Narrow Results

Some results on the relaxation processes (Glauber dynamics) obtained in the last decade are presented. This article is intended to be a short guided tour through these results for readers without prior knowledge of rigorous statistical mechanics or stochastic processes.

The average length and average relaxation time of attractors in sequence processing neural networks are investigated. The simulation results show that a critical point of α, the loading ratio, is found. Below the turning point, the average length is equal to the number of stored patterns; conversely, the ratio of length and numbers of stored patterns, grow with an exponential dependence exp (Aα). Moreover, we find that the logarithm of average relaxation time is only linearly associated with α and the turning point of coupling degree is located for examining robustness of networks.

We studied the dynamical phase transition in kinetic Ising ferromagnets driven by oscillating magnetic field in meanfield approximation. The meanfield differential equation was solved by sixth-order Runge–Kutta–Felberg method. The time-averaged magnetization plays the role of the dynamic order parameter. We studied the relaxation behavior of the dynamic order parameter close to the transition temperature, which depends on the amplitude of the applied magnetic field. We observed the critical slowing down along the dynamic phase boundary. We proposed a power law divergence of the relaxation time and estimated the exponent. We also found its dependence on the field amplitude and compared the result with the exact value in limiting case.

This paper carries out numerical simulation for pressure driven microscale gas flows in transition flow regime. The relaxation time of LBM model was modified with the application of near wall effective mean free path combined with a combination of Bounce-back and Specular Reflection (BSR) boundary condition. The results in this paper are more close to those of DSCM and IP-DSCM compared with the results obtained by other LBM models. The calculation results show that in transition regime, with the increase of Knudsen number, the dimensionless slip velocity at the wall significantly increases, but the maximum linear deviation of nonlinear pressure distribution gradually decreases.

This study extends the understanding of the spiral of silence theory by taking into account four factors, including the topology of networks, the time factor of information transmission, the node degree of individuals and the freedom of expression. Simulation experiments analyze the silencers, public opinion in steady state and relaxation time in small-world networks, scale-free networks and community-structured networks by adjusting the initial conditions. Results highlight that individuals are easier to keep silent in scale-free network, especially when the individual with big degree and minority opinion starts the discussion. Conversely, there are only a few individuals keep silent in the community-structured network when the two communities hold opposite opinions. Moreover, the number of silencers grows as the degree of coupling increases, and it decreases as the freedom of expression goes up. By analyzing the public opinion evolution, we also find some important conditions, such as the network topology, the potential public opinion distribution, and the status and sides of the first speaker, can drive the minority reversal.

We investigate the external field effect on opinion formation based on the majority rule and $q$-voter models on a complete graph. The external field can be considered as the mass media in the social system, with the probability $p$ agents following the mass media opinion. Based on our Monte Carlo simulation, the mass media effect is not strong enough to make the system reach a homogeneous state (complete consensus) with the magnetization $m=1$ for all values of $p$, indicating the existence of a usual phase transition for all values of $p$. In the $q$-voter model, the mass media eliminates the usual phase transition at $p\approx 0.21$. We obtain the model’s critical point and scaling parameters using the finite-size scaling analysis and obtain that both models have the same scaling parameters. The external field effect decreases both models’ relaxation time and the relaxation time following the power-law relation such as $\tau \sim N^{\beta }$, where $N$ is the population size and $\beta$ depends on the probability $p$. In the majority rule model, $\beta$ follows a linear relation, and in the q-voter model, $\beta$ follows a power-law relation.

The Lotka–Volterra model of competition has been studied by numerical simulations using the Runge–Kutta–Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The transient behaviors associated with reaching the stable fixed point are studied systematically. It is observed that the time of reaching the stable fixed point in any one of the basins of attraction depends strongly on the initial distance from the separatrix. As the initial point approached the separatrix, this time was found to diverge logarithmically. The divergence of the time, required to reach the stable fixed point, indicates the critical slowing down near the critical point in equilibrium phase transition. A metastable behavior was also observed near the saddle fixed point before reaching the stable fixed point.

We review our recent studies on the dynamical correlations in MC simulations from the view point of the statistical dependence. Attentions are paid to the reduction of the statistical degrees of freedom for correlated data. Possible biases on several cumulants, such as the susceptibility and the Binder number due to finite MC length are discussed. A new method for calculating the equilibrium relaxation time from the analysis of the statistical dependence is presented. We apply it to the critical dynamics of the Ising model to estimate the dynamical critical exponent accurately.

One of the challenges of the Environment-Induced Decoherence (EID) approach is to provide a simple general definition of the moving pointer basis or moving preferred basis. In this paper we prove that the study of the poles that produce the decaying modes in non-unitary evolution, could yield a general definition of the relaxation, the decoherence times, and the moving preferred basis. These are probably the most important concepts in the theory of decoherence, one of the most relevant chapters of theoretical (and also practical) quantum mechanics. As an example we solved the Omnès (or Lee–Friedrich) model using our theory.

In this study we analyzed the deformation of the polymeric rod impacting on the rigid wall which is called "Taylor impact test."" We simulated three-dimensional Taylor impact test depending on the various polymeric materials using the explicit finite element method by employing DYNA3D code. In simulation, polymeric materials were modeled using viscoelastic constitutive relations with the relaxation time and shear modulus. We have carried out the numerical simulation for the transient deformation characteristics and discussed effects of the viscoelastic constants on the deformation of the polymeric rod under impact.

A generalized form of surface dissipation function, for the description of the relative motion of the nematic director with respect to the polymer side chains in twisted chiral nematic samples is proposed, and the relaxation time of such samples are investigated, using the perturbation analysis method proposed by Alexe-Ionescu et al. Our results show that the presence of both the surface dissipation and the polymer side chains increase the relaxation time.

We study relaxation time T_c of time-delayed bistable system driven by two cross-correlated Gaussian white noises that one is multiplicative and the other is additive. By means of numerical calculations, the results indicate that: (i) Combination of noise and time delay can induce two critical points about the relaxation time at some certain noise cross-correlation strength λ under the condition that the multiplicative intensity D equals to the additive noise intensity α. (ii) For each fixed D or α, there are two symmetrical critical points which locates in the regions of positive and negative correlations, respectively. Namely, as λ equals to the critical value λ_c, T_c is independent of the delay time and the result of T_c versus τ is a horizontal line, but as |λ|>|λ_c| (or |λ|<|λ_c|), the relaxation time T_c monotonically increases (or decreases) with the delay time increasing. (iii) In the presence of D = α, the change of λ_c with D is two symmetrical curves about the axis of λ_c = 0, and the critical value λ_c is close to zero for a smaller D, which approaches to +1 or -1 for a greater D.

We characterized the ultrafast properties of LT-GaAs doped with silicon $\delta$-layers and introduced delta-doping ($\delta$-doping) as efficient method for enhancing the properties of GaAs-based structures which can be useful for terahertz (THz) antenna, ultrafast switches and other high frequency applications. Low temperature grown GaAs (LT-GaAs) became one of the most promising materials for ultrafast optical and THz devices due to its short carrier lifetime and high carrier mobility. Low temperature growth leads to a large number of point defects and an excess of arsenic. Annealing of LT-GaAs creates high resistivity through the formation of As-clusters, which appear due to the excess of arsenic. High resistivity is very important for THz antennas so that voltage can be applied without the risk of breakdown. With $\delta$-Si doping, control of As-clusters is possible, since after annealing, clusters align in the plane where the $\delta$-doping occurs. In this paper, we compare the properties of LT-GaAs-based planar structures with and without $\delta$-Si doping and subsequent annealing. We used pump-probe transient reflectivity as a probe for ultrafast carrier dynamics in LT-GaAs. The results of the experiment were interpreted using the Ortiz model and show that the $\delta$-Si doping increases deep donor and acceptor concentrations and decreases the photoinduced carrier lifetime as compared with LT-GaAs with same growth and annealing temperatures, but without doping.

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and coupled to a bath. We have considered two models for the bath: an Ohmic bath model and a non-Markovian Drude bath model with finite memory. The effect of finite memory on the dynamics of the quantum spin is studied in detail. In particular, we have studied the effect of memory on the expectation values of the magnetic moment and the spin correlation functions. The time evolution study of the spin correlation functions shows that the correlation functions exhibit a damped oscillatory behavior with the randomization time being determined by the damping rate. We have analytically shown that the damping gets affected by the finite memory time when the bath retains memory of the interaction with the system. We also analyze the spin response function of the system for the Ohmic bath. Our results qualitatively agree with the findings in spin noise spectroscopy experiments and our predictions can be tested in future ultracold atom experiments.

Nuclear magnetic resonance (NMR) is a phenomenon whereby magnetization is excited when static and time varying magnetic fields are applied simultaneously on a given medium such as human blood. The effect of the magnetization causes the protons of the medium to spinning. For several decades now, a set of three Bloch equations are used to describe the dynamics of the spinning protons. Exact solution of the Bloch equations has been the endeavors of many workers with partial success. In about a decade now, a milestone was the appearance of a single NMR fluid flow equation derived from the three set of Bloch equations. The single equation has been found insuperable up to now, defying all efforts to yield a closed form solution. Motivated by the exigency to achieve complete magnetization expression as a function of time and distance, for NMR signal calculations or experiments, we have actualized a closed form solution. We used the method of Laplace transforms and ultimately applied complex inversion theorem to obtain the inverse Laplace transforms. Our final expression is a labyrinth of several oscillatory systems that are characteristics of a nonlinear phenomenon. This is cognate with concepts of chaos.

By using the density functional theory (DFT) in combination with Boltzmann transport theory, the influence of Mg concentrations (x) doping on the thermoelectric properties of Hg${}_{1-x}$Mg_xSe ternary alloys was systematically investigated. The generalized gradient approximations of Perdew–Burke–Ernzerhof (GGA-PBE) have been used to illustrate the exchange correlation potential. The thermodynamic stability of the studied compounds was analyzed in terms of formation energy. Various thermoelectric transport parameters, such as the Seebeck coefficient (S), the thermal conductivity over relaxation time (k/$\tau$), the electrical conductivity over relaxation time ($\sigma$/$\tau$), the power factor (PF) and the figure of merit (ZT) have been deduced and discussed. The obtained results of thermoelectric properties show that the studied materials can be useful for thermoelectric devices at room temperature. It can also be seen that Mg concentrations can increase the thermal efficiency of the HgSe alloy.

The effects of the correlations between real and imaginary parts of the quadratic pump noise on the normalized intensity correlation function and the associated relaxation time of a single-mode laser model were investigated. The expressions of the intensity correlation function C(s) and the relaxation time T_c were derived. Based on numerical computations, we found that T_c monotonously increases as the strength λ_p of correlation between the real and imaginary parts of quadratic pump noise increases and the larger λ_p value is, the slower C(s) decays. The presence of correlations between the real and imaginary parts of the quadratic pump noise causes the intensity fluctuation to increase.

In this paper, we study the relaxation time of a bistable system driven by correlated noises when there are two different kinds of time delays in the deterministic (τ) and random (θ) forces, respectively. The expression for the relaxation time T_c is derived by the projection operator method, in which the effects of the memory kernels are taken into account. After introducing a dimensionless parameter R (R = D/α, where D is the strength of multiplicative noise and α is the strength of additive noise), and then performing numerical computations, we find the following: (1) for the case of R ≤ 1, the relaxation time T_c increases as τ increases, i.e. τ slows down the fluctuation decay of the dynamical variable for the case of R ≤ 1; (2) however, for the case of R > 1, T_c decreases as τ increases, i.e. τ enhances the fluctuation decay of the dynamical variable for the case of R > 1; (3) T_c decreases as θ increases, i.e. θ enhances the fluctuation decay of the dynamical variable for the three cases of R (R > 1, R=1, and R < 1).

Based on the Fokker–Planck description of a single-mode laser system and the projection operator method, the mean relaxation time T of a single-mode laser system with correlations between the real and imaginary parts of the quantum noise as well as the pump noise is studied. It is found that the mean relaxation time T increases with the increasing net gain a₀ and decreases with the increasing self-saturation coefficient A. T increases with the increasing pump noise strength Q but decreases with the increasing quantum noise strength D. The mean relaxation time T increases (decreases) with the increasing pump noise self-correlation time τ if a₀ > 0 (a₀ < 0). T decreases with the increasing |λ| (λ is the coefficient of cross-correlation between the real and imaginary parts of the quantum noise).

The LiCo_3/5Fe_2/5VO₄ ceramics has been fabricated by solution-based chemical method. Frequency dependence of the dielectric constant (ε_r) at different temperatures exhibits a dispersive behavior at low frequencies. Temperature dependence of ε_r at different frequencies indicates the dielectric anomalies in ε_r at T_c (transition temperature) = 190°C, 223°C, 263°C and 283°C with (ε_r)_max ~ 5370, 1976, 690 and 429 for 1, 10, 50 and 100 kHz, respectively. Frequency dependence of tangent loss (tan δ) at different temperatures indicates the presence of dielectric relaxation in the material. The value of activation energy estimated from the Arrhenius plot of log(τ_d) with 10³/T is ~(0.396 ± 0.012) eV.