Nonexponential quasiparticle decay and phase relaxation in low-dimensional conductors

We show that in low-dimensional disordered conductors, the quasiparticle decay and the relaxation of the phase are not exponential processes. In the quasi-one-dimensional case, both behave at small time as e(-(t/tau(in))3/2) where the inelastic time, tau(in), identical for both processes, is a power T-2/3 of the temperature. The nonexponential quasiparticle decay results from a modified derivation of the Fermi golden rule. This result implies the existence of an unusual distribution of relaxation times.     

Nonexponential decay law

The decay of a nonstationary state usually starts as a quadratic function of time and ends as an inverse power law (possibly with oscillations). Between these two extremes, the familiar exponential decay law may be approximately valid. The main purpose of this paper is to find the conditions which must be satisfied by the Hamiltonian and by the initial state, for the exponential law to have a significant domain of validity. It is shown that the evolution of a nonstationary state is governed by a nonnegative function W(E), having the dimensions of an energy. Among its properties are: the energy uncertainty is given by $\text{(ΔH)}{}^2\text{= ?W(E)dE}$, and the inverse lifetime by Γ = 2πW(E₀), where E₀ is the expectation value of H. The detailed shape of W(E) defines two characteristic times between which the exponential decay law is a good approximation: roughly speaking, the smoother W(E), the larger the domain of validity of the exponential law. For instance, if W(E) is very smooth ($\text{|}\text{dW}\text{dE}\text{| ? 1}$) except for a sharp threshold at E = E_thr, the transition from quadratic to exponential decay occurs for $\text{t ?}\text{1}\text{(E}{}_0\text{? E}{}_{\mathrm{<mtext>thr</mtext>}}\text{)}$, and the transition from exponential to inverse power law when $\text{Γt ?}\text{log}\text{[}\text{(E}{}_0\text{? E}{}_{\mathrm{<mtext>thr</mtext>}}\text{)}\text{Γ}\text{]}$.     

Nonexponential sound decay in concert halls

The paper presents acoustic measurement results for two concert halls in which nonexponential sound decay is observed. Quantitative estimates are given for how the obtained decay laws differ from exponential. Problems are discussed that arise when using reverberation time to assess the quality of room acoustics with nonexponential sound decay.     

Nonexponential decay of spin polarization in rubidium vapor

Experimental data on the decay of spin polarization in rubidium vapor are compared with inferences of the theory developed by the authors for spin-polarized Boltzmann gases. It is demonstrated that the nonexponential pattern of polarization decay points to the anisotropy of the indicatrix of inelastic scattering of rubidium atoms at high temperatures. Estimates are obtained of the degree of anisotropy of such inelastic scattering, i.e., scattering with variation of total spin. Under the experimental conditions, the indicatrix of inelastic scattering turns out to be highly extended forward, with the degree of anisotropy of the order of 1000.     

Nonexponential decay in the quantum dynamics of nanosystems

The quantum dynamical problem is solved for a system coupled to an equidistant-spectrum bath with the energy difference Ω between the neighboring levels n and n + 1 and the coupling matrix elements C _n ² = C ²(1 + Δ^?2 n ²)^?1 constraining the energy interval comprising the bath states interacting with the system. The evolution in the strong-coupling limit is determined by two parameters, Γ = πC ²/Ω ? 1 and α = Γ/Δ. If α ≠ 0, then the decrease in the population in the initial cycle with a period of 2π/Ω is not exponential and the effective rate constant increases with time. The results qualitatively explain the appearance of nonexponential relaxation regimes for a dense-spectrum nanosystem and predict the possibility of the multiple recovery of the initial-state population.     

Nonexponential relaxation of the methyl group in 3-methyl-2,4,10-trioxa-adamantan

During the nonexponential relaxation of a methyl group both magnetization components M_A and M_B can be observed. From these, correlation times characterizing the motion of the molecule in solution have been derived and related to the microscopic viscosity.     

Nonexponential decay via tunneling in tight-binding lattices and the optical zeno effect

An exactly-solvable model for the decay of a metastable state coupled to a semi-infinite, tight-binding lattice, showing large deviations from exponential decay in the strong coupling regime, is presented. An optical realization of the lattice model, based on discrete diffraction in a semi-infinite array of tunneling-coupled optical waveguides, is proposed to test nonexponential decay and for the observation of an optical analog of the quantum Zeno effect.     

Nonexponential nuclear spin-lattice relaxation in the isotropic phase of thermotropic liquid crystals

In the isotropic phase of nematic and smectic liquid crystals T₁ of CH3 and chain protons is larger than that of ring and ring-neighboured protons being caused by fast CH₃ reorientation and internal motions in chains, respectively.     

Spectroscopic observation of relaxation phenomena

A new technique is described, that allows the direct observation of relaxation processes. The technique consists in monitoring the intensity of selected bands in the Raman spectra, in a synchronized way with respect to an external perturbing field. The reliability of the technique is tested in the case of the monomer-dimer reaction in acetic acid.     

Nonexponential <Superscript>125m</Superscript>Te radioactive decay

Nonexponential decay of isomeric ^125mTe nuclei having intermediate Mössbauer levels and surrounded by their own decay products is observed and studied. A collective decay model is suggested for the nuclear systems of this type.     

Dielectric relaxation phenomena in lead titanate crystals

Relaxation properties of crystalline lead titanate are interpreted in terms of Maxwell-Wagner polarization.     

Analysis of relaxation phenomena in heavy-ion collisions

The transfer of mass, as well as the dissipation of relative kinetic energy and relative angular momentum in deeply inelastic heavy-ion collisions are studied as functions of time. Based on the determination of a parametrized deflection function from the experimental angular distributions, a classical model for the calculation of the mean interaction time as a function of initial relative angular momentum is presented. The method allows to include also those processes which correspond to long interaction times. The model is applied to determine mass transport coefficients from experimental mass (or element) distributions. The resulting mass drift and diffusion coefficients are accurate within less than 30% and compare well with the systematics obtained from the microscopic transport theory. The energy loss as function of interaction time is consistent with the following picture: Fast dissipation of the radial part of the kinetic energy accompanied by the loss of angular momentum with a larger relaxation time.     

On relaxation phenomena in filamentary NaCl crystals

The internal friction and reversible creep of filamentary sodium chloride crystals are investigated. An internal friction peak, associated with the reorientation of the impurity-vacancy complexes in an elastic field is detected. The activation energy of the process is determined. The correlation between the internal friction level and the size of the filamentary crystal, as well as its electric charge, are established. The relaxation time of the reversible creep of filamentary crystals in a 10 kV/cm electrical field is estimated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 101–104, April, 1973.     

Magnetic relaxation phenomena in a CuMn spin glass

Experiments on the temperature and time dependence of the response function and the field cooled magnetisation of a Cu(Mn) spin glass at temperatures below the zero field spin glass temperature are used to explore the non-equilibrium nature of the underlying spin configuration. The results imply that a certain spin configuration is imprinted on the system as the temperature is decreased at a constant cooling rate. The cooling rate governs the magnitude of the FC magnetisation ((H,T)). Any intermittent halt at a constant temperature, , imprints an extended spin configuration, a process that is reflected e.g. in a downward relaxation of . On continued cooling at the same rate, the magnitude of (T) remains at a lower level than that of a continuous cooling curve. These results are put into the context of the corresponding behaviour of the response function as observed in measurements of the relaxation of the zero field cooled magnetisation. Received 27 October 1998 and Received in final form 30 November 1998     

A quasi particle approach to relaxation phenomena

An evolution equation for the relaxation of a nucleus in a metal is derived, assuming that the electronic thermostat is the vacuum of quasi-particles. The relaxation originates in the successive creations of quasi-boson excitations of the electronic system.The author's interest in this subject was aroused through a collaboration with Prof. I. Berkes. He wishes to thank him. It is pleasure to thank also Prof. R. Coussement and Dr. P. Put for many helpfull discussions and for their hospitality at the I.K.S. Leuven.     

Mixing,ergodicity and slow relaxation phenomena

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation–dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.     

Muon spin relaxation measurements of spin-correlation decay in spin-glassAgMn

The field (H) dependence of the muon longitudinal spin-lattice relaxation rate well below the spin glass temperature inAgMn is found to obey an algebraic form given by (H) ^v –1 withv=0.54±0.05. This suggests that Mn spin correlations decay with time ast ^–v , in agreement with mean field theories of spin-glass dynamics which yieldv0.5. Near the glass temperature the agreement between the data and theory is not as good.We are grateful to C.E. Olsen for preparing the samples, C. Boekema, S.A. Dodds, G.A. Gist, R.L. Hutson, S.L. Rudaz and A. Yaouanc for help during the experiments and to D.L. Huber and R.E. Walstedt for useful discussions. This work was performed under the auspices of the U.S. Department of Energy and was also supported by the U.S. National Science Foundation, Grant No. DMR-8115543.