Slow algebraic relaxation in quartic potentials and related results

We present a detailed report [see S. Sen et al., Phys. Rev. Lett. 77, 4855 (1996)] of our numerical and analytical studies on the relaxation of a classical particle in the potentials V(x)= +/-x(2)/2+x(4)/4. Both of the approaches confirm that at all temperatures, the relaxation functions (e.g., velocity relaxation function and position relaxation function) decay asymptotically in time t as sin(omega(0)t)/t. Numerically calculated power spectra of the relaxation functions show a gradual transition with increasing temperature from a single sharp peak located at the harmonic frequency omega(0) to a broad continuous band. The 1/t relaxation is also found when V(x) is a polynomial in powers of x(2) with a nonvanishing coefficient accompanying the x(4) term in V(x). Numerical calculations show that in the cases in which the leading term in V(x) behaves as x(2n) with integer n, the asymptotic relaxation exhibits 1/t(phi) decay where phi =1/(n-1). We briefly discuss the analytical approaches to relaxation studies in these strongly anharmonic systems using direct solution of the equation of motion and using the continued fraction formalism approach for relaxation studies. We show that the study of the dynamics of strongly anharmonic oscillators poses unique difficulties when studied via the continued fraction or any other time-series construction based approaches. We close with comments on the physical processes in which the insights presented in this work may be applicable.     

Dielectric investigation of the temperature dependence of the nonexponentiality of the dynamics of polymer melts

Using broad band dielectric spectroscopy (10(-5)-10(9) Hz), combining time domain and frequency domain techniques, we study the temperature dependence of the non-Debye character of the alpha relaxation of polymer melts in the glass transition temperature T(g) range. The alpha relaxation process is described in terms of the Kohlrausch-Williams-Watts relaxation function which has a single parameter beta to characterize the nonexponentiality of the relaxation. At high temperatures, beta remains nearly insensitive to temperature changes, whereas in the vicinity of T(g) a nearly linear increasing of beta with temperature is found. The temperature range where the change of the beta(T) behavior occurs is located for all the polymers investigated around 1.2T(g). Moreover, our results indicate a common value of beta approximately equal to 1/3 at the temperature where the relaxation time diverges. The beta(T) behavior near T(g) is discussed in terms of a "rugged landscape" phase space which allows us to rationalize both the beta(T) behavior observed as well as the similarities of our findings near T(g) with the results reported in simulations on Ising spin glasses and other model systems.     

Activated scaling of classical and quantum spin glasses

A model for thermally activated dynamics in disordered systems shows that the linear and nonlinear susceptibility follows a generic exponential form with a "critical rounding," chi(1) proportional to chi(3) proportional to [T ln(t/tau(0)')/K](gamma/b phi) exp - [Tt(g)(phi b)ln(t/tau(0)'/K)](nu/b) (T=temperature, t=time, K=barrier constant, t(g) = 1 - T(SG)/T, and T(SG) = transition temperature; gamma>0 for chi(3) and <0 for chi(1)). This model, also valid in the presence of resonant tunneling states at energies K(0) < K [provided that K is replaced by K(0)+2T ln (1/Gamma(0)), where Gamma(0)(2) proportional, variant tunnel splitting of a spin S=1], is potentially applicable to a wide variety of systems opening the way for the study of thermally activated quantum phase transitions. The famous spin-glass system LiHo(x)Y(1-x) seems to follow this model.     

An interstitialcy theory of structural relaxation and related viscous flow of glasses

A theory of isothermal structural relaxation and creep of glasses below the glass transition temperature is given. According to the interstitialcy theory, the supercooled liquid state does not exist below a Kauzmann "pseudocritical" temperature T(k), which lies above the temperature T(K), commonly called the "Kauzmann temperature." Structural relaxation is simply a reduction with time of the interstitialcy concentration to the crystalline state for TT(k). The predicted viscosity eta is universal, given by eta=eta(0) + eta(T)t, in agreement with experiment. eta is continuous in T, with eta discontinuous at T(k) but linear in 1/T above and below T(k). The dependence of eta on the shear modulus directly connects kinetic and thermodynamic properties of glasses and liquids.     

Average shape of a fluctuation: universality in excursions of stochastic processes

We study the average shape of a fluctuation of a time series x(t), which is the average value (T) before x(t) first returns at time T to its initial value x(0). For large classes of stochastic processes, we find that a scaling law of the form (T) = T(alpha)f(t/T) is obeyed. The scaling function f(s) is, to a large extent, independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.     

Longitudinal relaxation of initially straight flexible and stiff polymers

The relaxation mechanism of an initially straight flexible or stiff polymer chain of length N in a viscous solvent is studied through Brownian dynamics simulations covering a broad range of time scales. After the short-time free diffusion, the chain's longitudinal reduction R2(0)-R2 approximately Nt1/2 at early intermediate times is shown to constitute a universal behavior for any chain stiffness caused by a quasisteady T approximately Nt(-1/2) relaxation of tensions associated with the deforming action of the Brownian forces. Stiff chains with a persistence length E > or = N are shown to exhibit a late intermediate-time longitudinal reduction R2(0)-R2 approximately N2E(-3/4)t1/4 associated with a T approximately N2E(-3/4)t(-3/4) relaxation of tensions affected by the deforming Brownian and the restoring bending forces.     

Transient optical absorption induced by an electron pulse in KPb<Subscript>2</Subscript>Cl<Subscript>5</Subscript> crystals

The efficiency of formation and time evolution of radiation-induced structural defects and pulsed luminescence in KPb₂Cl₅ crystals under the action of a single electron pulse (E = 250 keV, τ = 20 ns) have been investigated. The spectra (1.1–3.8 eV) and relaxation kinetics (time interval 5 × 10^?8?5 s) of transient optical absorption and the pulsed cathodoluminescence spectra and decay kinetics (1.4–3.1 eV) have been measured in the temperature range 80–300 K. It is revealed that the induced optical density and its time evolution depend strongly on temperature, and the absorption relaxation time contains several components and reaches several seconds at T = 300 K. The decay kinetics of transient absorption and pulsed cathodoluminescence kinetics have different orders and are controlled by different relaxation processes.     

Light-scattering study of a supercooled epoxy resin

The dynamics of the fragile glass-forming liquid diglycidyl ether of bisphenol-A was studied by depolarized Rayleigh-Brillouin light-scattering and photon correlation spectroscopy above the glass transition, in the temperature range from 261 to 473 K and in the frequency range from 1 Hz to 300 GHz. The structural (alpha-) relaxation process was revealed and no signature of the secondary relaxation previously evidenced by dielectric spectroscopy at about 0.1 GHz was observed. The characteristic time of the alpha process differs from that determined by dielectric spectroscopy of an amount, which increases with increasing temperature. The relaxation times were compared with viscosity data to test the predictions of the classic Stokes-Einstein-Debye model. The tau proportional, variant eta behavior was verified for dielectric data, while a fractional power law of viscosity tau proportional, variant eta(0.89) was obtained for light-scattering relaxation times, extending over more than seven decades in viscosity and time. This deviation of light scattering from viscosity data could be interpreted in terms of cooperative motion in the supercooled liquid with a characteristic length xi(a) proportional, variant(T-T0)(-v) where T(0)=229 K is the Vogel temperature and v is close to 2 / 3 which is consistent with the prediction of the fluctuation theory of glass transition.     

非晶Fe82Si5B13合金的磁导率驰豫

在0—300℃范围内考查了非晶Fe₈₂Si₅B₁₃合金的磁导率等温弛豫动力学行为,给出了等时弛豫谱,观察到四个弛豫峰。测量表明,总的磁导率弛豫由两种弛豫过程组成,即对于退磁可逆的普通减落和对于退磁不可逆的磁导率连续衰减。计算了弛豫时间和激活能的分布,表明弛豫时间和激活能有宽的分布。普通减落和磁导率衰减过程的最可几激活能分别为1.0eV和1.4eV。对退火的样品,观察到磁导率先是增大而后是衰减的广义cross-over效应。 关键词：     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Analysis of multi-exponential relaxation data with very short components using linear regularization

Linear regularization is a common and robust technique for fitting multi-exponential relaxation decay data to obtain a distribution of relaxation times. The regularization algorithms employed by the Uniform-Penalty inversion (UPEN) and CONTIN computer programs have been compared using simulated transverse (T2) relaxation data derived from a typical bimodal distribution observed in cartilage tissue which contain a component shorter than t(0), the time of the first decay sample. We examined the reliability of detecting sub-t(0) relaxation components and the accuracy of statistical estimates of T2 distribution parameters. When the integrated area of the sub-t(0) component relative to that of the total distribution was greater than 0.25, our results indicated a signal-to-noise threshold of about 300 for detecting the presence of the sub-t(0) component with a probability of 0.9 or greater. This threshold was obtained using both the UPEN and CONTIN algorithms. In addition, when using the second-derivative-squared regularizer, UPEN solutions provided statistical estimates of T2 distribution parameters which were substantially free of the biasing effect of the regularizer observed in analagous CONTIN solutions.     

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

NO2分子在440～495 nm范围内的激光诱导荧光激发谱

以 NdYAG脉冲激光器泵浦的光学参量发生器/放大器作激发光源, 获得了室温、低气压条件下, NO2分子在440～495 nm波长范围内的激光诱导荧光激发谱, 将所得谱线峰归属为NO2由基电子态X2A1态向第二电子激发态B2B1态的跃迁, 利用实验所得峰值波长计算了NO2分子B2B1态的角振动频率ωe. 通过对NO2分子B2B1→X2A1跃迁的荧光时间分辨光谱进行实验研究, 得到15 Pa气压下B2B1(0, 9, 0)振动态的能级寿命τ=49 μs. 测量了荧光寿命随气压的变化关系, 利用曲线拟合得到NO2 B2B1(0, 9, 0)振动态的自发辐射寿命τ0≈55 μs和无辐射跃迁弛豫速率常数. kq=1.2×10-9 cm3 molecule-1s-1.     

Use of Carr-Purcell pulse sequence with low refocusing flip angle to measure T₁ and T₂ in a single experiment

The Carr-Purcell pulse sequence, with low refocusing flip angle, produces echoes midway between refocusing pulses that decay to a minimum value dependent on T(2). When the refocusing flip angle was π/2 (CP(90)) and τ>T(2), the signal after the minimum value, increased to reach a steady-state free precession regime (SSFP), composed of a free induction decay signal after each pulse and an echo, before the next pulse. When τ相似文献   

NO分子A^2∑←X^2∏跃迁的激光双光子荧光激发谱

以Nd：YAD脉冲激光器泵浦的光学参量发生器／放大器(OPG／OPA)作激发光源,获得了420～472nm波长范围内NO分子的双光子激光荧光激发谱,并利用此技术对N0分子的能级结构进行了实验研究,将所得谱线峰归属为NO(A^2∑←X^2∏)的跃迁,荧光强度随激光强度的二次方变化关系表明此过程是一双光子激发过程。利用实验所得峰值波长计算了NO(A^2∑)态的基振动频率ωe和平衡位置的力常数k。通过对NO分子A^2∑←X^2∏跃迁的荧光时间分辨光谱进行实验研究,得到266Pa气压下A^2∑(v′=0)态的能级寿命r=53．76ns。测量荧光寿命随气压的变化,利用曲线拟合得到NOA。三(v′=0,1)两振动态的自发辐射寿命和无辐射跃迁驰豫速率常数。     

Control of the fragility of a glass-forming liquid using the liquid-liquid phase transition

When a liquid approaches its glass-transition temperatures T(g), the structural relaxation time tau dramatically increases. This basic feature is ubiquitous, but this increase of tau can be classified between strong and fragile extremes using T(g) as a scaling parameter. Liquids, whose tau obeys the Arrhenius law, are called "strong," while "fragile" liquids have the super-Arrhenius behavior. Here we report the first continuous control of the fragility of liquid of the same material over a wide range of fragility, using a continuous liquid-liquid transition. Our study clearly demonstrates that the fragility is not a material-specific quantity, but is controlled by the order parameter governing the liquid-liquid transition, which may be the fraction of locally favored structures in the liquid.     

Low-temperature relaxation in spin glasses

We analyze the mechanism governing the long-time, low-temperature relaxation of the thermoremanent magnetization (σ_TRM) in metallic spin glasses. Ideas of quantum tunneling and “screening” of the local magnetic moments are employed to explain the existence of a hierarchy of relaxation times. This results in a time decay which is described by anenhanced power law: $$\sigma _{TRM} = \sigma _0 \exp - A[\ln (\omega t)]^y = \sigma _0 (\omega t)^{ - A[\ln (\omega t)]y - 1} $$ withy≧1. A crossover is predicted below which most parameters become temperature-independent.     

Transverse relaxation mechanisms in articular cartilage

Relaxation rates in the rotating frame (R1rho) and spin-spin relaxation rates (R2) were measured in articular cartilage at various orientations of cartilage layer to the static magnetic field (B0), at various spin locking field strengths and at two different static magnetic field strengths. It was found that R1rho in the deep radial zone depended on the orientation of specimens in the magnet and decreased with increasing the spin locking field strength. In contrast, R1rho values in the transitional zone were nearly independent of the specimen orientation and the spin locking field strength. Measurements of the same specimens at 2.95 and 7.05 T showed an increase of R1rho and most R2 values with increasing B0. The inverse B0 dependence of some R2 values was probably due to a multicomponent character of the transverse magnetization decay. The experiments revealed that the dominant T1rho and T2 relaxation mechanism at B0 < or = 3 T is a dipolar interaction due to slow anisotropic motion of water molecules in the collagen matrix. On average, the contribution of scalar relaxation due to rapid proton exchange in femoral head cartilage at 2.95 T is about 6% or less of the total R1rho at the spin locking field of 1000 Hz.     

AC conductivity and dielectric studies of (C5H10N)2BiCl5 compound

The bis (3-dimethylammonium-1-propyne) pentachlorobismuthate (III) exhibits a structural phase transition at T₁?=?(337?±?2?K), which has been characterized by differential scanning calorimetric, X-ray powder analysis, AC conductivity and dielectric measurements. The dielectric dispersion yielded the real and imaginary parts of impedance of (C₅H₁₀N)₂BiCl₅ in the form of a semicircle in a complex plane. Besides, a Cole?CCole plot was observed at frequencies ranging from 209?Hz to 5?MHz, whose result was found to fit the theoretical resistor?Ccapacitor parallel circuit model. The temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law. The frequency-dependent conductivity data were fitted in the modified power law: $ \sigma = {\sigma_{dc}} + {B_1}(T){\omega^{{s_1}}} + {B_2}(T){\omega^{{s_2}}} $ . The imaginary part of the permittivity constant is analyzed with the Cole?CCole formalism. With regard to the modulus plot, it can be characterized by full width at half height or in terms of a non-exponential decay function $ \phi (t) = \exp {\left( {\frac{{ - t}}{{{\tau_\sigma }}}} \right)^\beta } $ . Besides, the activation energy responsible for relaxation has been evaluated and found to be close the DC conductivity.     

Glass transitions and dynamics in thin polymer films: dielectric relaxation of thin films of polystyrene

The glass transition temperature T(g) and the temperature T(alpha) corresponding to the peak in the dielectric loss due to the alpha process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in T(g) was observed with decreasing film thickness, while T(alpha) was found to remain almost constant for d>d(c) and to decrease drastically with decreasing d for d相似文献