Degenerate phase

Eye tech Smdy Group. Anti-vascular endotheUal growth factor therapy for subfoveal choroidal neovascularization secondary to age-related macular degeneration phase 11 smdy results. Ophthalmology 2003 10 979. 

Ising model this case corresponds to the limit Jx O, where the two-dimensional Ising lattice degenerates to the one-dimensional spin system. We are dealing with a degenerate phase transition ... 

Fig. 8 Sensitivity of the honeycomb photonic crystal fiber-based SPR sensor, (a) The solid curve shows loss of the fundamental core mode near the degenerate phase-matching point with two plasmon modes and = 1.32. Due to degeneracy, only one peak is distinguishable in the loss curve. Dashed line shows splitting of the degeneracy in plasmon modes when the analyte s refractive index is changed to = 1.322 (b) Dependence of the sensor amplitude sensitivity on wavelength (after [19] (C) 2007 OS A)...

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Solitan d ect in a 2ran polyacetylene chain separating the degenerate phases A and B... 

Antisoliton solitons are present in materials with two degenerate phases A and B. If a soliton is a kink between A and B phase, then an antisoliton is a kink between B and A phase. 

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In the degeneration-phase (fig. 7), however, the terminal bud still may develop but into shorter long shoots, but from nearly any lateral bud (from the uppermost, too) arise short shoots almost without exception. Thereby an obvious impoverishment of the branching pattern takes place and there are formed spears in the periphery of the crowns, which are to perceive from a long distance, too. 

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

The stoi7 begins with studies of the molecular Jahn-Teller effect in the late 1950s [1-3]. The Jahn-Teller theorems themselves [4,5] are 20 years older and static Jahn-Teller distortions of elecbonically degenerate species were well known and understood. Geomebic phase is, however, a dynamic phenomenon, associated with nuclear motions in the vicinity of a so-called conical intersection between potential energy surfaces. 

Equations (16)-(20) show that the real adiabatic eigenstates are everywhere smooth and continuously differentiable functions of Q, except at degenerate points, such that E (Q) — E, [Q) = 0, where, of com se, the x ) are undefined. There is, however, no requirement that the x ) should be teal, even for a real Hamiltonian, because the solutions of Eq. fl4) contain an arbitrary Q dependent phase term, gay. Second, as we shall now see, the choice that x ) is real raises a different type of problem. Consider, for example, the model Hamiltonian in Eq. (8), with / = 0 ... 

The sum excludes m = n, because the derivation involves the vector product of (n Vq H n) with itself, which vanishes. The advantage of Eq. (43) over Eq. (31) is that the numerator is independent of arbiriary phase factors in n) or m) neither need be single valued. On the other hand, Eq. (43) is inapplicable, for the reasons given above if the degenerate point lies on the surface 5. 

Figure 5. A cut across the ground state (GS) and the excited state (ES) potential surfaces of the H4 system. The parameter Qp is the phase preserving nuclear coordinate connecting the H(lll) with the transition state between H(I) and H(1I) (Fig, 4). Keeping the phase of the electronic wave function constant, this coordinate leads from the ground to the excited state. At a certain point, the two surfaces must touch. At the crossing point, the wave function is degenerate.

Figure 29, The effect of the phase-preserving component of the degenerate 2 distorting mode, It may be regarded as a major component of the reaction coordinate that leads to the A] structure (going left, one phase of the mode). Going right, the other phase of the same vibration, the B2 state is formed. (A type-V structure is also obtained along the same coordinate).

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