On the approach to kinetic theory due to Gross

A classical kinetic theory introduced by Gross is explored in further detail. The theory consists of a sequence of approximations to the Liouville distribution function, with each approximation leading to a truncation of the BBGKY hierarchy at successively higher order. We formulate the truncation scheme at general order in terms of a set of time-dependent equilibrium correlation functions. It has the correct symmetries and, as is implied by the work of Gross with the first two approximations, is such that the interparticle potential appears only implicitly via static equilibrium correlation functions. We arrange the theory as a sequence of linear kinetic equations for the phase-space density correlation function, and solve for the collision kernels which result in each order. The collision kernel of the second approximation, which involves only binary dynamics, is shown to be a mean-field generalization of the known low-density kernel. The third approximation gives a similar generalization of the triple-collision kernel. The nth approximation also reproduces the frequency moments of S(kω) through order ω²ⁿ. More generally, the approximations are shown to give a continued-fraction expansion of the collision kernel, with the levels governed by the dynamics of successively larger numbers of particles. This is a renormalized kinetic theory in the sense that the potential is eliminated and clusters of particles are never isolated.     

A quantum field theory of viscosity near the liquid-glass transition

The two band model is considered for randomly distributed atoms in the harmonic potential approximation. Taking into account the scattering processes due to random eigenfrequencies and random hopping matrices contributing to the self-energy parts and vertex parts in the correlation functions of the density fluctuations in the interband, we obtain the generalized frequency-dependent viscosity in the viscoelastic theory. The viscosity is proportional to the relaxation time of the atoms, the inverse of which consists of the mean-square deviation of random eigenfrequencies and that of random hopping matrices. The former is almost constant and the latter obeys the Vogel-Fulcher law. In the vicinity of the transition they cross over.     

A quantum field theory of localized and resonant modes in 3D nonlinear lattices at finite temperatures II

We solve the eigenvalue equation derived in paper I under the assumption that a localized or resonant mode is well-localized at a lattice site. Localized modes appear above the top of the phonon band for an appropriate positive quartic potential at any temperatures. Resonant modes appear in the middle of the phonon band for an appropriate negative quartic potential at low temperatures due to the frequency dependent coupling of the mode. This fact is essentially different from that in the force constant defect, where resonant modes appear in the lower frequency regions due to the frequency independent couplings. Both modes are investigated numerically using the tables of the Green's functions for monoatomic simple cubic lattices in terms of the Bessel functions. Resonant modes are also investigated in the Debye approximation.     

Density functional theory of a Gay—Berne film between aligning walls

It is shown that the simple Onsager second-virial approximation of density functional theory can successfully describe the orientational structure of a Gay-Berne film confined between aligning plates. The theory takes as input the density profile as determined by computer simulation and semi-quantitatively reproduces the variation in the nematic order parameter throughout the film, at different temperatures and for different surface potential strengths, without any adjustable parameters. In this context the validity of an earlier analytical approach is discussed where the density, order parameter and tilt angle profiles were assumed to be step functions.     

On the dynamics of impure classical Heisenberg chains

We present theoretical results on dynamic correlation functions of impure, classical, one-dimensional Heisenberg magnets with both ferromagnetic and antiferromagnetic coupling. The results are obtained in the framework of Mori's theory and in an approximation which includes correctly all moments of the relaxation function to lowest order in impurity concentration and temperature and which preserves the rotational symmetry of the system even at zero temperature. Explicit results are given for lineshifts and linewidths of quasi-spinwaves and the behaviour of correlation functions in the hydrodynamic limit is discussed.     

Quantum mechanical theory of fluctuations and relaxation in semiconductor lasers

Pumping, spontaneous emission and electron-electron scattering lead to relaxation terms in the mean equations of motion for the electron system. These terms are derived from a quantum mechanical basis by second order perturbation theory and by appropriate reservoir averaging. If the electron distribution is not too strongly degenerate, then a relaxation time approximation can be derived. The quantum mechanical Langevin method is used to include noise. The correlation functions of all fluctuation operators are calculated. From the knowledge of the equations of motion and of the correlation functions it is possible to calculate the noise properties of the laser light and of the junction current, as will be shown in other publications.     

Anharmonic phonons and structural phase transitions

Exact results for the order parameter and the meansquare displacement as functions of temperature are given for a quantum interacting phonon Hamiltonian with quartic anharmonicities. Upper bounds for the transition temperature are also derived. Approximate theories including the mean field approximation, the random phase approximation (or quasiharmonic approximation) and the self consistent approach (using Blume-Hubbard scheme) are compared with our exact results. The mean field approximation for the meansquare displacement is found to violate our bounds.The classical value is shown to form a lower bound for the kinetic energy. Upper bounds for the kinetic energy are obtained showing the region of temperature in which the use of the high temperature expansion of the fluctuation-dissipation theorem is justified. Comparison of the Hamiltonian and our results with electron-paramagnetic-resonance measurements are discussed.     

Normal quasiparticle scattering and kinetic effects in degenerate semiconductors

The influence of normal processes of electron-electron and phonon-phonon scattering on quasiparticle momentum relaxation in nonequilibrium electron-phonon systems of degenerate semiconductors is investigated. A system of kinetic equations is solved for the electron and phonon distribution functions, and the kinetic coefficients of a semiconductor are calculated in the linear approximation in the degeneracy parameter. The influence of normal scattering of quasiparticles on the electrical conductivity, thermopower, and heat conductivity of a degenerate semiconductor is analyzed. Redistribution of the phonon momentum in N processes within each branch of the vibrational spectrum, as well as among different branches, is taken into account.     

Cross-correlation effects involving curie spin relaxation in methyl groups

Cross-correlation effects arising in methyl protons due to the simultaneous presence of dipole-dipole, chemical shift anisotropy, and Curie spin relaxation mechanisms in paramagnetic systems are analyzed. We assess the potential of obtaining structural constraints from the cross-correlation of Curie spin relaxation with dipolar relaxation mechanisms among methyl proton spins. By theoretical analysis and numerical simulations we characterize the transfer functions describing the interconversion processes of different ranks of multispin order. The time dependence of these processes contains a new type of structural information, the orientation of the methyl C(3)-axis with respect to the electron center. Experimental confirmation is found for selected methyl groups in low spin Fe(3+) sperm whale myoglobin.     

A simple accurate formula for the energy levels of oscillators with a quartic potential

In this note we present a simple analytical formula which reproduces the energy eigenvalues E_k(λ) of the pure quartic and quartic anharmonic oscillators with high accuracy for all values of the anharmonicity parameter λ and the level number k.     

Laser induced ultrafast demagnetization in diluted magnetic semiconductor nanostructures

We present a dynamical model that reproduces the observed time evolution of the magnetization in diluted magnetic semiconductor films after weak laser excitation. Based on a many-particle expansion of the exact p–d exchange interaction, our approach goes beyond the usual mean-field approximation. Numerical results demonstrate that the hole spin relaxation plays a crucial role for explaining the ultrafast demagnetization processes observed experimentally. The influence of the laser power on the magnetization dynamics is also investigated.     

Velocity correlation functions for finite one-dimensional systems

Certain systems consisting of a one-dimensional gas of a finite number of point particles interacting with a “hard-core” potential are considered.We use the technique developed by Jepsen to calculate exactly the velocity correlation functions for these systems. We discover that after a slow decay for times of the order of the relaxation time, there is a “fast” decay to the equilibrium value on a macroscopic time scale characterized by L/v_TH (L is the length of the container and v_TH the thermal velocity).The dependence of the velocity correlation functions on the initial position of the specified particle is also considered. In particular, the behaviour approaching the boundary of the container is analyzed. These considerations are generalized to systems of higher spatial dimension.     

Self-consistent perturbation theory for dynamics of valence fluctuations

A perturbation-theoretic scheme is developed for dynamics of valence fluctuations in rare-earth systems with unstable 4f shells. The theory is formulated in close analogy to the standard Green-function method for many-body systems but without use of the linked-cluster theorem. This formulation regards hybridization between 4f and conduction-band states as perturbation and naturally incorporates the strong on-site 4f-electron correlation. Some favorable features are: (i) the approximation scheme automatically satisfies conservation laws required for response functions; (ii) realistic 4f-shell structures with crystalline-electric-field effects can be taken into account; (iii) the theory does not have divergence difficulties over the whole temperature range. In the lowest-order self-consistent approximation, explicit formulae for dynamical susceptibilities and 4f-electron density of states are presented. At high temperatures, the theory reproduces previous results obtained by the Mori method.     

A model dielectric response function for metallic nanotube ropes

We propose a model dielectric function for ropes of single-walled nanotubes distributed in a glassy graphite host medium. We study the significance of the bosonic charge excitations arising in interacting quasi-one-dimensional systems in the screening processes. We also pay special attention to the role of the intertube Coulomb interactions. In order to compare with experiments, weak relaxation processes are also considered in the relaxation-time approximation.     

Generalizing the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of fragmentation functions to the smallest values

An approach valid to any order which unifies the fixed order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of fragmentation functions at large x with soft gluon logarithmic resummation at small x is proposed. At lowest order, this approach, implemented with the double logarithmic approximation, reproduces exactly the modified leading logarithm approximation but is more complete due to the degrees of freedom given to the quark sector and the inclusion of the fixed order terms. We find that data from the largest x values to the peak region can be better fitted than with other approaches.     

Hopping Transport and Stochastic Dynamics of Electrons in Plasma Layers

We investigate the stochastic dynamics and the hopping transfer of electrons embedded into two‐dimensional atomic layers. First we formulate the quantum statistics of general atom ‐ electron systems based on the tight‐binding approximation and express ‐ following linear response transport theory ‐ the quantum‐mechanical time correlation functions and the conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the atom motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. In the last part we derive Pauli equations for the stochastic electron dynamics including nonlinear excitations of the atomic subsystem. We carry out Monte Carlo simulations and show that mean square displacements of electrons and transport properties are in a moderate to high temperature regime strongly influenced by by soliton‐type excitations and demonstrate the existence of percolation effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cross relaxation study on NaClO3 by NMR acoustic saturation

Cross relaxation rate between adjacent NMR lines of Na²³ in NaClO₃ was measured at room temperature by the NMR acoustic saturation method. When the angle φ between the [010] axis and H₀ in the (100) plane is 1.75°, two of the three NMR lines are superposed exactly. As φ is increased gradually, they split and they separate perfectly at φ = 2.75°. Cross relaxation probability between these two lines was measured as a function of the separation. The results are compared with the theory of overlap integral approximation. For small separation the theory reproduces fairly well the experimental results, but for larger separation disagreement appears, which may be due to the Gaussian approximation to the NMR line shape in the theory.     

Nonlinear relaxation and fluctuations of damped quantum systems

The paper reexamines the treatment of irreversible quantum systems by master equations. Shortcomings of the conventional theory of quantum Markov processes pointed out by Talkner are analyzed. It is shown that a frequently used quantum regression hypothesis is not correct, in general. A new generalized master equation determining the relaxation to equilibrium is derived by means of time-dependent projection operator techniques. It is shown that this master equation also determines the time evolution of equilibrium correlations and response functions. The Markovian approximation is discussed, and a new type of Markovian limit, the Brownian motion limit, is introduced besides the weak coupling limit. The shortcomings of the conventional approach are resolved by deriving new formulae for the time evolution of the correlation and response functions of a quantum Markov process. The symmetries of the process are emphasized, and it is shown how the fluctuation-dissipation theorem and the detailed balance symmetry emerge from the master equation approach.