@article{1437702,
      recid = {1437702},
      author = {Emamirad, Hassan,},
      title = {Scattering theory for transport phenomena /},
      pages = {1 online resource (xxi, 179 pages) :},
      abstract = {"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 Schrödinger 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"--Print  version, page 4 of cover.},
      url = {http://library.usi.edu/record/1437702},
      doi = {https://doi.org/10.1007/978-981-16-2373-8},
}