Hot luminescence and ultrafast configurational relaxation of F centers

Hot luminescence of F centers in RbCl, KBr and KCl single crystals at liquid helium temperatures is discovered and interpreted as the emission from the classical turning points of a configurational coordinate. The energy relaxation time is estimated by two different methods providing interesting information about the excited state relaxation dynamics.     

Quantum statistical relaxation in a classically chaotic system

Classical statistical relaxation is quantitatively characterized by the ergodicity, an important relation connecting the time-averaged and ensemble-averaged properties of dynamical observables. In principle, the quantum statistical relaxation should be characterized correspondingly by the quantum ergodicity. In this paper, we have theoretically shown that quantum ergodicity can only be realized under the condition M ΔN 1, and this condition can be readily satisfied as the effective Planck constant approaches zero. These theoretical results are numerically testified in a nuclear model, known as a three-level Lipkin model whose classical counterpart can exhibit classical chaos.     

Femtosecond pump-probe fluorescence signals from classical trajectories: comparison with wave-packet calculations

A classical approach to simulate femtosecond pump-probe experiments is presented and compared to the quantum mechanical treatment. We restrict the study to gas-phase systems using the I₂ molecule as a numerical example. Thus, no relaxation processes are included. This allows for a direct comparison between purely quantum mechanical results and those obtained from classical trajectory calculations. The classical theory is derived from the phase-space representation of quantum mechanics. Various approximate quantum mechanical treatments are compared to their classical counterparts. Thereby it is demonstrated that the representation of the radial density as prepared in the pump-process is most crucial to obtain reliable signals within the classical approach. Received 28 March 2001     

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.     

Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion

Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.     

Classical and quantum theories of radiation damping in ferromagnetic and antiferromagnetic resonance

Both classical and quantum theories of radiation damping in ferromagnetic and antiferromagnetic resonance relaxation are given. Effects of demagnetization and anisotropy, that is, of elliptical classical precession, are included. In the classical theory a phenomenological approach to ferromagnetic resonance relaxation by means of the Landau-Lifshitz equation is also presented. In the quantum theory, the magnon-photon interaction Hamiltonian is derived, and the radiation-damped linewidth is obtained by computing the transition matrix element and also the one-magnon self energy. As noted long ago by Einstein, each photon is emitted in a random but specific direction, and only on average does the quantum radiation pattern reproduce the classical. To first order, however, this reproduction is shown to be exact, correcting a recent calculation by Shrivastava.     

Nonlinear diffusion and Nelson-Brown movement

The nonlinear diffusion process, which can be described as the Nelson-Brown motion, is considered. The obtained equation becomes the classical linear diffusion equation for small relaxation times, and for long relaxation times it is transferred into the Schrödinger-like equation. The possible nonequilibrium stationary states are discussed.     

Classical and quantum molecular dynamics of cation in (CH3NH3)3 Sb2Br9 polycrystal as studied by 1H NMR.

¹H spin-lattice relaxation times and second moments were determined for polycrystalline (CH₃NH₃)₃Sb₂Br₉ sample in a wide range of temperature (5–200 K) at 24.6 and 55.2 MHz. ²H NMR spectra of (CD₃NH₃)₃Sb₂Br₉ were recorded between 5 K and room temperature. The relaxation time is interpreted as a result of motion of two different non-equivalent types of monomethylammonium cations occurring at the 2:1 proportion in a unit cell. Below 30 K, the relaxation processes via tunneling are suggested to dominate. Above 30 K, only classical behaviour of methylammonium cations is detected. Two monomethylammonium cations relax with the classical correlated C₃ reorientation and the rotational tunnelling mechanism, while the third cation exhibits only the classical correlated reorientation. The dynamic parameters of these motions have been determined.     

Relaxation properties of weakly coupled classical systems

The relaxation properties of a small classical system weakly coupled to a large classical system which acts as a heat bath are described using a generalized Fokker-Planck equation. The Fokker-Planck equation is derived in general using a modification of the elimination of fast variables techniques previously described. The specific example in which the small system is a harmonic oscillator linearly coupled to the heat bath is treated in detail and it is demonstrated that there is a dynamic frequency shift as well as a statistical shift of the oscillator frequency.     

Magnetic relaxations of antiferromagnetic nanoparticles in magnetic fields

We reexamine anomalous magnetic relaxations of ferritin in magnetic fields, the presence of which has been regarded as evidence suggesting the existence of thermally assisted macroscopic quantum tunneling in antiferromagnetic nanoparticles. In the present study, relaxation curves of ferritin are examined using an approach that is free from assumptions regarding distributions of various parameters of polydispersive particles. The results are not anomalous. In other words, the relaxation is accelerated by the field, as expected for classical superparamagnetic fluctuations.     

Creep,relaxation and viscosity properties for basic fractional models in rheology

The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin–Voigt, Maxwell, Zener, anti–Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.     

Physical meaning of conductivity spectra for ZnO ceramics

With the help of broadband dielectric spectroscopy in a wide temperature and frequency range, the conductivity spectra of ZnO polycrystalline ceramics are measured and the direct-current-like (DC-like) conductivity and relaxation polarization conductivity are observed successively along the frequency axis. According to the classical Debye theory and Cole-Cole equation, the physical meanings of the two conductivities are discussed. It is found that the DC-like conductivity corresponds to electron transportation over the Schottky barrier at the grainboundary. The relaxation polarization conductivity corresponds to electronic trap relaxation of intrinsic point defects (zinc interstitial and oxygen vacancy). When in the high frequency region, the relaxation conductivity obeys the universal law with the index n equal to the index α in the Cole-Cole equation as an indictor of disorder degree.     

Rotational dynamics of a molecular ensemble in the presence of a strong laser field

The rotational dynamics of a molecular ensemble in the presence of a strong laser field is investigated in the framework of the density-matrix approach. The results obtained are compared with the rotation of molecules in a classical ensemble. The thermal molecular motion in the ensemble is taken into account in a model of random collisions, and various values of the relaxation time are considered. The effect of the relaxation process on molecular alignment is analyzed for the laser-pulse action and in the afterpulse regime. The similarity between quantum and classical rotational dynamics of a molecular ensemble is examined.     

Long time behavior in the quantized standard map with dissipation

A dissipative version of the quantized standard map is constructed by analytical means and iterated numerically to study the long time behavior in various regions of the damping rate. For weak dissipation, stochastic transitions induced by the heat bath disrupt the localization in the action variable, which suppresses chaotic motion in the conservative quantized standard map, and tend to restore diffusion of action. A steady state is reached on the time scale of classical relaxation. For strong dissipation, observable deviations from classical behavior both in the transients and in the statey state are due to quantum noise. They are reproduced by a classical stochastic map which is approached by the dissipative quantum map as its semi-classical limit.     

Magneto-transport in the two dimensional Lorentz model

A recently developed theory for the motion of a classical particle in a random array of scatterers is improved and extended to discuss the effects of weak and intermediate magnetic fields. By deriving expressions for the general relaxation kernels it is shown that only the current relaxation kernel is the physical relevant one diverging at the percolation edge. The percolation density and localization length turn out to be independent of the magnetic field. A negative magneto resistance at low scatterer density, a positive magneto resistance at larger density and a non classical Hall coefficient are obtained. For the velocity correlation spectrum a shift of the cyclotron resonance to higher frequency and a new low frequency side peak is predicted.     

Observation of size-dependent thermalization in CdSe nanocrystals using time-resolved photoluminescence spectroscopy

We report heat dissipation times in semiconductor nanocrystals of CdSe. Specifically, a previously unresolved, subnanosecond decay component in the low-temperature photoluminescence decay dynamics exhibits longer decay lifetimes (tens to hundreds of picoseconds) for larger nanocrystals as well as a size-independent, ~25-meV spectral shift. We attribute the fast relaxation to transient phonon-mediated relaxation arising from nonequilibrium acoustic phonons. Following acoustic phonon dissipation, the dark exciton state recombines more slowly via LO-phonon assistance resulting in the observed spectral shift. The measured relaxation time scales agree with classical calculations of thermal diffusion, indicating that interfacial thermal conductivity does not limit thermal transport in these semiconductor nanocrystal dispersions.     

Large Time Dynamics of a Classical System Subject to a Fast Varying Force

We investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to the sum of a fixed, confining, Hamiltonian, and a small, time-oscillating, perturbation. The equation also involves an interaction operator which acts as a relaxation in the energy variable. This paper aims at providing a classical counterpart to the derivation of rate equations from the atomic Bloch equations. In the present classical setting, the homogenization procedure leads to a diffusion equation in the energy variable, rather than a rate equation, and the presence of the relaxation operator regularizes the limit process, leading to finite diffusion coefficients. The key assumption is that the time-oscillatory perturbation should have well-defined long time averages: our procedure includes general “ergodic” behaviors, amongst which periodic, or quasi-periodic potentials only are a particular case.     

H andH NMR Relaxation in Hydrogen-Bonded Solids Due to a Complex Motion: Classical Jumps over a Barrier and Incoherent Tunneling

Equations for the temperature dependence of proton and deuteron spin–lattice relaxation rates and second moments due to a complex motion consisting of classical jumps over a potential barrier and quantum mechanical tunneling through the barrier have been derived. Asymmetric double and triple potential wells are considered. These equations have been employed to analyze proton spin–lattice relaxation data for solid naphthazarin in the laboratory and rotating frames as a function of temperature. It is shown that tunneling plays an important role in the proton transfer dynamics of this compound.