Finite Relaxation Rate Research Articles

Non-Markovian thermalisation of a two-level atom

We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima–Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.

Conductance properties of nanotubes coupled to superconducting leads: signatures of Andreev states dynamics

We present a combined experimental and theoretical analysis of the low bias conductance properties of carbon nanotubes coupled to superconducting leads. In the Kondo regime, the conductance exhibits a zero bias peak which can be several times larger than the unitary limit in the normal case. This zero bias peak can be understood by analyzing the dynamics of the subgap Andreev states under an applied bias voltage. It is shown that the existence of a linear regime is linked to the presence of a finite relaxation rate within the system. The theory provides a good fitting of the experimental results.

Time-resolved probing of the Purcell effect for InAs quantum boxes in GaAs microdisks

We studied, by time-resolved microphotoluminescence (PL), the spontaneous emission dynamics of InAs/GaAs quantum boxes coupled to high Purcell factor (up to 155) whispering gallery modes of microdisks under nonresonant excitation. A global shortening of the PL decay by a factor of up to 12 was observed for the collection of quantum boxes on resonance with the modes. This behavior is well understood when the random distribution of the quantum boxes and the finite relaxation rate of the carriers are taken into account.

Effect of frequency detunings and finite relaxation rates on laser localized structures

We study, analytically and numerically, the effect of frequency detunings and relaxation processes in laser media on stability and bifurcations of dissipative optical localized structures (DOLS's) in a transversely one-dimensional laser with a saturable absorber. The approximate envelope equation, with an intensity dependent effective coefficient of the diffusion, is derived. Andronov-Hopf bifurcations resulting from frequency detuning and leading to oscillatory DOLS's are analyzed numerically. A numerical and analytical study of bifurcations of transversely motionless DOLS's in a laser with finite relaxation rates of amplifying and absorbing media is performed. New types of DOLS's are found, including those moving with a large transverse velocity and those moving with a periodically oscillating transverse velocity. Hysteresis between different types of DOLS's is demonstrated.

Small size tunneling contacts with superconductors

Tunneling conductivity in SC-I-metal tip junction of nanometer scale in the presence of an impurity state is examined theoretically by means of diagram technique for nonequilibrium processes. The theory takes into account two important factors: modification of the initial electronic spectrum of superconductor and finite relaxation rates for a nonequilibrium electronic density. The proposed model can be applied to various experimental situations, including STM/STS investigations of a clean SC surface. It is shown that in many cases dI/ dV dependencies are essentially modified and gap structure is distorted.

NUCLEAR RELAXATION IN IRREGULAR OR FRACTAL PORES

We apply a fractal description of pore surface irregularity to study the nuclear relaxation of a liquid confined in an irregular pore. Our calculation on a pre-fractal volume with infinite surface relaxation rate shows that the long time relaxation behavior is dominated by an exponential mode characterizing a free diffusive volume. At short time, the calculated magnetization follows closely the power-law behavior previously proposed by de Gennes. For finite surface relaxation rate, we extend our studies of the efficiency of exchange on fractal membranes to nuclear relaxation in the same geometry. We predict a decay involving two characteristic times. For very slow surface relaxation, there will exist exponential relaxation governed by the surface relaxation. These laws show that the pore surface irregularities may play an important role in nuclear relaxation.

NUCLEAR RELAXATION IN IRREGULAR OR FRACTAL PORES

We apply a fractal description of pore surface irregularity to study the nuclear relaxation of a liquid confined in an irregular pore. Our calculation on a pre-fractal volume with infinite surface relaxation rate shows that the long time relaxation behavior is dominated by an exponential mode characterizing a free diffusive volume. At short time, the calculated magnetization follows closely the power-law behavior previously proposed by de Gennes. For finite surface relaxation rate, we extend our studies of the efficiency of exchange on fractal membranes to nuclear relaxation in the same geometry. We predict a decay involving two characteristic times. For very slow surface relaxation, there will exist exponential relaxation governed by the surface relaxation. These laws show that the pore surface irregularities may play an important role in nuclear relaxation.

Observation of an Opticlike Phase Mode in an Antiferroelectric Liquid Crystal.

We have observed an acousticlike and an opticlike branch of phase excitations in a quasielastic light-scattering experiment performed in the antiferroelectric smectic-${C}_{A}^{*}$ phase of 4-(1-ethylheptyloxycarbonyl)phenyl-4\ensuremath{'}-alkylcarbonyloxy biphenyl-4-carboxylate. In contrast to the nearly gapless acoustic phason branch, the opticlike phase excitations always have a finite relaxation rate. The phenomenon is a direct consequence of a doubling of a smectic unit cell at the transition from the smectic-$A$ phase and is in remarkable agreement with a Landau-type model.

Electron relaxation in the quantum-Hall-effect geometry: One- and two-phonon processes.

The longitudinal-optical (LO) phonon-assisted electron relaxation has been investigated in a two-dimensional electron system in the quantum-Hall-effect geometry. The phonon emission rates versus inter-Landau-level separations are calculated. One LO- and two LO+LA-phonon emission processes via polar optical and deformation acoustical itneractions are considered. To obtain a finite relaxation rate associated with one-phonon emission, the allowance for the Landau-level broadening or for the LO-phonon dispesion is made. Below the LO-phonon energy ${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$ within an energy range of the order of \ensuremath{\Elzxh} \ensuremath{\surd}${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$/\ensuremath{\tau} the one-phonon relaxation rate exceeds 1 ${\mathrm{ps}}^{\mathrm{\ensuremath{-}}1}$. (Here \ensuremath{\tau} is the relaxation time deduced from the mobility, and ${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$ is the cyclotron fjrequency. In GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure with the mobility \ensuremath{\mu}=25 ${\mathrm{V}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{m}}^{2}$ this range makes up 0.7 MeV.) The two-phonon emission has a significant contribution to the relaxation above ${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$. At energy separations of the order of ${\mathit{ca}}_{\mathit{B}}^{\mathrm{\ensuremath{-}}1}$ (c is the sound velocity, ${\mathit{a}}_{\mathit{B}}$ is the magnetic length) the LO+LA-phonon emission provides a mechanism of subpicosecond relaxation while in a wide energy range of the order of \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$ the subnanosecond relaxation can be achieved.

Binding of Li atoms adsorbed on metal surfaces.

The local density of states LDOS(${\mathit{E}}_{\mathit{F}}$) at the Fermi energy and at the nucleus of an adsorbed Li atom can be determined quantitatively by nuclear-spin relaxation experiments, a special version of NMR experiments. Values between 0.1 and 0.2 ${\mathrm{eV}}^{\mathrm{\ensuremath{-}}1}$ A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}3}$ have been obtained for various single-crystal surfaces of Mo, Ru, W, Ir, and Pt. The finite values demonstrate unambiguously that Li adsorption on these metal surfaces cannot be purely ionic. Moreover, just the bare existence of a finite nuclear-spin relaxation rate demonstrates that fluctuating delocalized electron spins interact with the nuclear spin of the Li atom, while it is adsorbed on the metal surface.

Electronic instability a high flux-flow velovities-T c uperconducting films

The nonlinearity in the flux-flow process due to the finite energy relaxation rate of the quasiparticles has been studied in the mixed state of epitaxial c-axis oriented YBa 2Cu 3O 7−δ films. The inelastic quasipartcle scattering rate was found to decrease rapidly with decreasing temperature below T c.

Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations.

The effects of periodic pulsatile stimuli on a nonlinear limit-cycle oscillation are analyzed for various relaxation rates to the limit-cycle oscillation. In the infinite relaxation limit, the effects of periodic stimuli are analyzed by consideration of the bifurcations of circle maps. In the case of a finite relaxation rate, it is necessary to analyze two-dimensional maps of the disk. However, the simple structure of the limit cycle allows us to carry out detailed theoretical and numerical analyses of the dynamics. Using the Brouwer fixed point theorem, we show that for any finite nonzero frequency and amplitude of the stimulus, there will be a period-1 fixed point associated with a period-1 phase locking. We use analytical and numerical methods to determine the stability boundary of the period-1 fixed point as a function of the stimulation frequency, amplitude, and relaxation rate to the limit cycle. These results, combined with numerical studies give insight into the changes in the global organization of the phase locking zones as a function of the relaxation rate to the limit cycle.

Phasons and broken symmetries in ferroelectric liquid crystals.

The phason dispersion and the linear electro-optic response in the ferroelectric Sm C* liquidcrystalline phase have been measured in an external magnetic field up to 14 T. In the presence of an external field the originally continuous phason spectrum splits into an opticlike and an acousticlike phason branch, separated by a field-dependent gap. The band structure of the phason spectrum in the presence of the field is a consequence of the broken helical symmetry of the Sm C* phase and is analo­ gous to the energy spectrum of an electron in a crystal lattice. The observed magnetic-field dependence of the phason spectrum is in good agreement with theory. I. INTRODUCTION Some time ago Blinc and Zeks1 showed, that in the long-wavelength and low-frequency limit, the spectrum of collective excitations of the Sm C* phase of a ferroelec­ tric liquid crystal consists of the amplitudon and the phason dispersion branches, which merge into a doubly degenerate soft-mode branch at the Sm ^4—^Sm C* phase-transition point. The amplitudon branch represents collective, plane-wave fluctuations of the mag­ nitude of the tilt angle in the Sm C* phase. It exhibits finite relaxation rates at all wave vectors and tempera­ tures, except at the transition point Tc. The so-called phason branch of excitations represents the fluctuations of the phase of the tilt angle. In view of the continuous D œ symmetry of the Sm A phase, which is broken at the Sm A — >Sm C* transition point, the phason branch is ex­ pected to be gapless and should thus contain a zero fre­ quency symmetry-restoring Goldstone mode3 3 The nature of collective excitations in ferroelectric liquid crystals has been extensively studied by quasielastic light scattering4,5 and dielectric spectroscopy6 and is fairly well understood. For example, it has been shown that in the Sm A phase of a ferroelectric liquid crystal the soft mode freezes-out into form of a space-coherent helical wave5 at Tc, whereas in the Sm C * phase the experiments have confirmed the existence of a zero-frequency Goldstone mode in the phason excitation spectrum.4 In a recent paper7 we have reported the magnetic-field dependence of the phason branch in the Sm C* phase of ferroelectric liquid crystal. We observed that an external magnetic field, applied perpendicular to the helical axis of the Sm C* phase, induces a splitting of the originally sin­ gle phason branch into the so-called “acousticlike” and “opticlike” branch, respectively. These two branches are separated by a field-dependent gap G (H ), which is pro­ portional to the square of the magnetic field. The magnetic-field-induced splitting of the phason branch can be explained on the basis of pure symmetry arguments. The unperturbed Sm C* structure is a phase with a continuous helicoidal symmetry, as shown by the object in Fig. 1(a). This means, that any translation of the system along the helical axis, followed by an ap­ propriate rotation around the helical axis transforms the Sm C* phase into itself. As a result of this continuous helicoidal symmetry, phason excitations propagate along the helical axis in a form of plane waves with a gapless dispersion relation. This can be well understood by real­ izing that a phason propagating along the helix is a twistlike, periodic elastic deformation of the phase profile. Since all the points on the helix are equivalent with respect to such a deformation, a phason propagating along the helix “sees” a uniformly twisted structure, which is thus equivalent to a spatially uniform structure. This results in a plane-wave phason propagation.

On the flux bundle size in weakly pinned superconductors

Recently it was found that the transverse flux bundle size estimated from the observed irreversibility field in terms of the flux creep theory takes much smaller values than the prediction from the elastic correlation length of the fluxoid lattice. This is more remarkable for the case of larger correlation length, i.e., for superconductors with a weaker flux pinning strength. It is assumed that the flux bundle size is determined so that the critical current density under the flux creep is maximized. This assumption is analogous to the irreversible thermodynamic principle for the linear dissipation systems that the energy dissipation is minimized. The obtained flux bundle size is proportional to the one-third power of the value derived from the elastic correlation length. Qualitative and quantitative agreements are obtained between the prediction and the experiments. The theoretical result also explains the observed finite relaxation rates at ultra-low temperatures which have been believed to be explained only by the quantum tunneling mechanism.

Asymmetry between flux penetration and flux expulsion in Tl-2212 superconductors

dc magnetic hysteresis as well as flux penetration and flux expulsion were investigated in Tl2−yBa2CaCu2O8−x polycrystals and monocrystals. All measurements were performed at 35 K and in the 0–5 T field range. Hysteresis measurements revealed an irreversibility field of about 2 T. Existing models predict identical field-cooled (fc) and zero-field-cooled (zfc) magnetizations and vanishing time dependence above this field. Although the identical fc and zfc magnetizations are in fact observed, the time dependence vanishes only for flux penetration after zero-field cooling; a remanence is preserved after field cooling and decays with a finite relaxation rate. Activation energies calculated on the basis of the thermal activation model display a pronounced field dependence, and arelower for flux penetration than for flux expulsion in high fields (H≥3 T) for all orientations. This behavior of extreme layered superconductors contradicts classical theoretical models and questions the original definition of the irreversibility line as well. All of our results are consistent with the recent theory of lock-in transition, and can be well interpreted by using those principles.

Weak coupling analysis of the optical conductivity of the two dimensional Hubbard model

We analyze the dynamical conductivity at zero momentum transfer of the two dimensional Hubbard model applying a projection technique approach in Liouville space. In the limit of small correlation strength we present a perturbative evaluation of the relevant current selfenergy and the isothermal current susceptibility using a novel real space summation technique. A dicussion of our results for the zero frequency Drude weight, the finite frequency relaxation rate and the incoherent spectrum of the optical conductivity at various filling densities and for zero temperature will be given.

Stochastic dynamics of n-nonane and related molecules in solution compared with nuclear magnetic resonance coupled relaxation times

The motion of chain molecules in solution has been analyzed using both generalized Langevin equation (GLE) and ordinary Langevin equation (OLE) simulations. A numerical algorithm for solving the GLEs is developed in which the integrations over various forces have been performed explicitly. It is shown in the GLE simulations that the motion of chain segments is correlated closely with solvent relaxation giving significantly reduced friction forces. At temperatures higher than 233 K, a hydrodynamic description with a structure relaxation mode in the solvent (diglyme) is sufficient to yield Cartesian correlation times in good agreement with the NMR coupled relaxation results on n-nonane. The relative contributions of both overall tumbling and internal motion to the Cartesian and end-to-end direction relaxation and the possible couplings of these two motions are analyzed by calculating apparent activation energies for various motional modes and by using a harmonic approximation. It is found that the OLE model underestimates the contribution of internal motion to the relaxation of local Cartesian modes. The finite structural relaxation rate in the solvent can substantially alter not only the correlation times, but the dynamic features of the relevant relaxation processes in a full GLE calculation. In particular, it is shown that the short-time decay of the Cartesian correlation functions is underdamped oscillation in contrast with the overdamped behavior found from the OLE simulations.

Solution to the Glarum model with a finite relaxation rate

The one-dimensional version of the Glarum model of target relaxation by diffusing defects is generalized by considering a finite relaxation rate upon an encounter defect-target. This eliminates the difficulties associated with the instantaneous relaxation of the targets initially occupied by a defect. The diffusion and relaxation processes are described in terms of the master equation for a continuous-time random walk. An exact solution valid for all times and relaxation rates is obtained by the use of the van Kampen-Oppenheim method. The transition from exponential relaxation at short times to fractional exponential behaviour at long times is described in detail.

A simple model for elastic fracture in thin films

A simple model for the cracking of thin films has been developed and investigated. The film is represented by a network of bonds and nodes which initially form a triangular lattice in which each node is at the junction of six bonds. The nodes are also attached to a rigid substrate by bonds which are not broken but have a relatively small force constant. Cracking is simulated by a sequence of thermally activated bond breaking events followed by mechanical relaxation. If the stretching force constant associated with the bonds in the surface layer is large, linear cracks propagate rapidly and, at a later stage, are connected by secondary cracks which become less and less linear as the strain in the surface layer is relaxed by the cracking process. Many of our simulations exhibit a distint “initiation” period in which the bond breaking rate is low, followed by a period of rapid crack propagation in which a large fraction of the surface strain energy is released. This period is then followed by a second period of relatively slow bond breaking. During the first period isolated defects are formed, followed by linear cracks in the second period. During the third period non-linear cracks connect the linear cracks, and structures which resemble shear bands are formed. Results for the effects of finite relaxation rates for the elastic network (visco-elastic effects) are also presented.

Kinetics of saturation of the active medium of an oxygen-iodine laser

A theoretical study is made of the dependences of the gain for the 2P1/2(F= 3)→2P3/2(F' = 4) transition in the iodine atom on the intensity of the incident field and also on the rate constants of the processes occurring in the active medium of an oxygen-iodine laser. The main processes that determine the kinetics of saturation by the incident field are the exchange of the electronic energy between iodine atoms and oxygen molecules, translational relaxation of iodine atoms, van der Waals mixing of the sublevels of 2P3/2, and also mixing of the sublevels of 2P1/2 in the course of exchange interaction with oxygen molecules. It is shown that the translational and hyperfine relaxation processes play an exceptionally important role in the establishment of the emission spectrum. The influence of the anomalous dispersion effects on the divergence of laser radiation in the multimode lasing regime is discussed. A finite translational relaxation rate reduces severalfold the output power of an oxygen-iodine laser and increases the length of the lasing zone in the downstream direction.