Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Two-level systems and mass deficit in quantum solids

We study a disordered quantum solid incorporating two-level systems in which a group of atoms (or a single atom) can experience coherent tunnelling between two different positions and demonstrate that an effective mass deficit induced by the presence of such objects can manifest itself only at relatively high frequencies and should vanish in the low-frequency limit. The crossover to the regime which can be associated with the appearance of an effective mass deficit has been observed in recent torsional oscillator experiments.     

Two-level systems: Exact solutions and underlying pseudo-supersymmetry

Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a polynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.     

Simple one-dimensional interaction systems with superexponential relaxation times

Finite one-dimensional random processes with local interaction are presented which keep some information of a topological nature about their initial conditions during time, the logarithm of whose expectation grows asymptotically at least asM ³, whereM is the size of the setR _M of states of one component. ActuallyR _M is a circle of lengthM. At every moment of the discrete time every component turns into some kind of average of its neighbors, after which it makes a random step along this circle. All these steps are mutually independent and identically distributed. In the present version the absolute values of the steps never exceed a constant. The processes are uniform in space, time, and the set of states. This estimation contributes to our awareness of what kind of stable behavior one can expect from one-dimensional random processes with local interaction.Partially supported by NSF grant #DMS-932 1216.     

Quantum relaxation after a quench in systems with boundaries

We study the time dependence of the magnetization profile, m(l)(t), of a large finite open quantum Ising chain after a quench. We observe a cyclic variation, in which starting with an exponentially decreasing period the local magnetization arrives to a quasistationary regime, which is followed by an exponentially fast reconstruction period. The nonthermal behavior observed at near-surface sites turns over to thermal behavior for bulk sites. In addition to the standard time and length scales a nonstandard time scale is identified in the reconstruction period.     

Thermal relaxation of systems with quadratic heat bath coupling: I. Classical systems

We consider the evolution of systems whose coupling to the heat bath is quadratic in the bath coordinates. Performing an explicit elimination of the bath variables we arrive at an equation of evolution for the system variables alone. In the weak coupling limit we show that the equation is of the generalized Langevin form, with fluctuations that are Gaussian and that obey a fluctuation-dissipation relation. If the system-bath coupling is linear in the system coordinates the resulting fluctuations are additive and the dissipation is linear. If the coupling is nonlinear in the system coordinates, the resulting fluctuations are multiplicative and the dissipation is nonlinear.     

Criticality of relaxation in dislocation systems

Relaxation processes of dislocation systems are studied by two-dimensional dynamical simulations. In order to capture generic features, three physically different scenarios were studied and power-law decays found for various physical quantities. Our main finding is that all these are the consequence of the underlying scaling property of the dislocation velocity distribution. Scaling is found to break down at some cutoff time increasing with system size. The absence of intrinsic relaxation time indicates that criticality is ubiquitous in all states studied. These features are reminiscent of glassy systems and can be attributed to the inherent quenched disorder in the position of the slip planes.     

Longitudinal relaxation pathways in scalar-coupled systems

In applications to systems with resolved scalar couplings, the two-dimensional exchange experiment (NOESY) can provide greatly increased information if the flip angles of the two pulses that precede and follow the mixing interval τ_m are reduced (typically ,β ≈20°). The analysis of the amplitudes of individual signals within diagonal- and cross-peak multiplets allows one to gain insight into a variety of competing longitudinal relaxation mechanisms, not only for the fast- and slow-motion limits but also, in favorable cases, for critical correlation times.     

Dielectric relaxation effect in MIM systems

On applying voltage to a thin film Al-Al₂O₃-M system, one observes a decrease of the leakage current with time. After a long period (10³–10⁴ s) the current settles at a new value, lower by several orders of magnitude. After shortcircuiting the sample, there appears a discharge current of reversed polarity, with decay time again of the order of 10³ s. This effect has been reproducibly observed in the temperature range 80–500 K. The present paper is devoted to the experimental study of this relaxation phenomenon in dependence on the parameters of the system (thickness of the dielectric layer, temperature, and material of the upper electrode).The paper is based on RNDr Thesis of the first author.     

Coherence of two-level systems and relaxation

The relaxation of a two-level system interacting with radiation is studied using the method of coherent states. A solution of the equation for the quasiprobability density function is presented in two extreme cases of high and low photon field temperatures. In the first case, the equation has the form of a purely diffusion equation, and from the point of view of a spin interpretation, defines Brownian motion of a magnetic moment on a spherical surface. The second case leads to an equation of the general Fokker-Planck type, in which both diffusion and a systematic term are present. The results of an investigation of spontaneous emission of a system containing a large number of particles, using the quasiclassical approximation, are presented. In this approximation, a Gaussian distribution with a variable variance, whose center moves along a classical trajectory, is obtained for the quasiprobability distribution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 77–80, October, 1981.     

Semiclassical electrodynamics of alien atoms in interacting media II. Two-level systems

The previously developed self-consistent mean field theory of atoms entering an interacting medium is specialized to two-level alien atoms. It is shown that the medium may invert or split the original two levels, and that there is an intimate connection between the dressed atom spectrum and the statistical nature of the ensemble of alien atoms in the self-consistent mean field approximation. The optical susceptibility of alien atoms while inside the medium is calculated, and the lineshape and position of the optical resonance are shown to depend on the intensity of the optical field applied. There may be more than one phase possible for the atomic ensemble as a result of optical excitation.     

Quasi-stationary states and incomplete violent relaxation in systems with long-range interactions

We discuss the nature of quasi-stationary states (QSS) with non-Boltzmannian distribution in systems with long-range interactions in relation with a process of incomplete violent relaxation based on the Vlasov equation. We discuss several attempts to characterize these QSS. We show that their distribution is non-universal and explain why their prediction is difficult in general.     

Muon spin relaxation in heavy fermion systems

Heavy fermion systems have received a great deal of study by a wide variety of techniques, includingSR. In a number of systems, coexisting superconducting and magnetic states have been reported, leading to speculation of an intimate connection between magnetism and superconductivity in these compounds. We observe a spontaneous magnetic field in the superconducting phase of UPt₃. In addition, the broadening of the transverse field muon precession signal only onsets approximately 60 mK below the superconductingT _c. Our results provide evidence that the lower superconducting phase in theH-T phase diagram of UPt₃ is characterised by broken time-reversal symmetry. Measurements of URu₂Si₂ and CeCu_2.2Si₂ indicate that the magnetically ordered volume fraction is temperature dependent in both systems.