This book is a compilation of reprints of the major works by the prominent Soviet and Russian theoretical physicists, Leonid V Keldysh. He made important contributions to condensed matter theory, developing new approaches and methods, and discovering beautiful new physical effects later confirmed by experiments.Keldysh developed the consistent theory of phonon assisted tunneling in semiconductors and calculated the electric field induced shift of absorption edge in semiconductors, what is now called Franz–Keldysh effect. He also developed the original theory of deep levels in semiconductors. One of his most famous works was the 1964 theory of multiple photon ionization of atoms by intensive electromagnetic waves, thereby laying the foundation for the entire field of intense laser radiation interaction with atoms, ions, molecules, and solids. This theory introduced optical tunneling and beyond — threshold ionization, experimentally observed about 15 years later.His name is probably best known due to his 1964 work on general diagram technique for non-equilibrium processes. Introducing Green’s functions with time — ordering along what is now known as Keldysh contour, he was able to construct the standard Feynman diagrams for these Green’s functions at finite temperatures and for general non-equilibrium states. Since then, this approach has become a standard one, with multiple applications in solid state theory, the theory of quantum liquids, quantum field theory and even quantum cosmology.Since 1964, Keldysh’s interests moved to the problem of many excitons in semiconductors. He introduced the new concept of excitonic insulator. Actually this was a new mechanism of metal-insulator transitions. In later works by Keldysh and his collaborators it was definitely shown, that there are no superfluidity properties in this model, as was initially suspected by some authors and he moved to the studies of non-equilibrium system of excitons, appearing under intensive laser pumping of semiconductors, where superfluidity of excitons was shown to be possible.In 1968, Keldysh realized that in most semiconductors (with multiple bands), the non-equilibrium system of many excitons actually transforms into electron — hole quantum liquid (with excitons destroyed), forming electron-hole drops. This idea immediately stimulated the experimental studies and electron-hole drops were soon discovered, leading to many further experimental and theoretical works on this new state of matter. Keldysh was awarded numerous awards, including the Lenin prize (1974), the Hewlett–Packard Prize (1975), Alexander von Humboldt Prize (1994), Rusnanoprize (2009), Eugene Feinberg Memorial Medal (2011), Pomeranchuk Prize (2014) and the Grand Lomonosov Gold Medal of the Russian Academy of Sciences (2015). He was elected the foreign member of the USA National Academy of Sciences (1995) and the Fellow of the American Physical Society (1996).Key FeaturesThis book is unique "by definiton" as no collections L V Keldysh works were previously published anywhereStudying these classic papers may be equally inspiring both to young and well — experienced scientists, working in the fields of theoretical physics, condensed matter, semiconductors, optics and laser physicsMany stimulating ideas of L V Keldysh may still be helpful for modern physicists

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