Heisenberg interactions

Solving now the Heisenberg equations of motion for the a operators perturbatively in the same way as in the weak-coupling case, one arrives (at = 0) at the celebrated non-interacting blip approximation [Dekker 1987b Aslangul et al. 1985]... 

Quantum Electrodynamics in the Heisenberg Picture.— With the present section we begin our discussion of the quantum theoretical description of the interaction between the negaton-positon field and the radiation field i.e., of quantum electrodynamics proper. 

The application of the quantum mechanics to the interaction of more complicated atoms, and to the non-polar chemical bond in general, is now being made (45). A discussion of this work can not be given here it is, however, worthy of mention that qualitative conclusions have been drawn which are completely equivalent to G. N. Lewis s theory of the shared electron pair. The further results which have so far been obtained are promising and we may look forward with some confidence to the future explanation of chemical valence in general in terms of the Pauli exclusion principle and the Heisenberg-Dirac resonance phenomenon. 

The wave function is an irreducible entity completely defined by the Schrbdinger equation and this should be the cote of the message conveyed to students. It is not useful to introduce any hidden variables, not even Feynman paths. The wave function is an element of a well defined state space, which is neither a classical particle, nor a classical field. Its nature is fully and accurately defined by studying how it evolves and interacts and this is the only way that it can be completely and correctly understood. The evolution and interaction is accurately described by the Schrbdinger equation or the Heisenberg equation or the Feynman propagator or any other representation of the dynamical equation. 

A priori, one might have expected a [3Fe-4S] center to give a particularly simple EPR spectrum. Contrary to what was suggested in Ref. (13), the electronic structure of this cluster, which possess three ferric sites, is not liable to be complicated by valence delocalization phenomena, so that the intersite interactions can be described by the Heisenberg Hamiltonian ... 

Ding, X.-Q., Bominaar, E.L., Bill, E., Winkler, H., Traitwein, A.X., Driieke, S., Chaudhuri, P., and Wieghardt, K. 1990. Mossbauer and electron paramagnetic resonance study of the double exchange and Heisenberg-exchange interactions in a novel binuclear Fe(II/III) delocalized-valence compound. Journal of Chemical Physics 92 178-186. 

Much attention has been paid to Monte Carlo simulations of magnetic ordering, and its variation with temperature. Such models assume a particular form for the magnetic interactions, e.g. the Ising or Heisenberg Hamiltonian (see e.g. Binder... 

About the same time, Douglas Hartree, along with other members of the informal club for theoretical physics at Cambridge University called the Del-Squared Club, began studying approximate methods to describe many-electron atoms. Hartree developed the method of the self-consistent field, which was improved by Vladimir Fock and Slater in early 1930, so as to incorporate the Pauli principle ab initio.37 Dirac, another Del-Squared member, published a paper in 1929 which focused on the exchange interaction of identical particles. This work became part of what soon became called the Heisenberg-Dirac approach.38... 

Various predictive methods based on molecular graphs of Jt-systems as described in Section 3 have been critically compared by Klein (Klein et al., 1989) and can be extended to more quantitative treatments. In principle, the effective exchange integrals /ab in the Heisenberg Hamiltonian (4) for the interaction of localized electron spins at sites a and b are calculated as the difference in energies of the high-spin and low-spin states. It was Hoffmann who first tried to calculate the dependence of the M—L—M bond... 

The pure RKKY interaction is isotropic, and the canonical spin glass systems are therefore often referred to as Heisenberg spin glasses. However, some anisotropy is also present in those systems originating from dipolar interaction and interaction of the Dzyaloshinsky-Moriya (DM) type [73]. The latter is due to spin-orbit scattering of the conduction electrons by non-magnetic impurities and reads... 

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