical implication of the scheme is discussed. An example is worked out to explicitly show the effectiveness of the scheme.

Quantum Transfer Matrix Approach to Dynamical Correlation Functions for the Transverse Ising Chain

The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is applied to dynamical problems. The autocorrelation functions of the Transverse Ising chain are derived by this method as an example. The Trotter-directional correlation functions are interpreted as a Matsubara’s temperature Green function, so that the analytic continuation of the Green functions yields the desired autocorrelation functions. Subject Index: 040, 043, 046, 070, 370

Statistical mechanics and the physics of many-particle model systems

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green's functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasiparticle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spin-fermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasiaverages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.

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.

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green's functions of antiferromagnetic state in three-band Hubbard model are studied by using functional integrals and temperature Green's function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.

Diagram technique for models with internal Lie-group dynamics

Nanosystems and strongly correlated systems can possess a more complicated internal Lie-group dynamics in comparison with the Lie-group dynamics of Bose and Fermi systems described by the Heisenberg algebra and superalgebra, respectively. In order to investigate properties of such quantum systems, we represent operators of quantum systems by differential operators over a commutative algebra of regular functionals and develop a new diagram technique on the basis of the expansion of the generating functional for the temperature Green functions. The differential representation makes it possible to generalize functional equations and the diagram technique for the case of quantum systems on topologically nontrivial manifolds by the substitution of the generating functional on a sheaf of function rings on a nontrivial manifold for the generating functional of a constant sheaf of functions. Nontrivial cohomologies of the manifold, on which the quantum system is acted, lead to the existence of additional excitations. We consider the self-consistent-field approximation and the approximation of effective Green functions and interactions. Poles of the matrix of effective interactions and Green functions determine quasi-particle excitations of the quantum system. For special cases of models the diagram expansion is simplified. In particular, if the internal dynamics is determined by the Heisenberg algebra (superalgebra), the diagram expansion reduces to Feynman's diagrams for Bose (Fermi) quantum systems. We consider the reduction of the developed diagram technique and excitations for the case of the spin system with an uniaxial anisotropy.

A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces

We derive a formula connecting in any dimension the Green function on the (D + 1)-dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D-dimensional hyperbolic space. The relation takes a simple form in the momentum space where the Green functions are equal at the momenta (p0, p) for Rindler and for hyperbolic space with a simple additive relation between the squares of the mass and the momenta. The formula has applications to finite temperature Green functions, Green functions on the cone and on the (compactified) Milne spacetime. Analytic continuations and interacting quantum fields are briefly discussed.

CORRELATIONS IN HOT ASYMMETRIC NUCLEAR MATTER

The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and neutrons are studied as a function of the density and the asymmetry of the system. The proton states are more strongly depleted when the asymmetry increases, whereas the occupation of the neutron states is enhanced compared to the symmetric case. Preliminary results for the entropy and the free energy are also presented.

Quantum separability of thermal spin one boson systems

Using the temperature Green's function approach we investigate entanglement between two non-interacting spin 1 bosons in thermal equilibrium. We show that, contrary to the fermion case, the entanglement is absent in the spin density matrix. Separability is demonstrated using the Peres-Horodecki criterion for massless particles such as photons in black body radiation. For massive particles, we show that the density matrix can be decomposed with separable states.

On the spectral relations for multitime correlation functions

A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such contributions can be treated in a rigorous way using multitime temperature Green functions. Representation of the multitime Green functions in terms of the spectral densities and solution of the reverse problem -- finding of the spectral densities from the known Green functions are given for the case of the three-time correlation functions.

Description of a Heisenberg ferromagnet above the Curie point as a spin liquid

A Heisenberg ferromagnet (F) with spin S=1/2, found in a spin-liquid (SL) state at temperatures above the Curie point τC, is considered. In this spin-liquid state there is no long-range magnetic order but the short-range order is preserved, and the spin correlation functions are isotropic. The spin liquid is described in the framework of a second-order theory by the method of temperature Green functions. The main thermodynamic characteristics of the spin liquid are found as the result of a self-consistent numerical solution of a system of three integral equations. The Curie point τC+, at which the dc magnetic susceptibility at wave vector q=0 diverges, is determined. A comparison of the thermodynamic characteristics of the system in the F state (τ⩽τC, spin-wave theory) and in the SL state (τ⩾τC+) is made. It is shown that τC+>τC, and a modification of spin-wave theory in which τC reaches the value τC+ is indicated. At the point of the F-SL phase transition the spin correlation functions suffer a finite discontinuity, and with increasing temperature they fall off ∝ 1/τ. The heat capacity of the ferromagnet at τ→τC goes to infinity, while in the SL state the heat capacity remains finite at the point τC+ and falls off for τ≫τC+ in proportion to 1/τ2. The susceptibility obeys the Curie-Weiss law.

Correlations in hot asymmetric nuclear matter

The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and neutrons are studied as a function of the density and the asymmetry of the system. The proton states are more strongly depleted when the asymmetry increases while the occupation of the neutron states is enhanced as compared to the symmetric case. The self-consistent Green's function approach leads to slightly smaller energies as compared to the Brueckner Hartree Fock approach. This effect increases with density and thereby modifies the saturation density and leads to smaller symmetry energies.

Linearized Quantum Conductivity of Atomic Clusters and Artificial Molecules

ABSTRACTThe explicit expression for the linearized longitudinal quantum conductivity of inhomogeneous systems (such as semiconductor atomic clusters, artificial molecules, etc.) in weak electro-magnetic fields derived recently within a first principle quantum statistical mechanical approach in terms of the equilibrium two-time temperature Green functions (TTGFs) has been analyzed to develop analytical and computational means for its calculations. This has been done using a generalized continuous fraction method due to Zubarev and Tserkovnikov (ZT). The TTGFs have been related to Kubo's relaxation functions of the charge density and its gradients that can be computed using available quantum statistical mechanical algorithms and software. Thus, it becomes possible to predict the linearized quantum conductivity of any small system (in particular small semiconductor quantum dots (QDs)) as a function of external electromagnetic fields using a unified fundamental approach. This knowledge can be used to develop small semiconductor QD-based highly sensitive tunable sensors based on changes in the conductivity caused by external electromagnetic fields (in particular, radiation).

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

A hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite dimensional spaces. The local states restricted to the subalgebra generated by fluctuations of displacements of particles are in the center of the study. They are described by means of the corresponding temperature Green (Matsubara) functions. The result of the paper is a theorem, which describes the critical point convergence of such Matsubara functions in the thermodynamic limit.

Two-band soliton-like polaron model for MgB 2 superconductivity

Using a two-band soliton-like polaron model of a deformable continuum, the critical temperature, energy gap and other parameters in MgB 2 superconductor are studied in the framework of finite temperature Green's function technique. Two group of equations for the two energy gaps and two transition temperatures are derived by taking into account the different dimensionality of the relevant bands involved. Based on the ratio between the quasi-2D σ-band energy gap Δ 1 and the quasi-particle ground-state energy | E g1 |, we find, in agreement with recent findings, that the conventional ratio 2 Δ 1/ k B T c1 for the 2D σ-band can take a value ∼4.4. Based on the ratio of the quasi-particle kinetic energy and quasi-3D energy gap Δ 2, we find instead for the smaller π-band ratio 2 Δ 2/ k B T c2 the value ∼2.3. Both these estimates are in quantitative agreement with experimental measurements. The calculated transition temperatures, energy gaps, coherence length and Fermi velocity, are also in agreement with recent experimental data and ab initio calculations.