Renormalized vertex modification of Hall conductivity for dilute magnetic alloys

By means of the renormalized vertex procedure for the motion of Green's function developed by the authors, the vertex function of magnetic alloys, based on thes-d exchange interaction, is solved exactly and the corresponding Hall conductivity tensors are obtained. It is found that the value of the renormalized Hall conductivity is (1+h ²)^–1 times less than that before the renormalization (hereh is a reduced magnetic field). It is shown that the renormalized modification of the conductivity is very important in the cases with not too weak external magnetic field and slow relaxation time.     

A statistical-mechanical theory of self-diffusion in colloidal suspensions — application to colloidal glass transitions

A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama–Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.     

Dynamical renormalization of kinetic van der Waals spin models

An exact dynamical renormalization approach in differential form is proposed for kinetic van der Waals spin systems with general many-body interactions. The problem of restoring covariance in the evolution equation after renormalization of the model is solved by introducing a suitable renormalized time parameter, which depends also on the magnetization of the spin configuration. The study of the behavior of this renormalized time near criticality leads to a scaling relation for the linear relaxation time. This relation can be shown to imply the exact results for the dynamical critical behavior of the system.On leave of absence from Instituto di Fisica e Unità G.N.S.M. del C.N.R., Università di Padova, Padova, Italy.     

Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.     

A statistical-mechanical theory of self-diffusion in glass-forming liquids

A statistical-mechanical theory of self-diffusion in glass-forming liquids is presented. A non-Markov linear Langevin equation is derived from a Newton equation by employing the Tokuyama-Mori projection operator method. The memory function is explicitly written in terms of the force-force correlation functions. The equations for the mean-square displacement, the mean-fourth displacement, and the non-Gaussian parameter are then formally derived. The present theory is applied to the glass transitions in the glass-forming liquids to discuss the crossover phenomena in the dynamics of a single particle from a short-time ballistic motion to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of analyses of the simulation results by the mean-field theory proposed recently by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that for times longer than the β-relaxation time the dynamics of a single particle is identical to that discussed in the suspensions.     

Magnetic-field-induced enhancements of nuclear spin-lattice relaxation rates in the heavy-fermion superconductor CeCoIn5 using 59Co nuclear magnetic resonance

(59)Co nuclear spin-lattice relaxation has been measured for the heavy-fermion superconductor CeCoIn(5) in a range of applied fields directed parallel to the c axis. An enhanced normal-state relaxation rate, observed at low temperatures and fields just above H(c2)(0), is taken as a direct measure of the dynamical susceptibility and provides microscopic evidence for an antiferromagnetic instability. The results are well described using the self-consistent renormalized theory for two-dimensional antiferromagnetic spin fluctuations, and parameters obtained in the analysis are applied to previously reported specific heat and thermal expansion data with good agreement.     

Phonon renormalization and damping in a Heisenberg ferromagnet

A theoretical study of spin-phonon interaction in a Heisenberg ferromagnet is made on the basis of a Green function technique. We have calculated below and aboveT _c the renormalized phonon energy and the phonon damping for the first time beyond the RPA. The obtained temperature and magnetic field dependence of the phonon relaxation time is in good agreement with the experimental data.     

The twice-renormalized Rouse formalism of polymer dynamics: Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice-renormalized Rouse formalism, a refined version of Schweizer’s renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended to include the terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts (such as the reptation (tube) model or the polymer mode-mode coupling formalism), the predictions perfectly coincide with all the results of recent spin-lattice relaxation dispersion and diffusion experiments as well as with computer simulations. On the other hand, the twice-renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity is largely a manifestation of collective multichain modes. In the rigorous sense, no such multichain treatment has yet been established to our knowledge. The necessity to consider interchain cooperativity in any real comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions.     

Study of the paraelectric behavior of OH− ions in alkali halides with optical and caloric methods II.: Dynamics of the dipole alignment

The relaxation behavior of OH^? dipole centers in ten alkali halides was studied with electro-optical and electro-caloric methods as a function of applied field, temperature and host lattice system. The reorientation kinetics of the 〈100〉 oriented OH^? dipoles can be fitted successfully to a phonon-assisted (90°) orientational tunneling model. Below 5°K the observed time dependence of the optical dichroism and the T^?1 dependence of the relaxation time gives clear evidence for the predominance of one-phonon processes, while above 5°K the T^?4 dependence indicates multi-phonon processes. It could be demonstrated that in the one-phonon region of the dipole relaxation a population inversion among the dipole levels (with subsequent phonon emission) can be achieved after a fast reversal of the field polarity. An attempt is made to discuss the observed strong variation of the relaxation time (12 orders of magnitude) with the host lattice in terms of a tunneling matrix element renormalized due to the anisotropic lattice distortion around the defect.     

Spin relaxation in the presence of electron-electron interactions

The D'yakonov-Perel' spin relaxation induced by the spin-orbit interaction is examined in disordered two-dimensional electron gas. It is shown that, because of the electron-electron interactions, substantially different spin relaxation rates may be observed depending on the technique used to extract them. It is demonstrated that the relaxation rate of a spin population is proportional to the spin-diffusion constant D(s), while the spin-orbit scattering rate controlling the weak-localization corrections is proportional to the diffusion constant D, i.e., the conductivity. The two diffusion constants get strongly renormalized by the electron-electron interactions, but in different ways. As a result, the corresponding relaxation rates are different, with the difference between the two being especially strong near a magnetic instability or near the metal-insulator transition.     

Spin relaxation. The renormalized operator cumulant approach

Two-level systems under the influence of external noise are generic models of quantum relaxation processes. The spin 1/2 particle in a stochastic magnetic field is one of the best known examples. Interesting effects are observed if the noise is colored as is the case in most applications. The time-ordered operator cumulant expansion forms a convenient approach to this problem. Recently, a renormalization procedure has been proposed which corresponds to a partial summation of the naive expansion and hence constitutes an essential improvement over the second cumulant considered usually. For colored noise of intermediate strength and correlation time this approach is used to derive renormalized expressions for the transverse (T ₂) and longitudinal (T ₁) relaxation time and the frequency shift. In this parameter region, the ratioT ₁/T ₂= is found to deviate substantially from its value =2 valid for white noise exactly and for colored noise in the second cumulant approximation. This corroborates and extends results of Budimir and Skinner obtained by including the second and fourth cumulant only. However, their truncated expansion is shown to lead to unphysical results in the intermediate parameter region treated still correctly by the renormalized expansion.     

Dynamical renormalization group approach to relaxation in quantum field theory

The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.     

Thermal Relaxation of a QED Cavity

We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time asymptotics. We show that, whenever the atoms are distributed according to the canonical ensemble at temperature T>0 and some generic non-degeneracy condition is satisfied, the cavity field relaxes towards some invariant state. Under some more stringent non-resonance condition, this invariant state is thermal equilibrium at some renormalized temperature T ^*. Our result is non-perturbative in the strength of the atom-field coupling. The relaxation process is slow (non-exponential) due to the presence of infinitely many metastable states of the cavity field.     

From superoperator formalism to nonequilibrium Thermo Field Dynamics

Emphasizing that the specification of the representation space or the quasiparticle picture is essential in nonequilibrium quantum field system, we have constructed the unique unperturbed representation of the interaction picture in the superoperator formalism. To achieve it, we put the three basic requirements (the existence of the quasiparticle picture at each instant of time, the macroscopic causality and the relaxation to equilibrium). From the resultant representation follows the formulation of nonequilibrium Thermo Field Dynamics (TFD). The two parameters, the number distribution and excitation energy, characterizing the representation, are to be determined by the renormalization condition. While we point out that the diagonalization condition by Chu and Umezawa is inconsistent with the equilibrium theory, we propose a new renormalization condition as a generalization of the on-shell renormalization on the self-energy which derives the quantum transport equation and determines the renormalized excitation energy.     

Charge relaxation in polyampholytes of various statistics

We discuss theoretically the relaxation of charge fluctuations in polyampholyte solutions. It has been shown previously by some of us (J. Wittmer et al. Europhys. Lett. 24, 263 (1993)) that the charge distribution along the polyampholyte backbone has a dramatic influence on the polarization energy and hence on the solubility. Here it is demonstrated that a similar effect exists for the charge relaxation. The charge relaxation mechanism qualitatively depends on the statistics: for alternating polyampholytes the relaxation is mainly due to local dipole inversion and is not primarily driven by electrostatic interactions, whereas for random polyampholytes it is driven by electrostatic interactions. Intermediate statistics (with short-ranged (exponential) correlations) appear as a combination of these two limiting cases: short-wavelength modes are insensitive to the loss of correlations along the backbone, whereas long-wavelength modes correspond to a random statistics with renormalized charges. The relaxation of the dielectric constant is also calculated. Received: 20 December 2002 / Accepted: 13 March 2003 / Published online: 24 April 2003 RID="a" ID="a"e-mail: johner@ics.u-strasbg.fr     

Interaction of two-level tunneling system with phonons

Properties of two-level tunneling system which interacts with lattice vibrations are discussed in the framework of the polaron theory and the phase space approach. The decrease of the dynamic distortion of the lattice with increasing ratio η of the rigid-lattice tunneling matrix element to the small polaron binding energy is calculated in the intermediate coupling regime 0 < η < 2. A relatively sharp transition from the distorted to the undistorted state of the lattice takes place when η crosses the value 2. The expressions for the renormalized tunneling matrix element and for the longitudinal relaxation time T₁ are derived. A two-level tunneling model in which the double-well potential is asymmetric is also investigated.     

RENORMALIZED HALL CONDUCTIVITY FOR MAGNETIC ALLOYS

By means of the renormalized vertex procedure for the motion Green's function developed by the au-thors, the vertex function of magnetic alloys, based on the s-d exchange interaction, is solved exactly and the corresponding Hall conductivity tensors are obtained. It is found that the renormalized modification of the conductivity is very important in the cases of not too weak extermal magnetic field and slow relexaction time.     

二维静态时空中Dirac场的重正化能动张量和Casimir效应

在一般渐近平直的二维静态黑洞时空中,利用重正化能动张量的一般性质, 对位于两“平行板”间满足Dirichlet条件的无质量Dirac场的重正化能动张量的真空期待值进行了分析和计算, 得到了一般表达式.利用该表达式可以给出各种具体渐近平直二维静态黑洞时空中的相应Casimir力.对于重正化能动张量及Casimir力与真空态定义(包括Boulware 真空态、Hartle-Hawking真空态和Unrum真空态三种情况)、Hawking辐射和反常迹的关系分别进行了讨论，给出了相应的表达式和计算结果. 关键词： 能动张量 Casimir 效应 黑洞 真空态     

Renormalized operator form of quantum action principle

The derivatives of the renormalized field operator with respect to the parameters (coupling constants, masses) are discussed. Two ways of obtaining the finite result in terms of renormalized perturbation expansion are shown. Throughout the paper the operator language is used; in particular the operator formula for renormalized powers of the field operators (normal products) is employed. The λ?⁴ theory is considered as an illustrative example.     

Unitary renormalization of the Lee model Y4

The Lee model Y₄ is renormalized by unitary transformation. A norm convergent (in each sector) sequence of unitary dressing transformations, which transform a sequence of renormalized cut-off Hamiltonians to a sequence of operators converging strongly on a dense set of states, is defined. The self-adjointness and semiboundedness (in each sector) of the renormalized Hamiltonian are proved.