By Alois Würger

ISBN-10: 3540614249

ISBN-13: 9783540614241

From Coherent Tunneling to leisure is a magnificent evaluate of ten years of growth in our knowing of interacting tunneling platforms. The dielectric and elastic reaction of (111) off-center impurities in alkalide halides is investigated intimately and the coherent movement of an impurity pair is mentioned in view of lately saw rotary echoes. The low-temperature houses of illness crystals with an impurity focus greater than a hundred ppm are reviewed and the dipolar interplay is proven to force the cross-over to relaxational dynamics. This entire presentation of the idea is illustrated via experimental facts for lithium, cyanide, and hydroxyl impurities in a number of host crystals. This monograph is a perfect reference ebook for scientists operating with disorder crystals and glasses

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Extra resources for From Coherent Tunneling to Relaxation: Dissipative Quantum Dynamics of Interacting Defects (Springer Tracts in Modern Physics)

Example text

30) For zero asymmetry A = 0, the eight states are distributed over six equidistant levels with spacing 7?. In the case of finite 3 , the energy of the levels a= = - 1 is lowered, and that of a= = +1 increases by the same amount. (Compare Fig. 2), A=O E0 T A=T] (111) E0- ~ - - (ill) Eo - 2 r / - - ~ ( l l i ) , (1il) Eo 3r~-- (ili), (iil) E0 5n (iii) T --~ Fig. 2. 30) with ~0 -- ~?. Both cases of zero and finite asymmetry A are shown. The states are labelled by the quantum numbers (r. 11). In the opposite case ~/A ~ 0, we find f ~ : --* v/2 and f S : --* 0, which corresponds to states where the two impurities are localized at either !

43), the absolute value of the total dipole moment is found to be IPl = qd. 36). ) factorizes with respect to the quantum numbers ax, ay, and ~rz. 36) first. Thus calculation of the response function reduces to a two-level problem with the states ax = +1. Both the statistical operator and the time evolution operator are diagonal in the energy eigenstates. n,2T]2 a x x ( 7 ) = heo ~ u j ~ ( tanh E ) 2--k~nT sin ( - ~ ) O(T). 46) Note that the susceptibility involves only the x direction; there is no linear response along the axes y and z.

50) . 50) account for the data shown in Fig. 5, where the linear response has been found to vanish for shear waves with polarization direction [1i0]. Temperotur T 50 r. 10 9 i 5 3 I I 0 ,~lbp--i--n -1 2 u-i--I " ~:)-3 I n--m n--i-- 9 [110] -". \ I 60 inv. Temperdtur IO0/T (K-1) Fig. 5. Change of transverse sound velocity arising from 100 ppm Li impurities in KC1, for two different polarizations, [001] and [li0]. The shear waves with a frequency of 30 MHz propagate in [110] direction. 63). Data are from [28].

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