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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Scattering Theory for Transport Phenomena (Hardcover, 1st ed. 2021)
Loot Price: R3,273
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Scattering Theory for Transport Phenomena (Hardcover, 1st ed. 2021)
Series: Mathematical Physics Studies
Expected to ship within 10 - 15 working days
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The scattering theory for transport phenomena was initiated by P.
Lax and R. Phillips in 1967. Since then, great progress has been
made in the field and the work has been ongoing for more than half
a century. This book shows part of that progress. The book is
divided into 7 chapters, the first of which deals with
preliminaries of the theory of semigroups and C*-algebra, different
types of semigroups, Schatten-von Neuman classes of operators, and
facts about ultraweak operator topology, with examples using
wavelet theory. Chapter 2 goes into abstract scattering theory in a
general Banach space. The wave and scattering operators and their
basic properties are defined. Some abstract methods such as smooth
perturbation and the limiting absorption principle are also
presented. Chapter 3 is devoted to the transport or linearized
Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism
is introduced in scattering theory for the transport equation. In
their seminal book, Lax and Phillips introduced the incoming and
outgoing subspaces, which verify their representation theorem for a
dissipative hyperbolic system initially and also matches for the
transport problem. By means of these subspaces, the Lax and
Phillips semigroup is defined and it is proved that this semigroup
is eventually compact, hence hyperbolic. Balanced equations give
rise to two transport equations, one of which can satisfy an
advection equation and one of which will be nonautonomous. For
generating, the Howland semigroup and Howland's formalism must be
used, as shown in Chapter 5. Chapter 6 is the highlight of the
book, in which it is explained how the scattering operator for the
transport problem by using the albedo operator can lead to recovery
of the functionality of computerized tomography in medical science.
The final chapter introduces the Wigner function, which connects
the Schroedinger equation to statistical physics and the Husimi
distribution function. Here, the relationship between the Wigner
function and the quantum dynamical semigroup (QDS) can be seen.
General
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