By P. W. Anderson
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In the course of 1989 the Centre for Mathematical research hosted a unique software in Mathematical Physics. This quantity of the complaints of the Centre for Mathematical research comprises experiences of a few of the most important talks provided at a mini-conference on Geometry and Physics held within the Centre from February 20 to 23, 1989 to coincide with a trip to Australia of Sir Michael Atiyah.
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A third striking experimental similarity between ferromagnetism and ferroelectricity lies in the domain structure. It is well-known that in order to explain the magnetic hysteresis loop Weiss and others postulated that a ferromagnetic specimen is divided into a system of regions, or domains, each polarized to saturation in a certain direction. At zero applied field, however, the magnetic domain polarizaa For a review see C. Kittel, Rev. Mod. Phys. 21, 541 (1949). * G. C. Danielson, unpublished.
We present merely the result, which includes the identical sums for initial and final states. For the simple Stark effect we get the following S 2 sum, applicable to collisions of the radiating molecule, quantum numbers Ji and Ki, with molecules of any J2 and K2 (n2 in the general formula (46) of Part I for the two-molecule case being here J 2 , K2). KSK* S2(J2, K2)—~ o j W / ^ + l X ^ / d - l ) (Stark effect). Ji2-K*i) X- h /12(2/1+1)(2J1-1) -(rot. ) (9a) • (9b) 52(/1+I,A:2)=- 9 bW KJi+iy-KSjLiJi+D'-Kt'i X2 (/1+l) (2/1+l)(2/1+3) For collisions with molecules of / 2 = / i ± l , one must add (9a) or (9b) and (8) together to get the total 5 2 sum.
In either case, a reduces to the following then the average in (41) gives the following equation simple form: for?. p(da in dr) = nvdadr. W) 1 1 . J (42) aa%= (PB)«2 (43) r X It is obvious that the shift in frequency and the linebreadth follow from the real and imaginary parts of the number a, precisely according to (28). Thus the problem of the line-shape is solved in principle. Before proceeding further with the evaluation of a, the "collision cross section for line-broadening," it is necessary to generalize formula (43) to a case which we shall frequently treat—that in which the interaction Hamiltonian Hi'(t) is a matrix involving the quantummechanical states of both the perturbing molecule and the radiating molecule.