Weak Fluctuation Regime Research Articles

Ginzburg-Landau theory of fluctuation magnetization of two-dimensional superconductors.

Large fluctuation-induced magnetization has been observed recently in the quasi-two-dimensional high-${\mathit{T}}_{\mathit{c}}$ materials. A satisfactory theoretical description of this phenomenon is absent at the moment. We present an extensive study of the fluctuation magnetization ${\mathit{M}}_{1}$ of two-dimensional superconductors within the Ginzburg-Landau theory in different regions of the phase diagram. In the normal state one has to distinguish the regions of weak/Gaussian and strong/critical fluctuations. Different kinds of scaling dependencies for ${\mathit{M}}_{1}$ are predicted for these regions. An important feature of the field dependence of ${\mathit{M}}_{1}$ in the weak-fluctuation regime is saturation of the magnetization at high fields. Taking into account both regular and critical contributions to ${\mathit{M}}_{1}$ we obtain an expression that is valid in both regions. In the mixed state at high fields the fluctuation magnetization is completely determined by the thermal elastic fluctuations in the lattice state. Due to suppression of the elastic modulii, ${\mathit{M}}_{1}$ increases mainly as 1/(${\mathit{H}}_{\mathit{c}2}$-B) as the field approaches the critical region near the upper critical field ${\mathit{H}}_{\mathit{c}2}$. At small fields, B\ensuremath{\ll}${\mathit{H}}_{\mathit{c}2}$, there are two independent contributions to ${\mathit{M}}_{1}$ which can be treated separately. One comes from the Gaussian excitations in the vortex cores and the other from the thermal motion of the vortices. We demonstrate that the vortex system in this limit is equivalent to the model of the one-component two-dimensional Coulomb plasma. Using Monte Carlo results for this model, we estimate ${\mathit{M}}_{1}$ in the vortex-lattice as well as in the vortex-liquid state.

Asymptotic analysis of finite-beam scintillations in a turbulent medium

Abstract Asymptotic analysis of on-axis intensity fluctuation variance of a finite-sized light beam is performed starting from the functional integral representation for the field in a random medium. Collimated, diverging and converging beams with different diffraction properties are considered. A complete set of asymptotes is obtained using the main and additional coherence channels approach to the fourth moment of field analyses. We study the conditions of weak and strong fluctuation regimes for all these types of beams and obtain relatively simple formulae for on-axis intensity variance, which are valid for the case of stratified turbulence. It is shown that scintillations in the vicinity of the beam focus are governed by double-scattering processes for weak scintillations and double scattering from coherence channels for strong fluctuations.

Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence

A generalized Huygens–Fresnel integral, valid for optical wave propagation through random inhomogeneities in the presence of any complex optical system characterized by an ABCD ray matrix, is used to derive a general expression for the mutual coherence function (MCF) associated with a Gaussian-beam wave in the weak-fluctuation regime. The mean irradiance obtained from this expression shows excellent agreement with all known asymptotic relations. By introducing a pair of effective beam parameters Θt and Λt that account for additional diffraction on the receiving aperture, resulting from turbulence, the normalized MCF and the related degree of coherence are formally extended into the regime of strong fluctuations. Results for the normalized MCF from this heuristic approach compare well with numerical calculations obtained directly from the formal solution of the parabolic equation. Also, the implied spatial coherence length from this analysis in moderate-to-strong-fluctuation regimes generally agrees more closely with numerical solutions of the parabolic equation than do previous approximate solutions. All calculations are based on the modified von Karman spectrum for direct comparison with established results.

Macroscopic shape of critical droplets in first-order wetting transitions

In a first-order wetting transition the decay of a metastable non-wet state occurs by nucleation and growth of supercritical droplets on the wall of the system. Based on an effective interface model for the wetting fluid the shape of the critical droplet is calculated outside a microscopic region near the wall for a class of long-range interface potentials. The solution has a surprisingly simple form if the dimension of the system coincides with the boundary dimension between the so-called strong and weak fluctuation regimes.

Fluctuations, correlation functions and interfacial Hamiltonians for the complete wetting phase transition

Exact statistical mechanical sum rules are combined with thermodynamic scaling arguments to determine the leading-order singular contributions to the transverse moments of the density-density correlation function G of a simple fluid undergoing a complete wetting phase transition, from off-bulk coexistence, at a structureless substrate (wall). Contrary to our earlier suggestion, capillary-wave-like fluctuations do manifest themselves throughout the wetting film and lead to a transverse correlation length ξ‖(a), for both particles near the wall, which diverges with the same critical exponent as ξ‖, the correlation length appropriate for both particles in the depinning liquid-gas interface. Explicit results from a mean-field (density functional) calculation are consistent with our general predictions. In the weak fluctuation regime (d < 3), scaling methods are used to derive the short distance expansions of the density profile and moments of G for short ranged forces. These expansions, which describe singula...

A universal parameterization of finite-size effects for interfaces in two dimensions, conformal mappings and local scale invariance

The author shows that all equilibrium statistical properties of an interface confined in a strip geometry, with arbitrary aspect ratio, exactly at a second-order, fluctuation dominated, interfacial unbinding (wetting) transition are determined by a single number q for interfacial binding potentials that are conformally mapped from the semi-infinite plane. The parameter q distinguishes the fluctuation regimes describing the wetting transition and can be directly related to wetting critical exponents. In the strong-fluctuation regime one finds q=0 whilst in the weak-fluctuation regime q=1. The values of q at all intermediate-fluctuation scaling regimes are also determined. He shows that the eigenstates of the transfer differential operator for conformally mapped marginal long-ranged potentials are the simplest possible generalization of the eigenstates corresponding to systems with short-ranged forces. He speculates that the universal parametrization of the finite-size effects at fluctuation dominated wetting transitions is a consequence of local scale invariance.

Universal fluctuation-induced corrections to the Kelvin equation for capillary condensation

Interfacial fluctuations in complete wetting films give rise to important corrections to the macroscopic Kelvin equation for the location of the shifted first-order (condensation) transition that occurs when a fluid (or an Ising magnet) is confined between two parallel adsorbing walls. The wall separation L that enters the usual Kelvin equation must be replaced by L- phi l( mu *), where l is the thickness of the wetting film at the chemical potential mu * at which capillary condensation occurs and phi is an amplitude. For pure systems with short-ranged forces thermal wandering is insufficient to renormalize the simple geometric result phi =2 for bulk dimensions d>or=3. However, in d=2, where fluctuations are much stronger, the authors predict phi =3 throughout the weak fluctuation regime of complete wetting which includes long-ranged dispersion forces as well as short-ranged forces. Their prediction is supported by an explicit analysis of a d=2 interfacial Hamiltonian. This shows that pseudo-phase coexistence, characterized by an exponentially large transverse correlation length, occurs for an exponentially narrow range of mu * determined by the corrected Kelvin equation with phi =3.

Universal and non-universal short-distance expansions in the strong, weak and intermediate fluctuation regimes of critical wetting

The author studies the scaling properties of the density profile rho (z) of a fluid near a wall undergoing a critical wetting transition in the strong-fluctuation and in the weak-fluctuation scaling regimes. A critical exponent theta describing the short-distance algebraic decay of the density profile (for distances z normal to the wall much less than the perpendicular correlation length zeta perpendicular to ) is calculated explicitly in dimension d=2 using an effective interfacial Hamiltonian model. The exponent theta is found to be universal in the strong-fluctuation regime ( theta =1) and in the weak-fluctuation regime ( theta =3). In contrast to the other standard critical exponents theta is non-universal at the weak-fluctuation/mean-field borderline. The author discusses the origin of the universality of theta in the different fluctuation regimes and derives expressions for theta , valid for general d, in terms of known critical exponents.

Adsorption transitions of polymers and crumpled membranes.

Adsorption transitions of polymers and crumpled membranes are studied for general substrate potentials in d-dimensional systems. Several regimes for the critical behavior are identified: (i) a weak-fluctuation regime for sufficiently long-ranged potentials which is well described by an ensemble of independent blobs; (ii) a complex intermediate fluctuation regime with infinite-order, second-order, and anomalous first-order transitions; and (iii) a strong-fluctuation regime for sufficiently short-ranged interactions which is characterized by second-order transitions with universal critical behavior.

Critical wetting in the presence of power-law surface fields.

The mean-field and weak-fluctuation regimes of critical wetting transitions can be understood in the context of a rigorous many-body theory for fluids in the presence of power-law external fields. Exact sum rules are fully consistent with phenomenological knowledge of the significance of capillary-wave fluctuations and the expected scaling behavior of thermodynamic quantities. The general many-body structure is such that explicit results for the scaling functions are readily derived. This discussion is relevant to most experiments on critical wetting in three-dimensional systems.

Irradiance fluctuations of a spherical wave propagating under saturation conditions*

The physical model of strong optical scintillation of plane waves is extended to the case of spherical-wave propagation. The spherical-wave amplitude filter function is derived and compared to the corresponding plane-wave result. Specifically, we calculate the spherical- to plane-wave log-amplitude-variance ratio. For weak fluctuations, our results are identical to the results of perturbation theory, with which the spherical-wave log-amplitude variance is less than the corresponding plane-wave result. On the other hand, for strong fluctuations (i.e., in the saturation regime), the plane- and spherical-wave log-amplitude variances saturate to the same constant value. Expressions are presented, in the saturation regime, for the plane- and spherical-wave log-amplitude covariance function and compared with the corresponding results in the regime of weak fluctuations.