Symmetry changes, external fields

Spin-orbit(SO) coupling is an important mechanism that influences the electron spin state [1], In low-dimensional structures Rashba SO interaction comes into play by introducing a potential to destroy the symmetry of space inversion in an arbitrary spatial direction [2-6], Then, based on the properties of Rashba effect, one can realize the controlling and manipulation of the spin in mesoscopic systems by external fields. Recently, Rashba interaction has been applied to some QD systems [6-8]. With the application of Rashba SO coupling to multi-QD structures, some interesting spin-dependent electron transport phenomena arise [7]. In this work, we study the electron transport properties in a three-terminal Aharonov-Bohm (AB) interferometer where the Rashba interaction is taken into account locally to a QD. It is found that Rashba interaction changes the quantum interference in a substantial way. 

If there is no external field, the director m in nematics is entirely arbitrary. Thus the equilibrium state of nematics is not unique and can be changed by infinitesimal perturbation. This property, generally called broken symmetry in statistical mechanics, necessitates a special treatment in the mathematical handling of the kinetic equation, and introduces a new type of constitutive equation, unique to the ordered fluid. 

NaKC4H40e 4H2O), monopotassium dihydrophosphate (KH2PO4), or barium titanate (BaTiOs). At sufficiently high temperatures ferroelectrics show normal dielectric behavior. However, below a certain critical temperamre (so called. Curie temperature), even a small electric field causes a large polarization, which is preserved even if the external field is switched off. This means that below the Curie point ferroelectric materials show spontaneous polarization. The phase transition at the Curie temperature is related to the change of the lattice symmetry of the sample. 

Curie understood that under stress, or in the presence of external electric or magnetic fields, the symmetry of a system is changed. The Neumann principle still applies but should no longer be based on the symmetry of the isolated crystal, but on that of the combined system of crystal and external field, as we have considered in Sect. 3.9. In the case of ammonia, application of an electric field has the Coov symmetry of a polar vector. The symmetry that results from the superposition of the field with the molecular point group 3 depends on the orientation (see Appendix B). In the coordinate frame of Fig. 3.1 one has ... 

The optical properties of ceramics are naturally affected either directly or indirectly by factors such as the constituent elements constituting the ceramic, the crystalline symmetry, the microstructure of the ceramic, and changes in the external field. Table 7.1.2 lists some of the typical factors that affect the optical properties of ceramics. Even in single crystals—which are the simplest form of ceramics under the broad definition—these factors rarely act individually on the optical properties. And in a polycrystalline material, the situation is obviously much more complicated. 

Inhomogeneous stresses produced by localized defects may induce local phase transitions above the normal phase transition temperature Tc, causing the material to have mixed low and high symmetry phases in certain temperature regions. Such a two-phase mixture is usually very sensitive to external fields or stresses since the phase change among the mixture becomes barrierless even for a first order phase transition [10]. 

The electric field effect on the fluorescence yield of the primary donor ip reflects the competition between the radiative rate and the field modulated rate k or k, respectively. For isotropically distributed RCs, the lowest term in the expansion for the field dependence of the fluorescence change = (E)- (O) is proportional to (/lE), since any linear contribution cancels due to mirror symmetry with respect to the electric field. In fact a quadratic dependence of was observed (see [12] and Fig.l), which holds up to external fields of about S-IO V/cm. At such fields an electric field induced fluorescence increase of ci 80% is observed. A least square fit of the data in Fig.l gives an exponent of 1.98 0.02 for... 

Debye relaxation time — A stationary ion is surrounded by an equally stationary ionic cloud only thermal movement causes any change in the actual position of a participating ion. Upon application of an external electric field the ions will move. At sufficiently high frequencies / of an AC field (1// < r) the symmetry cannot be maintained anymore. The characteristic relaxation time r is called Debye relaxation time, the effect is also called... 

---