Density Matrix Theory And Applications

Starting from basic principles, the book systematically covers both Heisenberg and Schrödinger realizations of quantum mechanics (in this order). The material traditionally presented in quantum textbooks is illustrated with applications which are (or will become) cornerstones of future technologies. The emphasis in the matrix formulation focus the attention on the spin, the most important quantum observable, and paves the way to chapters on quantum information (including crytography, teleportation and computation), on recent tests of quantum physics and on decoherence. Additions and changes found in the second edition include; a more friendly presentation to Hilbert spaces; more practical applications e.g. scanning tunneling microscope (potential barrier); quantum dots (single-particle states in semiconductors); lasers and masers (induced emission); real experiments that have recently provided a qualitative change in the foundations of quantum physics; and an outline of the density matrix formalism as applied to a simple model of decoherence.

This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps.

This book presents the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.

This book describes, as simply as possible, the mechanisms of scattering (both elastic and inelastic) of electrons with solid targets (electron–atom, electron–plasmon, and electron–phonon interactions). It also presents the main strategies of the Monte Carlo method, as well as numerous comparisons between simulation results and the experimental data available in the literature. Furthermore it provides readers with all the information they need in order to write their own Monte Carlo code and to compare the obtained results with the many numerical and experimental examples presented throughout the book.