Mori Formalism Research Articles

Conductivity of an interacting two-channel Tomonaga-Luttinger model.

Conductivity of a coupled two-channel dirty Tomonaga-Luttinger model is calculated from the Mori formalism. We find that the conductivity becomes enhanced as the interchannel interaction is turned on even when the interaction is repulsive. This effect is opposite to those from the 2${\mathit{K}}_{\mathit{F}}$ charge-fluctuation coupling in systems with the channel separation 1/${\mathit{k}}_{\mathit{F}}$, and is considered to come from the suppressed charge-density-wave fluctuations.

A generalized langevin equation for wave functions. Intramolecular vibrational dephasing as a stochastic process

A generalized Langevin equation satisfied by time-evolving wave functions is derived by adapting the Mori formalism to the Schrödinger time dependent equation. The equation obtained describes both deterministic and stochastic time evolution of wave functions. Memory kernel of the ”delayed friction” term of the equation obtained consists of the temporal correlation function (in the quantum mechanical sense) among non-stationary wave function, i.e., wave packets. The memory is likely to decline rapidly essentially due to the dispersion of the wave packets, so that a “Markov” limit is justified. An ensemble of probability amplitudes of different quantum states is considered, and the probability distribution of these probability amplitudes is discussed. This probability distribution is connected with spectroscopic observables: It can be derived from excitation profiles of Raman scattering amplitudes with many different final states. By assuming the “random force” term of the Langevin equation to be Gaussian white noise, a Fokker-Planck equation is derived. The solution of this Fokker-Planck equation describes how “randomization” proceeds in intramolecular vibrational dephasing. As time goes to infinity, all the accessible states are equally populated on the average, but fluctuation around the “microcanonical equilibrium” remains.

Anomalous vortex dynamics in two-dimensional superconducting arrays.

The dynamical response of a superconducting array, modeled by the two-dimensional classical XY model, is studied by using equations of motion for vortices and spin waves. The vortex conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathit{v}}$ is evaluated in the framework of Mori's formalism. ${\mathrm{\ensuremath{\sigma}}}_{\mathit{v}}$ has a finite zero-frequency limit in the case of a spin dynamics corresponding to the resistively shunted junction model, but it goes to zero logarithmically with frequency for a Landau-Ginzburg dynamics. The latter behavior has been observed in recent experiments and computer simulations.

Mori approach to exciton memories in initially unrelaxed excitonphonon systems: direct and reorganized perturbation expansions

Starting from the Mori formalism, memory functions of excitons coupled to harmonic phonons in periodic crystals with linear exciton-phonon coupling are calculated in two limiting cases: that of the narrow unrenormalized exciton band with only site local coupling and that of the weak exciton-phonon coupling. Mutual correspondence as well as that with results of analogous works is discussed. By a mathematical trick, perturbational series for memory kernel of initially unrelaxed excitons interacting locally with harmonic phonons is then reorganized. Using that, full agreement is achieved with previous results obtained by Generalized Master Equations for initially relaxed excitons in case of narrow exciton band width. For the weak exciton-phonon coupling case, appreciable reduction of damping of the quasicoherent channel may be achieved on account of polaron effects. Crucial role of the exciton bandwidth beyond the lowest order is found in both cases for the low-temperature exciton diffusivity. Some predictions on the temperature dependence of the phonon-scattering limited exciton diffusion constant are given

Free carrier contribution to dynamic dielectric function of heavily doped semiconductors. Application to n‐type silicon

AbstractA new approximation to calculate the free carrier contribution to the infrared dielectric function in n‐type silicon at room temperature that interpolates the quantum and classical absorption regimes is proposed. This approximation generalizes the Drude‐Lorentz approximation by introducing a frequency dependence of the relaxation parameter which is calculated via Mori formalism. Calculations of carrier concentration and wavelength dependences of the relaxation parameter, dielectric constant and optical constants for concentration intervals from 1.3 × 1015 to about 1.3 × 1020 cm−3 and in the wavelengths range from 1 to 30 μm are performed. The deviations from the Drude‐Lorentz approximation are discussed.

Dynamical theory for strongly correlated two-dimensional electron systems.

We describe a method for treating the time-dependent behavior of the electron cloud surrounding each electron in a two-dimensional electron gas. The method is based on a conserving solution of the quantum kinetic equation for the relaxation function of the system using the Mori formalism with two distinct memory functions, one for the collective degrees of freedom and one for the single-particle modes. At lower electron densities these dynamic effects are shown to become increasingly important and to play a part in the eventual solidification into a Wigner crystal. We find that the plasmon resonance energy ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$(q) is strongly depressed compared with the random-phase approximation, leading to a negative dispersion for large q in the low-density region. We have determined the width of the plasmon peak and find that as the Wigner-crystal transition point is approached, the plasmon peak remains well defined even for q comparable to the Fermi momentum. For ${\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}20, we observe a low-energy peak in the excitation spectrum of the electron liquid for values of q matching the reciprocal vector of the Wigner lattice. The occurrence of this peak is matched by the appearance of a large peak in the static susceptibility at that q value.

Microscopic derivation of multiple-trapping equations for amorphous semiconductors

We consider a one band Hamiltonian which contains a dynamical random potential, for the electrons in an amorphous semiconductor. Using time and space resolved Wigner operators, we apply Mori's formalism to obtain, at zero temperature, Anderson localization in the same way as Gotze and, at finite temperature, phononic delocalization. Deriving a hydrodynamic equation for the density fluctuations, we identify the so-called capture and release rates of the multiple-trapping model with our microscopic expressions.

A Projection Operator Approach to Extended Irreversible Thermodynamics

Based on the projection·operator formalism established by Mori for Langevin equations, a general theory is formulated which is applicable to the description of transient irreversible processes. A time-smoothed density matrix (previously discussed by the present author) is used to define the projection operator in place of the equilibrium density matrix in Mori's formalism. It is shown that a statistical mechanical theory for transient processes can be developed in our formalism that dovetails perfectly with extended irreversible thermodynamics. 1 ) has been undeniably useful for the analysis of many phenomena in non-equilibrium macroscopic systems, it presents some very well-known limitations. The traditional theories are closely modeled on classical Fourier-N avier-Stokes theory, and it has long been accepted that they share the difficulty of predicting infinite propagation speeds for thermal ·and viscous disturbances. The parabolic character of the equations has been a source of concern. Mtiller 2 ) proposed that one way of generalizing linear irreversible thermodynamics was to modify the local-equilibrium assumption by introducing an extended entropy which depends on both the classical extensive variables and their fluxes. This proposal has given rise to the present form of extended irreversible thermodynamics. 3 )

A Projection Operator Approach to Extended Irreversible Thermodynamics

Based on the projection-operator formalism established by Mori for Langevin equations, a general theory is formulated which is applicable to the description of transient irreversible processes. A time-smoothed density matrix (previously discussed by the present author) is used to define the projection operator in place of the equilibrium density matrix in Mori's formalism. It is shown that a statistical mechanical theory for transient processes can be developed in our formalism that dovetails perfectly with extended irreversible thermodynamics.

Diffusion of particles in an inhomogeneous medium: High-friction limit.

We develop an inverse friction expansion for the diffusion of particles in an inhomogeneous medium based on the Mori formalism starting from a microscopic Hamiltonian. The friction is related to the vibrational correlation function of the substrate. An analytic formula is obtained for the diffusion constant in the high-friction limit.

The temperature dependence of the direct current electrical conductivity in quasi-one-dimensional organic metals

The dc electrical conductivity above the Peierls-transition temperature Tc of quasi-one-dimensional (1D) organic metals is calculated by an ab initio single-particle theory based on the Kubo–Mori formalism. The respective inverse relaxation time in this approach is calculated numerically. The theory allows for a reliable reproduction of experimentally derived normalized conductivity curves of highly anisotropic organic metals. The applicability of the model is reduced with decreasing anisotropy. Phenomenologically it can be shown that a T−2 law of decay of the dc electrical conductivity above Tc is conventionally connected with large anisotropies. Decreasing anisotropy leads to T−n curves, where n is sizeably smaller than 2. The theoretical approach reproduces a T−n, n≊2, law of decay in the framework of one-phonon electron scattering processes. Therefore it is suggested that the deviations from the T−1 behavior of conventional three-dimensional metals is caused by the strong Kohn anomaly in 1D systems. The influence of the electron–phonon coupling and the Debye temperature on the analytic structure of the normalized dc electrical conductivity curves has been studied. A general theoretical description is suggested to account for the influence of electronic correlations on the magnitude of the electron–phonon coupling as well as on the Peierls-transition temperature. It is shown qualitatively that the organic metals belong to a class of valence fluctuating systems where charge fluctuations are conserved also in the limit of strong electronic correlations.

Molekülinterne Dipolorientierung und dielektrische Absorption in verdünnter Lösung bei Mikro-und Submillimeterwellen. V.Acetyl-Verbindungen

Abstract The dielectric loss of sixteen molecules, eleven with the acetyle group in aromatic bonds and five in aliphatic bonds, has been measured in very dilute solutions of cyclohexene at 20 °C. Five of these molecules are investigated in decalene solutions, too. The measurements have been made at wavenumbers in the range 0.08 to 140 cm -1 above 8 cm -1 making use of a pumped molecular laser. They are supplemented by the data of a Fourier transform spectrometer up to 300 cm -1. All microwave spectra of loss factor ε″ are analysed in terms of three absorption areas using the two variable Mori formalism. On the other hand, Lorentz curves are fitted to the FIR absorption spectra of α(v̄). The fast relaxation process of the aliphatic compounds is suggested to be due to intramolecular reorientation of the acetyle group itself, since in acetyle cyclohexene the remaining part of the molecule is rigid. To the contrary, the acetyle group is not able to reorientate swiftly, if bounded to aromatic rings. Presumably, it is fixed by mesomeric interaction with the dipole in the plain of the ring. However, 2-methyl acetophenone and 1-acetyle naphthone show some quick dipole reorientation, which coincides with a steric hindrance of the group in entering the plain of the ring.

Calculation of transport coefficients using a modified Mori formalism

Calculation of transport coefficients using a modified Mori formalism

Molekülinterne Dipolorientierung und dielektrische Absorption in verdünnter Lösung bei Mikro-und Submillimeterwellen. IV.Chlormethyl-Verbindungen

Abstract The dielectric loss of eight molecules with the polar group in aromatic bonds and three in aliphatic bonds has been measured in very dilute solutions of cyclohexane at 20 °C. The measurements have been made at microwave frequencies in the range 2 to 130 GHz and at five wave numbers in the range 8 to 85 cm-1 (generated by a pumped molecular laser). These measurements are supplemented using a Fourier transform spectrometre up to 300 cm-1. The dielectric loss spectra ε″(γ̄) have been separated into a number of absorption regions (three or four in the microwave area) using the two variable Mori formalism. The power absorption spectra α(γ̄) are fitted to the Lorentzian shapes in order to determine the FIR resonances. The dielectric dispersion step determined from loss measurements contains the contributions from all orientational processes of the permanent molecular dipole moment. The distribution of relaxation times indicates that the polar group reorientates by a fast intramolecular rotational process in five of the eight aromatic molecules investigated. Furthermore these five substances show character­istic broad resonance centred at approximately 39 cm-1. In order to determine the influence of the other substituted groups, the components of the dipole moment parallel and perpendicular to the internal axis of rotation are calculated from the dispersion steps. The perpendicular component does contribute as well to the Debye relaxation according to the Budo model as to the Poley and FIR absorptions. The relative magnitudes of these contributions are rather similar in the five molecules. In two other molecules, the intramolecular orientational process plays a relatively minor role due to the steric hindrance by a neighbouring group. However in dichloro-o-xylene, the two neighbour­ing groups do not prevent the fast process except that the net dipole moment is significantly reduced. Again, due to sterichindrance, the aliphatic bonded group molecules do not exhibit the fast dipolar orientational process or the characteristic resonance at 39 cm-1.

Rate equations for the dynamics of mixed valence ions

The high temperature dynamics of mixed valent 4f-shells is studied by means of rate equations. Symmetries and detailed balance considerably reduce the number of independent rates. Rates are calculated by Fermi's golden rule. The approach presented here provides an elementary and transparent reproduction of results previously obtained using Mori's formalism.

Model description of the dephasing of optical impurities in glasses.

A microscopic model is used to calculate the optical line shape of impurities in amorphous hosts. The dynamics of the glass are described by an ensemble of two-level systems which interact with the phonons of the matrix and which are coupled to the impurity. Within linear-response theory, a line-shape expression is derived. Equations of motion for the pertinent correlation functions are obtained through Mori's formalism and solved approximately for the full many-body problem. Discussing the line-shape expression, we justify an averaging procedure for the description of the linewidth. Numerical linewidth calculations are presented, and several ways to explain the temperature dependence of experimentally observed linewidths within the model are discussed.

Quantum field theories out of thermal equilibrium: (I). General considerations

The approach to thermal equilibrium of quantum fields is described. Using a hydrodynamical picture and a Mori (i.e. linear response) formalism, general expressions for the transport coefficients are presented as auto-correlation functions of certain currents. Some results are given for an interacting scalar field.

The moment problem in statistical mechanics: Correlation functions of purely dissipative systems

The question of convergence of the Mori formalism is investigated in the frame of the classical theory of moments. The autocorrelation functions (acfs) of purely dissipative systems admit of both moment and continued fraction expansions (like that obtained by Mori). New physical conditions for the convergence of the latter ones are related to the analytical behaviour of the corresponding spectral moment sequences. From discussion of the analytical properties of such continued fractions it is also proved that the knowledge of the spectral moments does not suffices for determining infinite acf eigenvalue spectra. Mori's continued fraction always converges at zero frequency, thus reproducing the value of the acf relaxation time correctly. Finally, our predictions are verified by comparison with the analytical results for the Verhulst model published recently by Jung and Risken.

Calculation of transport coefficients using a modified Mori formalism

Transport coefficients calculated using the conventional version of Mori's continued-fraction formalism will in general be incorrect because of the approximate nature of the closure one must supply for a memory function. This is true even if the truncation is applied at arbitrarily high order. We propose an alternative method which involves taking the geometric mean of two successive levels of approximation. This yields the correct result in the absence of long-time tails.

Self-correlation functions in liquid metals

Calculations are presented for the normalised velocity autocorrelation function, its power spectrum and self-diffusion coefficient as well as the self-dynamic scattering function for a model of liquid rubidium via the Mori formalism. The frequency spectrum and the self-diffusion coefficient respectively are in good agreement with the molecular dynamic calculation and experimental results. The self-dynamical structure factor exhibits the characteristics which are expected of simple liquids as shown, for instance, by the closeness of some of the parameters calculated from it to their known values in the hydrodynamic limit.