Constant Order Parameter Research Articles

The Density of States for Fermi Superfluids with Layered Structures in the Order Parameter: With Application to a Solution 3He in 4He at Low Temperatures

The density of states of Fermionic excitations in s-wave Fermi superfluids is calculated. The order parameter is assumed to have a layered structure with a variation along only a single direction and the Fermions are allowed to move over the full three-dimensional space. The density of states for such a system is calculated using the Bogoliubov Hamiltonian in which the quadratic momentum dependence of the kinetic energy is approximated by a linear dependence. A representation of the density of states in terms of a Fredholm determinant is derived. For the case of a piecewise constant order parameter, the Fredholm determinant is calculated exactly. Explicit results for the density of states are presented for an order parameter with a periodic variation along a single direction.

Recent advances in nematic and smectic A anchoring on amorphous solid surfaces [1

Abstract New anchoring properties of liquid crystals on amorphous solid surfaces are presented. In nematics (N), angular anchoring is usually described in terms of the Rapini-Papoular form, assuming constant surface order parameter. We generalize this expression, predicting a decrease of surface order for strong surface disorientation. Recent experiments on anchorings of varying strength confirm these predictions. Conjectures for the angular anchoring of smectic A on a solid amorphous surface explain the two easy layer orientations, normal to the surface or parallel, faceting inside a small critical angle. Roughness-induced surface transitions are discussed. For antagonistic nematic and smectic anchorings, we expect, below the N–SA transition, a bent nematic surface boundary layer, recently observed by smectization under an electric field. Finally, the positional anchoring strength of smectics is introduced in terms of shear induced surface melting, and confirmed by a recent observation of oscillating she...

Structures of the cholesteric liquid crystal droplets with parallel surface anchoring

Abstract Model structures of cholesteric liquid crystal droplets embedded in a medium which enforces parallel surface anchoring are treated. Structures with disclination lines of integer and half-integer strength are obtained by minimising the Frank free energy. The constant order parameter approximation appropriate for droplets which are large compared to the cores of defects and the approximate ansatz with the molecular director everywhere tangential to the concentric spherical surfaces are used. Within this approach the structure with a diametrical disclination line is the most stable. Its free energy is compared to that of the non-twisted bipolar structure and to that of the two twisted structures. The well-known structure with a radial disclination line and that with a double radial disclination line not found in the known literature are presented. It is shown that surface free energy terms, usually omitted in the minimization, do not influence substantially the stability of the structures discussed....

Doping disorder and level structures in conjugated polymers

Electronic states in conducting polymers containing impurities are analyzed. Assuming an ideal random distribution of the impurities, we use the coherent potential approximation to study the influence of backward- and forward-scattering (bond and site) impurities in the TLM model. The electronic states are half-filled and a uniform dimerization is represented by a constant order parameter. The order parameter, electronic level structure, and density of states are obtained as functions of the impurity concentration and strengths of impurity potentials. At low concentrations, the formation of impurity bands in the gap is suppressed if the strength of the bond-impurity is larger than that of the site-impurity, because of the one-dimensional nature of the system where the scattering processes on the Fermi surface are limited. When the site-impurity is stronger, an isolated impurity band arises. It broadens, as the concentration increases, and is finally absorbed by either the valence or the conduction band, thereby reducing the magnitude of the gap. At higher impurity concentrations, the order parameter and the gap vanish when the site-impurity is strong enough. Phase diagrams are extensively given, the concentration and the two impurity strengths being used as variables. They give boundaries among five phases, each of which is characterized by the number of impurity bands and the order parameter. Consequences for the interpretation of experiments are discussed.

Nematic-isotropic transition in some lattice models for rigid cores having semiflexible tails: Segmental Lennard-Jones interactions

Two average-environment simple cubic lattice models---a refined model and a simple model, both having site-site (segmental) pair Lennard-Jones (LJ) interactions---for molecules composed of rigid cores having semiflexible tails are presented. The calculated values of the following properties at the nematic-isotropic transition for rigid rods of varying length are compared with relevant experimental data for PAA ($p$-azoxyanisole, or 4,4\ensuremath{'}-dimethoxyazoxybenzene): temperature, core orientational order parameter, nematic density and volume, relative density change, and relative entropy change. The temperature change as a function of volume change at constant order parameter is also discussed. In general, both LJ models give considerably better quantitative agreement with experiment, especially for the temperature and the relative density change, than do the earlier lattice models with hard repulsions, with or without constant segmental pair interaction energies. In most aspects, these LJ models give good quantitative agreement with experiment. These LJ models elucidate the importance of realistic intermolecular potentials, especially the role of soft repulsions, in describing an order-disorder transition between two condensed phases.

Molecular motions in lipid bilayers. II. Magnetic resonance of multilamellar and vesicle systems

The chain motion model developed in part I is shown to be consistent with a range of NMR data on Lα phase lipid multilayers and vesicles. A simple treatment of correlation effects within the intramolecular (crankshaft) rotations in the weak collision limit leads to a realistic T1 profile along the acyl chain, despite the assumption of a constant order parameter profile. The observed dependence of T1 on chain length is not reproduced however. The measured activation energy (∼13 kJ/mol) for T1 relaxation is consistent with the model, as are the ’’anomalously’’ low T1 and C–D order parameters observed on the methene groups in monounsaturated chains. A very small angular dependence for the 2H methylene T1 at high frequency (≳50 MHz) is suggested. This accords with observation and is a direct consequence of the crankshaft geometry. At temperatures sufficiently above Tm, the nematic fluctuation model of part I semiquantitatively predicts the components of multilayer T1 and T1ρ relaxation rates linear in ω−1/2. However, the description fails for ω∼108 and T∼Tm, in a manner possibly indicating nonrigid chain axis fluctuation on this time scale. A two-dimensional formulation of the nematic model provides a simple description of small vesicle 1H and 2H NMR linewidths, consistent with the experimental data.

Anderson localization, branched polymers and the Yang-Lee edge singularity

We show that a recently proposed field-theoretic model of Anderson localization has the same critical behaviour as that found in the problem of branched polymers. Thus this model in D dimensions is in the same universality class as that studied by Parisi and Sourlas, which includes the Yang-Lee edge singularity in D — 2 dimensions. We stress that critical properties can be studied either at constant order parameter or at constant field and that critical exponents in the two cases are related by a Fisher renormalization. We note that constant order parameter exponents diverge at a critical dimension Dc.

Interpretation of Thermodynamic Derivatives Near the Liquid Crystal Phase Transition inp-Azoxyanisole

Abstract A general theory of phase transitions described by a sigle order parameter is applied to the nematic liquid crystal PAA. From previously published results on expansivity, sound velocity, and specific heat, it is shown for the nematic-isotropic phase transition in this substance (a) the coexistence curve is a curve of constant order parameter, and (b) the order parameter slightly below the transition is a function of V 4.3 T, where V is volume and T is temperature.

Thermodynamic Fluctuations of the Order Parameter in Type-II Superconductors near the Upper Critical FieldHc2

Abstract : An investigation was made of the mean square deviation of the order parameter from its equilibrium for Type II Superconductors, assuming that the Gibbs free energy is given by a Ginzburg-Landau type functional. It turns out, that the equilibrium function, which is already varying with position because of the penetrating magnetic flux, resists distortion much less than the constant order parameter in type I superconductors. Therefore, the mean square deviation becomes equal in magnitude to the square of the equilibrium order parameter in the magnetic field range ((H sub c2)-B)/(H sub c2) approx. < 0.0001 to 0.00001. This means, that the range of magnetic fields, in which Ginzburg-Landau type descriptions should fail and a singular behavior might show up seems not entirely out of reach of present experimental techniques in contrast to the situation in type I superconductors. (Author)

Flux Penetration in Cylindrical Superconducting Films. I. Spatially Constant Order Parameter

We calculate the effective penetration depth ${\ensuremath{\lambda}}_{\mathrm{eff}}$ in thin cylindrical films [$dl\ensuremath{\xi}(T)$, $\ensuremath{\Lambda}(T)$ where $\ensuremath{\xi}(T)$ and $\ensuremath{\Lambda}(T)$ are, respectively, the temperature-dependent coherence length and zero-field penetration depth and $d$ is the film thickness] for rf fields while the film is in an axial static field $H$ close to the tangential critical field ${H}_{\ensuremath{\parallel}}$ for a second-order phase transition. We find ${\ensuremath{\lambda}}_{\mathrm{eff}}\ensuremath{\approx}[\frac{{\ensuremath{\Lambda}}^{2}(T)}{d}][\frac{H_{\ensuremath{\parallel}}^{}{}_{}{}^{2}}{(H_{\ensuremath{\parallel}}^{}{}_{}{}^{2}\ensuremath{-}{H}^{2})}]$. In addition, we show that one may expect sizeable harmonic generation for static fields close to ${H}_{\ensuremath{\parallel}}$ and for sufficiently thin films.