Matsubara Functions Research Articles

Phonon affected transport through molecular quantum dots

To describe the interaction of molecular vibrations with electrons at a quantum dotcontacted to metallic leads, we extend an analytical approach that we previously developedfor the many-polaron problem. Our scheme is based on an incomplete variationalLang–Firsov transformation, combined with a perturbative calculation of theelectron–phonon self-energy in the framework of generalized Matsubara functions. Thisallows us to describe the system at weak-to-strong coupling and intermediate-to-largephonon frequencies. We present results for the quantum dot spectral function and for thekinetic coefficient that characterizes the electron transport through the dot. With theseresults we critically examine the strengths and limitations of our approach, and discuss theproperties of the molecular quantum dot in the context of polaron physics. Weplace particular emphasis on the importance of corrections to the concept of ananti-adiabatic dot polaron suggested by the complete Lang–Firsov transformation.

Magnon–phonon coupling in two-dimensional Heisenberg ferromagnetic system

A magnon–phonon interaction model is set up for a two-dimensional insulating ferromagnetic system. By using Matsubara function theory, we have studied the magnon spectrum and calculated the magnon dispersion curve on the main symmetric point and line in the Brillouin zone for various parameters of the system. The results show that at the boundary of Brillouin zone, there is a strong magnon softening. The contributions of longitudinal and transverse phonons on the magnon softening are compared and the influences of various parameters are also discussed.

Magnon damping in two-dimensional Heisenberg ferromagnetic system

A magnon–phonon interaction model is set up for a two-dimensional insulating ferromagnetic system. By using Matsubara function theory we have studied the magnon damping − I m Σ ∗ ( 1 ) ( k → ) and calculated the magnon damping − I m Σ ∗ ( 1 ) ( k → ) curve on the main symmetric point and line in the Brillouin zone for various parameters in the system. It is concluded that at the boundary of Brillouin zone there is a strong magnon damping. However, the magnon damping is very weak on the zone of small wave vector and the magnon damping reaches maximal value at very low temperature. The contributions of longitudinal phonon and transverse phonon on the magnon damping are compared and the influences of various parameters are also discussed.

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.

Matsubara-Green's function approach to tunnelling in mesoscopic junctions

An expression for the ensemble-averaged current in a mesoscopic tunnel junction that is connected to a voltage source, via an impedance, is presented. The quantum description of the system includes the quantum fluctuations due to the environment. Iterative calculation of the spectral density function associated with the Matsubara function of the external circuit yields the time-averaged characteristics.

Influence of isotopic disorder on phonon frequencies and phonon linewidths of an anharmonic crystal

Based on a perturbation theory using Matsubara functions and a diagrammatic treatment, it is shown that the phonon linewidths of an anharmonic crystal with isotopic impurities include two different contributions, a disorder-induced temperature-independent part, caused by harmonic scattering processes of phonons at isotopic impurities, and a disorder-influenced temperature-dependent part, caused by anharmonic decay processes. Whereas in case of an anharmonic ideal crystal it is usual to restrict the corresponding self-energy on diagonal elements only, this is no longer sufficient in the presence of impurities. For that reason it is shown that only nondiagonal elements of the effective vertex function of the harmonic phonon propagator contribute to the disorder-induced contribution to the phonon linewidth, whereas the corresponding harmonic and the anharmonic frequency shifts are determined by diagonal and nondiagonal elements as well. As an application, numerical results of the disorder-induced temperature-independent as well as the disorder-influenced temperature-dependent contribution to the phonon linewidths of a diatomic linear chain with a single mass defect are presented. {copyright} {ital 1996} {ital The American Physical Society}

Theory of phonon-phonon interaction in anharmonic crystals with randomly distributed isotopic impurities.

In the expansion of well known results of dynamic properties of anharmonic ideal crystals, a perturbation theory using Matsubara functions and diagrammatic treatment has been carried out to describe the phonon-phonon interaction in anharmonic crystals with randomly distributed isotopic impurities. Taking explicitly into account anharmonic contributions of the potential expansion as well as mass changes between impurities and host-lattice particles, it is shown that the anharmonic phonon propagator can be written as a sum of terms, which are added up within a Dyson equation. In contrast to the results obtained recently using the formalism of the double-time retarded Green functions, our proper self-energy of the nonaveraged crystal includes explicitly the influence of the isotopic disorder. As an application, a diatomic linear chain with a single mass defect was chosen and numerical results of the impurity-influenced two-phonon density of states as well as the anharmonic damping function are presented.

Matsubara functions of ( p, q)-deformed phonon systems

The Matsubara functions and their Fourier transforms of “free” ( p, q)-deformed phonon systems with two possible Hamiltonians are discussed. It is shown that with the ( p, q)-deformation of phonons, the Matsubara functions are changed both in the strength and the pole structure. Some fermionic bound states will appear via a hidden interaction between “free” ( p, q)-deformed phonons.

Infrared Absorption in Anharmonic Crystals with Impurities: An Application to a Diatomic Linear KI‐Chain

AbstractIn expansion of well‐known results of dynamic and optical properties of anharmonic ideal crystals, a perturbation theory, using Matsubara functions and diagrammatic treatment is carried out to describe anharmonic crystals with impurities. Taking explicity into account anharmonic contributions of the potential expansion up to fourth order, mass changes as well as force constant changes between impurity and host‐lattice particles, it is shown that the anharmonic phonon propagator can be written as a sum of terms, which are added up within a Dyson equation. The corresponding proper self‐energy includes impurity‐activated harmonic as well as impurity‐influenced anharmonic contributions. As an application the infrared absorption of a diatomic linear KI‐chain with next‐neighbour interaction, a single mass defect, and consideration of anharmonicities up to second order of the van Hove parameter (O(α2)) is chosen. Numerical calculations of temperature‐dependent lineshapes and shifts of defect and main absorption lines are presented and discussed together with results of defect‐induced in‐band absorption.

Matsubara functions of (p, q)-deformed phonon systems

Matsubara functions of (p, q)-deformed phonon systems

Many-body Green functions of q-deformed oscillators

Certain thermal (Matsubara) Green functions are obtained for a “free” system of quantum-deformed harmonic oscillators. It is shown that the form of the single-particle Matsubara function is changed, with an explicit dependence on s = 1n q appearing in a simple form and suggesting that quantum-deformed commutation rules intrinsically incorporate interactions even in the “free case”. A two-particle Matsubara function gives no evidence of a bound state energy shift.

Exciton-phonon interaction and temperature-dependent optical bistabilities of semiconductor CdS

In this paper we consider the exciton absorption and the effect of phonons. We derive a Hamiltonian for the system of an optically bistable material — a semiconductor CdS film, in which the exciton density is not too high. By the Matsubara function and the Feynman diagram expansion technique, we obtained the photon density, the rate between outgoing and incident light intensity at room- and cryo-temperature, and the results agree very well with experiments. Also, we have obtained the curve of the switching power versus temperature which can be used to design low consuming-power and high-speed optical devices, especially an optical computer.