Linear systems with adiabatic fluctuations

We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of fluctuations and 1/|\mu| refers to the time scale of evolution of the unperturbed system to obtain a linear differential equation for the average solution. The theory is applied to the problems of a damped harmonic oscillator and diffusion in a turbulent fluid. The result is the realization of `renormalized' diffusion constant or damping constant for the respective problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page

Universal magnetic and structural behaviors in the iron arsenides

Commonalities among the order parameters of the ubiquitous antiferromagnetism present in the parent compounds of the iron arsenide high temperature superconductors are explored. Additionally, comparison is made between the well established two-dimensional Heisenberg-Ising magnet, K$_2$NiF$_4$ and iron arsenide systems residing at a critical point whose structural and magnetic phase transitions coincide. In particular, analysis is presented regarding two distinct classes of phase transition behavior reflected in the development of antiferromagnetic and structural order in the three main classes of iron arsenide superconductors. Two distinct universality classes are mirrored in their magnetic phase transitions which empirically are determined by the proximity of the coupled structural and magnetic phase transitions in these materials.Comment: 6 pages, 4 figure

Theory of Adiabatic fluctuations : third-order noise

We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$, where $\alpha$ is the strength of fluctuations and $|\mu|$ is the damping rate. We show that probability distribution functions obey the differential equations of motion which contain third order terms (beyond the usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of adiabatic fluctuations in velocity space which is the counterpart of Brownian motion for fast fluctuations, has been solved exactly. The characteristic function and the associated probability distribution function are shown to be of stable form. The linear dissipation leads to a steady state which is stable and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.

Antiferromagnetic Critical Fluctuations in BaFe2_2As2_2

Magnetic correlations near the magneto-structural phase transition in the bilayer iron pnictide parent compound, BaFe$_2$As$_2$, are measured. In close proximity to the antiferromagnetic phase transition in BaFe$_2$As$_2$, a crossover to three dimensional critical behavior is anticipated and has been preliminarily observed. Here we report complementary measurements of two-dimensional magnetic fluctuations over a broad temperature range about T$_N$. The potential role of two-dimensional critical fluctuations in the magnetic phase behavior of BaFe$_2$As$_2$ and their evolution near the anticipated crossover to three dimensional critical behavior and long-range order are discussed.Comment: 6 pages, 4 figures; Accepted for publication in Physical Review

Heat capacity study of BaFe2_{2}As2_{2}: effects of annealing

Heat-capacity, X-ray diffraction, and resistivity measurements on a high-quality BaFe$_{2}$As$_{2}$ sample show an evolution of the magneto-structural transition with successive annealing periods. After a 30-day anneal the resistivity in the (ab) plane decreases by more than an order of magnitude, to 12 $\mu\Omega$cm, with a residual resistance ratio $\sim$36; the heat-capacity anomaly at the transition sharpens, to an overall width of less than K, and shifts from 135.4 to 140.2 K. The heat-capacity anomaly in both the as-grown sample and after the 30-day anneal shows a hysteresis of $\sim$0.15 K, and is unchanged in a magnetic field $\mu_{0}$H = 14 T. The X-ray and heat-capacity data combined suggest that there is a first order jump in the structural order parameter. The entropy of the transition is reported

The nature of the magnetic and structural phase transitions in BaFe2_{2}As2_{2}

We present the results of an investigation of both the magnetic and structural phase transitions in a high quality single crystalline sample of the undoped, iron pnictide compound BaFe$_2$As$_2$. Both phase transitions are characterized via neutron diffraction measurements which reveal simultaneous, continuous magnetic and structural orderings with no evidence of hysteresis, consistent with a single second order phase transition. The onset of long-range antiferromagnetic order can be described by a simple power law dependence $\phi(T)^2\propto(1-\frac{T}{T_N})^{2\beta}$ with $\beta=0.103\pm0.018$; a value near the $\beta=0.125$ expected for a two-dimensional Ising system. Biquadratic coupling between the structural and magnetic order parameters is also inferred along with evidence of three-dimensional critical scattering in this system.Comment: New figure and discussion added. Length: 11 pages, 7 figure

Gradient and Amplitude Scattering in Surface-Corrugated Waveguides

We investigate the interplay between amplitude and square-gradient scattering from the rough surfaces in multi-mode waveguides (conducting quantum wires). The main result is that for any (even small in height) roughness the square-gradient terms in the expression for the wave scattering length (electron mean free path) are dominant, provided the correlation length of the surface disorder is small enough. This important effect is missed in existing studies of the surface scattering.Comment: 4 pages, one figur

Manifestation of the Roughness-Square-Gradient Scattering in Surface-Corrugated Waveguides

We study a new mechanism of wave/electron scattering in multi-mode surface-corrugated waveguides/wires. This mechanism is due to specific square-gradient terms in an effective Hamiltonian describing the surface scattering, that were neglected in all previous studies. With a careful analysis of the role of roughness slopes in a surface profile, we show that these terms strongly contribute to the expression for the inverse attenuation length (mean free path), provided the correlation length of corrugations is relatively small. The analytical results are illustrated by numerical data.Comment: 13 pages, 3 figure