Long-range order in smectic liquid crystals

1978 ◽  
Vol 21 (8) ◽  
pp. 1005-1008
Author(s):  
�. V. Gevorkyan
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Range Order ◽  
Smectic Liquid Crystals ◽  
Long Range Order

scholarly journals Nonlinear Optical Phenomena in a Silicon-Smectic A Liquid Crystal (SALC) Waveguide

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2086 ◽  
Author(s):  
Boris I. Lembrikov ◽  
David Ianetz ◽  
Yosef Ben-Ezra
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Nonlinear Optical ◽  
Optical Nonlinearity ◽  
Range Order ◽  
Smectic Layer ◽  
Long Range Order ◽  
Smectic A ◽  
Optical Phenomena ◽  
Nonlinear Optical Phenomena

Liquid crystals (LCs) are organic materials characterized by the intermediate properties between those of an isotropic liquid and a crystal with a long range order. The LCs possess strong anisotropy of their optical and electro-optical properties. In particular, LCs possess strong optical nonlinearity. LCs are compatible with silicon-based technologies. Due to these unique properties, LCs are promising candidates for the development of novel integrated devices for telecommunications and sensing. Nematic liquid crystals (NLCs) are mostly used and studied. Smectic A liquid crystals (SALCs) have a higher degree of long range order forming a layered structure. As a result, they have lower scattering losses, specific mechanisms of optical nonlinearity related to the smectic layer displacement without the mass density change, and they can be used in nonlinear optical applications. We theoretically studied the nonlinear optical phenomena in a silicon-SALC waveguide. We have shown theoretically that the stimulated light scattering (SLS) and cross-phase modulation (XPM) caused by SALC nonlinearity can occur in the silicon-SALC waveguide. We evaluated the smectic layer displacement, the SALC hydrodynamic velocity, and the slowly varying amplitudes (SVAs) of the interfering optical waves.

scholarly journals QUASI-LONG RANGE ORDER IN GLASS STATES OF IMPURE LIQUID CRYSTALS, MAGNETS, AND SUPERCONDUCTORS

2001 ◽  
Vol 15 (22) ◽  
pp. 2945-2976 ◽  
Author(s):  
D. E. FELDMAN
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Disordered Systems ◽  
Critical Dimension ◽  
Range Order ◽  
Long Range Order ◽  
Weak Disorder ◽  
Random Anisotropy ◽  
Ordered Phases ◽  
Amorphous Magnets

We consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder destroys long range order in the O(N) model. We demonstrate that at weak disorder and low temperatures quasi-long range order emerges. In quasi-long-range-ordered phases the correlation length is infinite and correlation functions obey power dependencies on the distance. In pure systems quasi-long range order is possible only in the lower critical dimension and only in the case of Abelian symmetry. In the presence of disorder this type of ordering turns out to be more common. It exists in a range of dimensions and is not prohibited by non-Abelian symmetries.

Quasi-long-range order in columnar liquid crystals

1996 ◽  
Vol 54 (5) ◽  
pp. R4544-R4547 ◽  
Author(s):  
Alain Caillé ◽  
Matthieu Hébert
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Range Order ◽  
Long Range Order

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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