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Presenting in a coherent and accessible fashion current results in
nanomagnetism, this book constitutes a comprehensive, rigorous and
readable account, from first principles of the classical and
quantum theories underlying the dynamics of magnetic nanoparticles
subject to thermal fluctuations.Starting with the Larmor-like
equation for a giant spin, both the stochastic (Langevin) equation
of motion of the magnetization and the associated evolution
(Fokker-Planck) equation for the distribution function of the
magnetization orientations of ferromagnetic nanoparticles
(classical spins) in a heat bath are developed along with their
solution (using angular momentum theory) for arbitrary
magnetocrystalline-Zeeman energy. Thus, observables such as the
magnetization reversal time, relaxation functions, dynamic
susceptibilities, etc. are calculated and compared with the
predictions of classical escape rate theory including in the most
general case spin-torque-transfer. Regarding quantum effects, which
are based on the reduced spin density matrix evolution equation in
Hilbert space as is described at length, they are comprehensively
treated via the Wigner-Stratonovich formulation of the quantum
mechanics of spins via their orientational quasi-probability
distributions on a classically meaningful representation space.
Here, as suggested by the relevant Weyl symbols, the latter is the
configuration space of the polar angles. Hence, one is led, by
mapping the reduced density matrix equation onto that space, to a
master equation for the quasi-probability evolution akin to the
Fokker-Planck equation which may be solved in a similar way. Thus,
one may study in a classical-like manner the evolution of
observables with spin number ranging from an elementary spin to
molecular clusters to the classical limit, viz. a nanoparticle. The
entire discussion hinges on the one-to-one correspondence between
polarization operators in Hilbert space and the spherical harmonics
allied to concepts of spin coherent states long familiar in quantum
optics.Catering for the reader with only a passing knowledge of
statistical and quantum mechanics, the book serves as an
introductory text on a complicated subject where the literature is
remarkably sparse.
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