Peculiarities of the complicated dynamics of a driven nonlinear oscillator

Saratov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 2, pp. 182–190, February, 1990.     

Observation of a noise-induced phase transition in a parametric oscillator

We have observed a phase transition induced by external noise, using a parametric oscillator driven by a random current, additionally supplied to the sinusoidal pumping current.     

Oscillations in ultrasonic attenuation near a phase transition

It is shown that the oscillations in ultrasonic attenuation observed in KH₂PO₄ near phase transition temperature cannot be due to velocity changes and interference of a coherent source with the echo as suggested by Steinitz et al. recently.     

Elastic anomalies near a surface-induced phase transition

An analysis is made of the influence of elastic degrees of freedom on a surface-induced phase transition. It is found that elastic interactions give rise to a nonlinear correction to the boundary conditions for the order parameter, with the result that the surface transition is of the second order despite the fact that a first order phase transition occurs in the bulk. The propagation of Rayleigh waves near such a transition is discussed.     

Consolidated expansions for estimating the response of a randomly driven nonlinear oscillator

We consider a nonlinear oscillator driven by random, Gaussian noise. The oscillator, which is damped and has linear and cubic terms in the restoring force, is often called the Duffing Equation. The Fourier transform of the response is expanded in a series in the coefficient of the nonlinear term. This series is then squared and averaged, and each term in the resulting response spectrum series is expressed in terms of the response spectrum of the linearized harmonic oscillator (i.e., without the cubic term). Since the forcing function is Gaussian, the linear solution is Gaussian. The terms in the series for the response spectrum are then regrouped so that common quantities can be factored out. This process leads to consolidated equations for the response spectrum and the common factors. These consolidated equations are truncated in various ways, and the corresponding solutions are compared with an analog computer experiment. This technique was proposed for turbulent flow by Kraichnan and followed up by Wyld, and has yielded some good results. The numerical results indicate that the truncated consolidated equations can provide a substantial improvement over some other methods used to solve this type of problem. The methods compared with it are (1) the traditional truncated parametric expansion, (2) statistical linearization, and (3) use of the joint-normal hypothesis to express the fourth and sixth moments in terms of the second.Adapted from the Ph.D. dissertation of J. B. Morton, October 1967. Work supported by Fluid Dynamics Branch, Office of Naval Research, while J. B. M. held a N.A.S.A. traineeship.     

Collective dynamics near a phase transition in confined fluids

We performed molecular dynamics simulations in the microcanonical ensemble (MEMD) for a "simple" fluid confined between two solid substrates. From the calculation of the intermediate scattering function F(k( parallel ),t) and through the memory function formalism, we extract material ( i.e. transport and thermodynamics) coefficients in the vicinity of the liquid-gas phase transition. Our results show that approaching the limit of stability ( i.e. the spinodal), the dynamics of the system changes markedly.     

Nonequilibrium phase transition in a periodically driven XY spin chain

We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-? chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.     

Electron kinetic effects in the nonlinear evolution of a driven ion-acoustic wave

The electron kinetic effects are shown to play an important role in the nonlinear evolution of a driven ion-acoustic wave. The numerical simulation results obtained (i) with a hybrid code, in which the electrons behave as a fluid and the ions are described along the particle-in-cell (PIC) method, are compared with those obtained (ii) with a full-PIC code, in which the kinetic effects on both species are retained. The electron kinetic effects interplay with the usual fluid-type nonlinearity to give rise to a broadband spectrum of ion-acoustic waves saturated at a low level, even in the case of a strong excitation. This low asymptotic level might solve the long-standing problem of the small stimulated Brillouin scattering reflectivity observed in laser-plasma interaction experiments.     

Ising自旋体系的非平衡动态相变

在平均场理论架构下, 以含时金兹堡-朗道和Glauber动力学这两类动态模型为基础，研究 了受外场和温度共同驱动的Ising自旋体系的非平衡动态相变.确定了界定动态无序(动态顺 磁相P)和动态有序(动态铁磁相F)转变的动态相界.并根据动态序参量Q和Binder参数U随系统 温度t(r₀)、驱动外场频率ω和振幅h₀的变化规律，就上述两类模 型的动态相界上是否存在区分连续动态转变和非连续动态转变的三临界点这一引发争议的问 题做出了进一步分析说明. 关键词： Ising自旋体系 非平衡动态相变 含时金兹堡-朗道模型 Glauber 动力学模型     

Localized charge inhomogeneities and phase separation near a second-order phase transition

Localized charge inhomogeneities and phase separation are described in the framework of the phenomenological theory of phase transitions. It is shown that Coulomb interaction determines the charge distribution and the characteristic size of the emerging inhomogeneities. Phase separation associated with charge segregation becomes possible because of a high dielectric constant and a low excess charge density in the localization region. The phase diagram of the system is calculated, and estimates are obtained for the gain in energy associated with the emerging state. The role of Coulomb interaction is exposed, and corresponding estimates are given.     

Nonlinear transport near a quantum phase transition in two dimensions

The problem of nonlinear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions. Using the nonequilibrium Schwinger round-trip Green function formalism, we obtain the scaling function for the nonlinear conductivity in the quantum-disordered regime. We find that the conductivity scales as E2 at low fields but crosses over at large fields to a universal constant on the order of e(2)/h. The crossover between these two regimes obtains when the length scale for the quantum fluctuations becomes comparable to that of the electric field within logarithmic accuracy.     

Loschmidt echo near a dynamical phase transition in a Bose-Einstein condensate

We show that the quantum Loschmidt echo can be employed to characterize the dynamical phase transition, from a tunnelling phase to a self-trapping phase, of a Bose-Einstein condensate in a double-well potential. The echo is found to have a relatively fast decay in the transition region, with a Gaussian decay in the self-trapping phase and a stretched exponential decay in the tunnelling phase.     

Features of the spectral intensity of scattered light near the phase transition point in quartz crystals

The isofrequency dependences of inelastic light scattering in quartz crystals near the phase transition point are calculated taking into account both spatially inhomogeneous fluctuations of the order parameter and the finite spectral width of the spectrometer slit. It was found that the theory is in satisfactory agreement with the experimental data on dynamic opalescence observed in quartz crystals during phase transformations.     

Elastic interaction between adatoms near a distortive phase transition

The indirect elastic interaction between two adatoms on substrates with a very small shear modulus such as V₃Si and Nb₃Sn near the transformation temperature T_M is calculated. As the temperature decreases towards T_M, the shear moduli of these materials go to zero, and the strength of the interaction increases dramatically. The interaction is strongly attractive if the adatoms are aligned along a cube axis and repulsive if they are at 45° to the axis.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.