Vacancy noise measurements in metals: Calculation of the power spectrum

Fluctuations in the number of vacancies in metals in thermal equilibrium lead to resistivity fluctuations. Analysis of these fluctuations permits measurement of both formation and migration enthalpy of the vacancies. The power spectrum of the fluctuations is calculated using a series of statistically independent pulses. It can be derived from the diffusion equation for any geometry of the vacancy sinks. Vacancy diffusion to the surface of a thin plate or of a sphere are treated as examples. The measurability of vacancy noise is assessed. It should also be possible to measure vacancy noise during irradiation. It is predicted that correlated vacancy creation, which may occur during irradiation, will cause an increase in the power spectrum.     

Spin fluctuations in metals: Application to the actinides

We present here a review of the spin fluctuation theory and of its applications to transition and actinide systems, with a particular emphasis to the latter where some very anomalous properties find an explanation in terms of spin fluctuation effects. Firstly, we summarize the development of the spin fluctuation model which had been initially applied to transition metals and alloys such as palladium or Pd–Ni alloys. Then, we present the extension of the paramagnon model to nearly magnetic actinide systems by taking into account explicitly the temperature dependence of the Stoner susceptibility, because the 5f-band of actinides is much narrower than the d-band of transition metals. As a result the paramagnon contribution to the resistivity departs from the usual T ² and T power laws at temperatures higher than the spin fluctuation one and saturates at high temperatures, with eventually the presence of a maximum at intermediate temperatures. We present also the calculation of the other properties of actinide systems, namely the thermal resistivity, the thermoelectric power, the magnetic susceptibility, the specific heat capacity and the NMR relaxation rate, which are generally enhanced by the presence of paramagnons. Finally, we have introduced the concept of ‘antiferromagnetic-like’ spin fluctuations which have a maximum of the q-dependent susceptibility _χ(q) at a q value different from q =0, in contrast to the regular ferromagnetic spin fluctuations; both types of spin fluctuation give the same resistivity behaviour, while they yield a markedly different behaviour of the magnetic susceptibility, in agreement with experiment. The spin fluctuation theory is applied successfully to the different properties of neptunium and plutonium metals and of many nearly magnetic compounds such as UAl₂.     

Experimental evidence of extreme value statistics in Raman fiber lasers

We present an experiment in which the intracavity broadened spectrum of a Raman fiber laser is sliced by using a narrow-bandwidth optical filter. High-contrast fast fluctuations of the Stokes power are observed at the output of the optical filter. The statistics of the power fluctuations strongly change with the central wavelength of the filter, and rare extreme events are found to be generated in the far wings of the spectrum.     

Dimers on a Simple-Quartic Net with a Vacancy

A seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple-quartic net obtained by Fisher, Kasteleyn, and Temperley (FKT) in 1961. An outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites. Here we consider this vacant-site problem with a single vacancy occurring at certain specific sites on the boundary of a simple-quartic net. First, using a bijection between dimer and spanning tree configurations due to Temperley, Kenyon, Propp, and Wilson, we establish that the dimer generating function is independent of the location of the vacancy, and deduce a closed-form expression for the generating function. We next carry out finite-size analyses of this solution as well as that of the FKT solution. Our analyses lead to a logarithmic correction term in the large-size expansion for the vacancy problem with free boundary conditions. A concrete example exhibiting this difference is given. We also find the central charge c=–2 in the language of conformal field theory for the vacancy problem, as versus the value c=1 when there is no vacancy.     

Scaling of 1/<Emphasis Type="Italic">f</Emphasis> noise in nonequilibrium phase transitions

Investigation of the dynamics of fluctuations of heat and mass transfer reveals that its crisis and transient modes exhibit high-energy pulsations with a power spectrum that is inversely proportional to frequency (flicker or 1/f fluctuations). Such a spectrum suggests energy transfer from high-to low-frequency modes and the possibility of large-scale catastrophic outbursts in the system being considered. The theory shows that such fluctuations arise in the system owing to the simultaneous occurrence of interacting phase transitions in the presence of white noise having a sufficiently high intensity. The distribution of fluctuations for scale transformations of the set of stochastic equations that describe the generation of 1/f noise is investigated. It is shown that, under a scale transformation, the Gaussian distribution of a random process having a 1/f spectrum passes to an exponential distribution, which is characteristic of the statistics of extreme outbursts. The probability of such outbursts must be taken into account in predicting the stability of various heat-transfer modes.     

Tunneling resistivity of a one-dimensional random lattice and the petersburg problem

The resistivity of a one-dimensional lattice consisting of randomly distributed conducting and insulating sites is considered. Tunneling resistance of the form ₀ ne ^bn is assumed for a cluster ofn adjacent insulating sites. In the thermodynamic limit, the mean resistance per site diverges at the critical filling fractionp _c =e^–b, while the mean square resistivity fluctuations diverge at the lower filling fraction =p _c ² . Computer simulations of large but finite systems, however, show only a very weak divergence of resistivity atp _c and no divergence of the fluctuations at . For finite lattices, calculation of the resistivity at the critical filling is shown to be simply related to the Petersburg problem. Analytic expressions for the resistivity and resistivity fluctuations are obtained in agreement with the results of computer simulations.     

Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy

In this paper we compute the leading correction to the bipartite entanglement entropy at large sub-system size, in integrable quantum field theories with diagonal scattering matrices. We find a remarkably universal result, depending only on the particle spectrum of the theory and not on the details of the scattering matrix. We employ the “replica trick” whereby the entropy is obtained as the derivative with respect to n of the trace of the nth power of the reduced density matrix of the sub-system, evaluated at n=1. The main novelty of our work is the introduction of a particular type of twist fields in quantum field theory that are naturally related to branch points in an n-sheeted Riemann surface. Their two-point function directly gives the scaling limit of the trace of the nth power of the reduced density matrix. Taking advantage of integrability, we use the expansion of this two-point function in terms of form factors of the twist fields, in order to evaluate it at large distances in the two-particle approximation. Although this is a well-known technique, the new geometry of the problem implies a modification of the form factor equations satisfied by standard local fields of integrable quantum field theory. We derive the new form factor equations and provide solutions, which we specialize both to the Ising and sinh-Gordon models.     

Chemical analysis using coincidence Doppler broadening and supporting first-principles theory: Applications to vacancy defects in compound semiconductors

The Doppler broadening of the positron annihilation radiation contains information on the chemical environment of vacancy defects trapping positrons in solids. The measured signal can, for instance, reveal impurity atoms situated next to vacancies. As compared to integrated quantities such as the positron annihilation rate or the annihilation line shape parameters, the full Doppler spectrum measured in the coincidence mode contains much more useful information for defect identification. This information, however, is indirect and complementary understanding is needed to fully interpret the results. First-principles calculations are a valuable tool in the analysis of measured spectra. One can construct an atomic-scale model for a given candidate defect, calculate from first principles the corresponding Doppler spectrum, and directly compare results between experiment and theory. In this paper we discuss recent examples of successful combinations of coincidence Doppler broadening measurements and supporting first-principles calculations. These demonstrate the predictive power of state-of-the-art calculations and the usefulness of such an approach in the chemical analysis of vacancy defects.     

Negative power spectra in quantum field theory

We consider the spatial power spectra associated with fluctuations of quadratic operators in field theory, such as quantum stress tensor components. We show that the power spectrum can be negative, in contrast to most fluctuation phenomena where the Wiener-Khinchin theorem requires a positive power spectrum. We show why the usual argument for positivity fails in this case, and discuss the physical interpretation of negative power spectra. Possible applications to cosmology are discussed.     

Thermal noise as a spectroscopic tool to determine transport properties

The utilization of thermal fluctuations or Johnson/Nyquist noise as a spectroscopic method to determine transport properties in conductors or semiconductors is developed. The autocorrelation function is obtained from power spectral density measurements thus enabling electronic transport property calculation through the Green–Kubo formalism. This experimental approach is distinct from traditional numerical methods such as molecular dynamics simulations, which have been used to extract the autocorrelation function and directly related physics only. This work reports multi-transport property measurements consisting of the electronic relaxation time, resistivity, mobility, diffusion coefficient, electronic contribution to thermal conductivity and Lorenz number from experimental data. Double validation of the experiment was accomplished through the use of a standard reference material and a standard measurement method, i.e. four-probe collinear resistivity technique. Thermal noise measurements resulted in a 1.1 and 5% agreement with the reference material and four-probe values, respectively. Additional measurements were also taken on nanoscale Au and Cu thin films. Specifically, the validated spectroscopic methodology was applied to 30 nm Au and Cu thin films to obtain transport property data that was again compared to four-probe resistivity measurements. Comparative analysis of the resistivity data showed agreement within 13.6 and 4.8% for the Au and Cu samples, respectively, thus lending further credibility to the experimental method and theory.     

The influence of the dynamics of ionic multiplets onto electronic transport properties of heavy-fermion systems: a semi-phenomenological approach

We present calculations of the electronic transport properties of heavy-fermion systems within a semi-phenomenological approach to the dynamical mean field theory. In this approach the dynamics of the Hund's rules 4f (5f )-ionic multiplet split in a crystalline environment is taken into account. Within the scope of this calculation we use the linear response theory to reproduce qualitative features of the temperature-dependent resistivity and hall conductivity, the magneto-resistivity and the thermoelectric power typical for heavy-fermion systems. The model calculations are directly compared with experimental results on CeCu ₂ Si ₂. Received 30 June 2000 and Received in final form 15 December 2000     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

The unambiguous identification of vacancy migration stage in resistivity recovery of irradiated metals based on trapping of vacancies at probe impurity atoms

The method of resistivity recovery is a powerful tool for studying point defects in irradiated metals. However, the method is nonspecific with respect to a type (vacancy or interstitial) of investigated defects. To overcome this shortcoming, we made use of opposite signs of excess electric charges of the vacancies and self-interstitial atoms in a lattice. Resistivity loss takes place on trapping of vacancies at impurity atoms if excess charges of the impurity atom and defect are opposite in sign. A way of selecting the impurity atoms with the excess charge opposite in sign to that of vacancies is proposed. The specific evolution of resistivity recovery spectrum induced by vacancy trapping at the selected impurity atoms (probe traps) allows one to unambiguously identify the stage of free long-range vacancy migration.     

Physical properties of titanates,semiconductors and nickelates derived from ionization energy theory

Ionization energy theory is exploited to predict the changes to atomic polarizability for both anions and cations, the polarization in doped titanates and the energy gap in III–V and II–VI semiconductors. We then extend the above analysis to discuss the physics of metallic and superconducting phases in the recently discovered superconducting nickelates. In doing so, we are able to prove the existence of Ni²⁺ cations and oxygen vacancy in the metallic normal state of nickelates. We find that the normal state resistivity of the nickelates follows exactly as predicted by the ionization energy theory. Quantitative estimates are also given for the concentrations of Ni²⁺ and oxygen vacancy in superconducting nickelates.     

Theoretical derivation of 1/f noise in quantum chaos

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the 1/f (1/f(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.     

Origin of laser-output noise of cataphoretic HeSe+ lasers

We investigated noise and fluctuations of the output power of cataphoretic HeSe⁺ lasers in positive column plasma. Direct coupling of laser output power noise and fluctuations of the local population inversion was found. An investigation of the positive column plasma showed moving striations being responsible for the gain fluctuations. Whereas the local plasma properties are dominated by high frequency striations in the 100 kHz range, integrated quantities such as laser gain per pass are most strongly influenced by low-frequency waves with a continuous noise spectrum below 200 kHz. External modulation of the discharge voltage or current at a frequency near thehf striations reduces laser noise and increases laser output power.     

Fluctuations and viscoelasticity

Viscoelasticity is exhibited by polymers, metals undergoing diffusion creep, etc. The strain is a linear functional of the stress, but there is no unique equilibrium relationship between them. Under a constant stress, the strain does not saturate to an equilibrium value. This divergence is the main difficulty facing a first-principles theory of viscoelasticity, in contrast to anelasticity which has already been understood as a relaxation process in terms of response theory, fluctuations and related concepts. We now present such a theory, based on the recognition that viscoelasticity occurs whenever the spontaneous fluctuations of the strainrate, butnot of the strain, form a stationary random process. We give fundamental formulas for the creep function and the complex compliance, in terms of the spontaneous fluctuations of the strain rate, that apply to both viscoelasticity and anelasticity. A detailed stochastic analysis of the basic viscoelastic network equation corroborates and complements these results. The unphysical instantaneous response of the network is eliminated, and the network parameters are related to internal fluctuations. A certain functional form of the creep function is derived that is common to several physical situations, a few of which are mentioned. Detailed applications will be taken up elsewhere.     

Statistics of low-frequency pulsations in critical regimes of heat mass exchange with phase transitions

Experimental investigation of fluctuation dynamics in critical and transitional modes of heat mass exchange shows existence of irregular high-energy pulsations with power spectrum inversely proportional to the frequency—so called 1/f spectrum. Such regimes are characterized by the fact that an essential part of the pulsations energy is connected with very slow processes and mean that large high-energy bursts are possible in the system. Another characteristic feature of such regimes is scale invariance of the fluctuations distribution function. According to the theory, the 1/f fluctuations can emerge in physical systems due to simultaneous phase transitions in presence of sufficiently intensive white noise. This paper is devoted to detailed investigation of relaxation processes at steadying of stationary stochastic process in non-equilibrium phase transitions in system of two nonlinear stochastic differential equation. Such an information reveals statistical patterns of particular large-scale low-frequency bursts. Discontinuous “forgetting” of the initial conditions takes place. It is shown by numerical methods that distributions of duration and maximal values of the low-frequency extreme bursts have the power-like form. Experimental investigation results of statistical characteristics of fluctuation processes at ultrasonic cavitation and flash boiling of overheated water jets are presented. Results of the experiments carried out fit conclusions of the theoretical model for interacting heterogeneous phase transitions.     

Chaotic diffusion and 1/f-noise of particles in two-dimensional solids

We investigate the classical nonlinear dynamics of a particle moving conservatively in a two-dimensional periodic potential. The particle exhibits diffusive motion in the absence of random forces. In a broad range of energies above the potential barrier, the diffusion process is anomalously accelerated and associated with 1/f-noise in the power spectrum of velocity fluctuations. The analysis of Poincaré surfaces of section and the distribution of free paths indicate that the phenomenon is caused by a trapping of orbits in a self-similar hierarchy of nested cantori. We describe a statistical theory for this mechanism in terms of a renewal process and a random walk on a hierarchical lattice.Work supported by Deutsche Forschungsgemeinschaft