Connected order parameter

The question concerning order in the amorphous state of polymers and oligomers is still a matter of controversy. Through the identification of transition phenomena like the Tn transition and the transitions- within the liquid state, this controversy took on a new dimension. This is evident because the occurrence of a phase transition generally suggests the question about structural changes at the transition and the nature of the connected order parameter(s). The Tn and T transitions seem to be of a different nature. Whereas the former is mainly observed in noncrystallizable polymers, the latter manifests itself mainly in oligomers and polymers which are able to crystallize. But the T transition has also been detected recently in a noncrystallizable side chain liquid crystalline polymer (cf. II1.2).lO... 

FIG. 13 Herringbone order parameter and total energy for N2 (X model with Steele s corrugation). Quantum simulation, full line classical simulation, dotted line quasiharmonic theory, dashed line Feynman-Hibbs simulation, triangles. The lines are linear connections of the data. (Reprinted with permission from Ref. 95, Fig. 4. 1993, American Physical Society.)... 

The standard molar enthalpy change connected with intracrystalline disorder is also a function of ordering parameter... 

Connections to other types of phase diagrams can be obtained if order parameters are exchanged for intensive variables. Figure 17.2 is replotted with the order parameter V as the ordinate in Fig. 17.36. The diagram predicts the phases that would exist for a molar volume fixed by a rigid container at different temperatures. The tie-lines connect equilibrium molar volumes at the same temperature... 

In 1962, B. Josephson recognized the implications of the complex order parameter for the dynamics of the superconductor, and in particular when one considers a system consisting of two bulk conductors connected by a weak link." This research led to tile development of a series of weak link devices commonly called Josephson junctions. See also Josephson Tunnel-Junction. These devices hold much promise for achieving ultra high-speed computers where switching time is of the order of 1CT11 second. 

It is important to emphasize (see Ref. [2]) that the TC in this case differs from the TC realized in the superfluid He3 and, for example, in materials like Sr2RuC>4 [4], The triplet-type superconducting condensate we predict here is symmetric in momentum and therefore is insensitive to non-magnetic impurities. It is odd in frequency and is called sometimes odd superconductivity. This type of the pairing has been proposed by Berezinskii in 1975 [5] as a possible candidate for the mechanism of superfluidity in He3. However, it turned out that another type of pairing was realized in He3 triplet, odd in momentum p (sensitive to ordinary impurities) and even in the Matsubara frequencies w. It is also important to note that while the symmetry of the order parameter A in Refs. [4, 5] differs from that of the BCS order parameter, in our case A is nonzero only in the S layers and is of the BCS type. It is determined by the amplitude of the singlet component. Since the triplet and singlet components are connected which each other, the TC affects A in an indirect way. 

We defined the parameters of our model and made numerical calculations of temperature dependent of two gaps. It is a qualitative agreement with experiments. We proposed a two channel scenario of superconductivity first a conventional channel (intraband gi) whichis is connected with BCS mechanism in different zone and a unconventional channel (interband gi) which describes the tunneling of a Cooper pair between two bands. The tunneling of Cooper pair also stabilizes the order parameters of superconductivity [9-12] and increases the critical temperature of superconductivity. 

Fig. 11 Out of the material parameters connected with the order parameter, only /3 jn — has a measurable effect on the critical values. Some more parameters can influence the amplitudes of the order parameter undulation, namely L and Mo (the latter is only present in the case of the nematic order parameter). All amplitudes have been normalized such that = 1. Note that...

In order to link An to the orientational order parameter 5, one needs to develop a molecular model to connect n, a macroscopic property, to the related molecular property, the polarizability a. One widely used model is that described by Vuks and others, which leads to a quantity Kv(hdX is directly proportional to 5(7) ... 

A spectroscopic technique that probes membrane fluidity can either directly measure mobility and order parameters for membrane constituents (NMR) or use probes (ESR, fluorescence). Some fluorescent and ESR probes are shown in Fig. 4. The connection between the rotational correlation time of a membrane embedded probe and the membrane fluidity can be illustrated using the example of a simple isotropic liquid, in which fluidity is merely a reciprocal viscosity ri and the rotational correlation time Xc for a molecule with a hydrodynamic volume V is given by the well-known Debye-Stokes-Einstein relation Xc = r VlkT, where k is the Boltzmann constant and T is the... 

The photoinduced susceptibility shown in Equation 11.14a is the sum of two terms one with exp(-2Dt) (relaxation of the first-order parameter A ) decay and the second with exp(-12D ) (relaxation of the third-order pammeter A3) decay. Hence, the first very rapid decay may contain the fast exp(-12D ) contribution. However, as can be seen from Figure 11.14, the relative magnitude of this initial very fast decay does not depend on the optimization of the intensity ratio between the writing beams. So, this first rapid decay may not be due to the decay of the third-order parameter A3. In addition, because the hyperpolarizability P of DRl is different in the ds and in the trans state, the first very rapid decay also contains a contribution connected with the hferime of the metastable ds form, which is due to molecules coming back to the trans form without any net orientation. A better model would have to account for a distribution of diffusion constants for molecules embedded with various free volumes, which may explain the multiexponential behavior of the decay. 

Abstract Keeping in mind the pedagogical goal of the presentation the first third of the review is devoted to the basic definitions and to the description of the cooperative Jahn-Teller effect. Among different approaches to the intersite electron correlation in crystals the preference is with the most fundamental and systematic Hamiltonian shift transformation method. Order parameter equations and their connection to the crystal elastic properties and to the orbital ordering are considered. An especial attention is paid to the dynamics of Jahn-Teller crystals based on the coupled electronic, vibrational, and magnetic excitations which are of big interest nowadays in orbital physics. 

Given that the supercooling of a liquid can lead to structurally distinct possibilities (the stable crystal or a glass), structural order parameters are especially valuable in understanding low-temperature metastabiUty. In particular, it has been demonstrated (van Duijneveldt and Frenkel, 1992) that the bond-orientational order parameters introduced by Steinhardt et al (1983) are well suited for detecting crystalline order in computer simulations of simple supercooled liquids. The bond-orientational order parameters are so named because they focus on the spatial orientation of imaginary bonds" that connect molecules to their nearest neighbors defined as above with... 

---