Field mixed states

The electric field mixes states of opposite parity. Therefore, if the atom entering the interferometer is in a state with definite parity (e.g. in the 2s state), the probability of it emerging in the 2s or 2p state does not depend on the sign of the field. 

We hope that by now the reader has it finnly in mind that the way molecular symmetry is defined and used is based on energy invariance and not on considerations of the geometry of molecular equilibrium structures. Synnnetry defined in this way leads to the idea of consenntion. For example, the total angular momentum of an isolated molecule m field-free space is a conserved quantity (like the total energy) since there are no tenns in the Hamiltonian that can mix states having different values of F. This point is discussed fiirther in section Al.4.3.1 and section Al.4.3.2. 

The MMVB force field has also been used with Ehrenfest dynamics to propagate trajectories using mixed-state forces [84]. The motivation for this is... 

Thus, the neglect of the off-diagonal matrix elements allows the change from mixed states of the nuclear subsystem to pure ones. The motion of the nuclei leads only to the deformation of the electronic distribution and not to transitions between different electronic states. In other words, a stationary distribution of electrons is obtained for each instantaneous position of the nuclei, that is, the elechons follow the motion of the nuclei adiabatically. The distribution of the nuclei is described by the wave function x (R i) in the potential V + Cn , known as the proper adiabatic approximation [41]. The off-diagonal operators C n in the matrix C, which lead to transitions between the states v / and t / are called operators of nonadiabaticity and the potential V = (R) due to the mean field of all the electrons of the system is called the adiabatic potential. 

The major contribution to the components of the D tensor as well as the deviations of the g values from 2.0023 arises from the mixing of ligand field states by SOC other contributions to D result from direct spin-spin coupling, which mixes states of the same spin S. The D tensor and the g matrix both carry chemical information as they are related to the strength and symmetry of the LF, which is competing and counteracting to the effects of SOC. Details on the chemical interpretation of the parameters by quantum chemical means is found in Chap. 5. 

Takahashi and Umezawa introduced thermofield dynamics (TFD), a canonical formalism, for finite temperature theory (Y. Takahashi et.al., 1975 1996 1982 1993). TFD keeps the analogy with the zero-temperature field theory by describing thermal state, a mixed state, as a thermal... 

High-spin hemes have a strong axial zero field splitting which splits these states into three doublets, and because the value of the zero field splitting parameter D is positive (typically 5-10 cm ) for hemes the doublet consisting of the Sj = -1-, — states is lowest lying. There is usually also a smaller rhombic term E which cannot split the Kramers doublets but mixes states differing in by 2. The main net effect of E is to remove the equivalence of the x and y (in heme plane) directions so that g, and gy are unequal. 

Results on the thermal conductivity in the superconducting mixed state have been reported for LuNi2B2C for temperatures down to 70 mK (7c/200) and magnetic fields from H — 0 to above Hc2 = 70 kOe (Boaknin et al. 2001, see fig. 24). It was found that as soon as vortices enter the sample, the thermal conductivity at T - 0 grows rapidly, showing unambiguously that delocalized quasiparticles are present even at the... 

Fig. 57. Specific heat contribution y(H) of the vortex core electrons in the mixed state (normalized by the Sommerfeld parameter /n) of the Yj[Lu jrNi2B2C samples from fig. 56 as function of the applied magnetic field (normalized by //c2(0)). The straight line y(H)

An unexpected concentration dependence is found for the parameter which describes, according to eq. (8), the deviation of the field dependence of the electronic specific heat in the mixed state from the linear law expected (Nohara et al. 1997) for isotropic s-wave superconductors in the dirty limit. The large deviations from this linear y(H) law observed... 

Fig. 60. Concentration dependence of various properties of polycrystalline Y(Ni xPt )2B2C obtained by specific heat measurements transition temperature Tc exponent a and parameter Hc2 from eq. (6) upper critical field Hc2(0) at T =0, where the dotted line schematically describes the dirty limit corresponding to the isotropic single band case (in reality there is a finite intersection with the field-axis for the dotted asymptotic line, see Shulga and Drechsler 2002) exponent fi of eq. (8) for the curvature of the electronic specific heat in the mixed state and Sommerfeld constant xn (after Lipp et al. 2001).

Fig. 61. Magnetic field dependence of the specific heat contribution y(H) of the vortex core electrons in the mixed state for Y(Nio.7sPto.25)2B2C. The dashed line is a fit according to eq. (8) with /) = 0.17, the solid line corresponds to the y(H)

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