Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

玻璃超声吸收的红外发散理论

本文采用低频涨落、耗散、弛豫过程的统一理论来研究玻璃热活化弛豫过程的超声吸收。与现有的弛豫时间分布理论不同,只采用单一弛豫时间τ_p,但可以说明弛豫时间分布理论所不能解决的玻璃超声吸收的实验特征,并解释这些实验特征与具体材料无关的普适性。 关键词：     

Efficiency of paramagnetic relaxation enhancement in off-resonance rotating frame

Transferring from laboratory frame to off-resonance rotating frame for the (1)H spin can compensate the relaxivity loss for paramagnetic agents at the magnetic field strength higher than 3 Tesla and enhance water relaxation rate constant significantly. A comprehensive theory for calculating the relaxation rate constants in the off-resonance rotating frame is described. This theory considers the contributions from both inner shell and outer shell water. The derived relaxation rate constants and relaxation enhancement efficiency as a function of the magnetic field strength and the effective field parameters are directly correlated to the structures, dynamics and environments of paramagnetic agents. To validate the theoretical predictions, we have measured the relaxation enhancement efficiency for a series of macromolecule conjugated gadolinium chelates at 9.4 Tesla. The experimental results confirmed the theoretical predictions. The theory also predicts the relaxation enhancement for T(2)-type paramagnetic agents at high magnetic fields. Promising fields of applications include situations where T(1)- or T(2)-type paramagnetic agents are used for labeling molecular/cellular events.     

Non-newtonian flow for concentrated polymer systems

The modified Graessley theory with the three-dimensional Maxwell model can well explain some of the nonlinear viscoelastic behavior of concentrated polymer systems at least qualitatively with the assumption of a box-type relaxation spectrum for the equilibrium state.

The relaxation spectrum of concentrated polymer systems in shear flow is obtained by means of Graessley's theory. It is assumed that the characteristic time for the entanglement formation is the same order as that for its breakage and that the spectral density of the relaxation spectrum in the flow system is proportional to the number of entanglements between two molecules. The spectral density decreases approximately proportionally to 1/γ for relaxation times larger than 1/γ The non-Newtonian viscosity and other viscoelastic properties, such as the so-called stress overshoot and the stress relaxation, are calculated by using the obtained relaxation spectrum. Our theory explains very well the experimental results in many cases. Good agreement with experimental results is found if we assume that the so-called box-type relaxation spectrum in the equilibrium state has a finite gradient of the order of ?0.5 in the edge region of larger relaxation time on log-log plots.     

A theory of quantum diffusion localization

The quantum localization of chaotically diffusive classical motion is reviewed, using the kicked rotator as a simple but instructive example. The specific quantum steady state, which results from statistical relaxation in the discrete spectrum, is described in some detail. A new phenomenological theory of quantum dynamical relaxation is presented and compared with the previously existing theory.     

Nonlinear nonstationary theory of light propagation through a resonance medium taking into account optical pumping of atoms

The general nonstationary theory of propagation of an elliptically polarized pulse resonantly interacting with the 1/2–1/2 transition is presented. The theory that takes into account relaxation processes is developed in terms of irreducible tensor operator representation allowing diagonalization of the relaxation matrix and introduction of effective decay times governing relaxation of both population and coherence between magnetic sublevels of the resonant system. It is shown that interference of magnetic sublevels in the field of polarized radiation that optically pumps the atoms can result in inversionless amplification of radiation.     

Four complementary theoretical approaches for the analysis of NMR paramagnetic relaxation

Four theoretical and computational approaches used at the University of Michigan to analyze NMR paramagnetic relaxation enhancement (NMR-PRE) are described. The primary objective of the theory is to describe the relationship of the NMR-PRE phenomenon to the electron spin hamiltonian and the spin energy level structure when zero field splitting interactions are significant. Four formulations of theory are discussed: (1) spin dynamics simulation; (2) the laboratory frame "constant H(S)" formulation; (3) the Molecular Frame "constant H(S)" formulation; and (4) the zfs-limit "constant H(S)" formulation. No single theoretical approach describes all important aspects of the relaxation mechanism in a fully satisfactory way. We use the four formulations in a complementary manner to provide as complete a picture of the relaxation mechanism as possible. We also discuss the integration of NMR-PRE theory and recently developed theory of electron spin relaxation which accounts for effects of the permanent zfs hamiltonian.     

快离子导体玻璃滞弹性弛豫的红外发散响应

本文依据Ngai(倪嘉陵)的低频激发、弛豫、耗散理论和非晶态快离子导体的特点,提出了非晶态快离子导体的滞弹性弛豫理论。认为快离子导体玻璃中的超声吸收主要来源于与玻璃网络呈微弱联系的快离子的热激活弛豫及伴之而来的低能激发的损耗。理论成功地描述了超声吸收的频率、温度依赖关系,解释了弛豫时间分布理论所不能解释的快离子导体玻璃的实验特征。     

An Ising model for the stress relaxation of solids

A kinetic theory of stress relaxation of solids as a cooperative process is proposed. The theory is based on a two-state model for the relaxation. It is shown that the conventional mean field approximation leads to an exponential dependence of the rate of stress relaxation on the stress while the multiplicative approximation of Vol'kenstein et al. leads to a power law. It is argued that the exponential law should be valid initially in the relaxation process while the power law is appropriate when the system is nearer equilibrium, which is in qualitative agreement with recent experimental findings.     

A Mössbauer study of potassium ferric alum

The first temperature-dependent Mössbauer spectra from polycrystalline samples of KFe alum are presented. The FWHM varies considerably with temperature. Application of isotropic relaxation theory suggests that the variation is caused by a change in electron relaxation time due to competition between spin-spin and spin-lattice relaxation processes.     

Determination of the Maier-Saupe strength parameter from dielectric relaxation experiments: a molecular dynamics simulation study

Molecular dynamics simulations have been performed to investigate the rotational motion in the nematic and isotropic phases of a model mesogenic system in which the interactions between the molecules are represented by the Gay-Berne potential. First-rank end-over-end rotational relaxation times, analogous to those measured using dielectric relaxation spectroscopy for real mesogens with a longitudinal electric dipole, have been determined as a function of temperature and density. The relaxation times at temperatures throughout the nematic region are found to be larger than the values extrapolated from the isotropic phase to the same temperature. The simulation results are compared with the extended Debye theory for dielectric relaxation in the nematic phase. This relates the reduction in the relaxation rate to the retardation factor which depends on the Maier-Saupe strength parameter, and in turn is defined uniquely by the second-rank orientational order parameter. The simulations indicate that the retardation factor at constant strength parameter is density dependent, a feature neglected in the relaxation theory. We compare the simulation results where possible with experiment.     

Theory for the optimal control of time-averaged quantities in quantum systems

We present a variational theory for the optimal control of quantum systems with relaxation over a finite time interval. In our approach, which is a nontrivial generalization of previous formulations and which contains them as limiting cases, the optimal control field fulfills a high-order Euler-Lagrange differential equation, which guarantees the uniqueness of the solution. We solve this equation numerically and also analytically for some limiting cases. The theory is applied to two-level quantum systems with relaxation, for which we determine quantitatively how relaxation effects limit the control of the system.     

Dipole-dipole relaxation of paraelectric impurities

Paraelectric impurities can relax via dipole-dipole interaction. This mechanism requires a statistical distribution of strong internal electric fields. The combination of relaxation via this process and via the coupling to the phonons can show a maximum in the relaxation time vs. temperature curve. The theory is applied to the paraelectric relaxation of OH-dipoles in KCl under two-dimensional compression.     

Influence of relaxation on the acoustic self-induced transparency

Using a singular perturbation theory for the method of the inverse scattering transform, the influence of transverse relaxation on the acoustic self-induced transparency is considered. It is shown that account of the relaxation improves the quantitative agreement of the theory with experiment.     

A second order full coulomb relaxation theory of spectral line broadening in plasmas

A second-order, quantum-mechanical relaxation theory of spectral line broadening in plasmas that uses a full Coulomb potential to describe the radiator-perturbing electron interactions is presented. A Fourier representation of the interaction is used rather than a multipole expansion. The results for the Lyman-alpha transition in hydrogen are compared with experimental data and with a corresponding relaxation theory computation that uses a dipole approximation.     

Equilibration of a one-dimensional quantum liquid

We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures, the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids, these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum.     

Stress relaxation in entangled melts of unlinked ring polymers

Stress relaxation in unlinked ring polymer melts poses an important challenge to our theoretical understanding of entangled polymer dynamics. Recent experiments on entangled unlinked ring melts show power-law stress relaxation with no hint of a rubbery plateau, usually the hallmark of entangled polymers. Here we present a theory for stress relaxation in rings analogous to the successful approach for star polymers. We augment our theory with mesoscale Monte Carlo dynamics simulations of equivalent "lattice animal" configurations. We find a stress relaxation function G(t)～t(-α) with α≈1/2 consistent with experiment, emerging ultimately from the disparate relaxation times of more- and less-central portions of ring conformations.     

Carrier mobility and relaxation time in BiCuSeO

To obtain thermoelectric properties of materials, a constant relaxation time approximation is generally employed. By employing deformation potential theory, a derivation of relaxation time and carrier mobility of BiCuSeO system is proposed combining with density functional theory calculation. And the inter-valley scattering, acoustic phonon scattering and ionized impurity scattering were considered in the model. The calculated values of relaxation time and carrier mobility in BiCuSeO are in good agreement with the results of experiment. The results suggest that acoustic phonon scattering is in dominant and the constant relaxation time approximation is reasonable in lightly doped sample, and the ionized impurity scattering play a significant role in heavily doped system.     

时间和空间无序对玻璃超声弛豫的影响——红外发散响应理论的推广

本文采用时间连续无规行走(CTRW)的分形理论(Fractal),讨论玻璃超声弛豫过程中时间和空间无序对缺陷态激发寿命几率分布和特征弛豫时间的影响,并由此修正红外发散响应(IDR)理论,使其可能解释金属玻璃态超声弛豫现象。 关键词：