This interesting book provides the physical and mathematical background for a theory describing the universe as a quantum superfluid, and how dark energy and dark matter arise. Presenting a novel theory spanning many different fields in physics, the key concepts in each field are introduced.The reader is only expected to know the rudiments of condensed matter physics, quantum field theory and general relativity to explore this fascinating new model of dark matter and dark energy as facets of a cosmic superfluid.

This text presents a general overview of analogies between phenomena in condensed matter physics and quantum field theory and elementary particle physics.

This book reports on the latest developments in the field of Superfluidity, one of the most fundamental, interesting, and important problems in physics, with applications ranging from metals, helium liquids, photons in cavities, excitons in semiconductors, to the interior of neutron stars and the present state of the Universe as a whole.

Covers the State of the Art in Superfluidity and SuperconductivitySuperfluid States of Matter addresses the phenomenon of superfluidity/superconductivity through an emergent, topologically protected constant of motion and covers topics developed over the past 20 years. The approach is based on the idea of separating universal classical-field superf

Volume 2 of Novel Superfluids continues the presentation of recent results on superfluids, including novel metallic systems, superfluid liquids, and atomic/molecular gases of bosons and fermions, particularly when trapped in optical lattices. Since the discovery of superconductivity (Leyden, 1911), superfluid 4He (Moscow and Cambridge, 1937), superfluid 3He (Cornell, 1972), and observation of Bose-Einstein Condensation (BEC) of a gas (Colorado and MIT, 1995), the phenomenon of superfluidity has remained one of the most important topics in physics. Again and again, novel superfluids yield surprising and interesting behaviors. The many classes of metallic superconductors, including the high temperature perovskite-based oxides, MgB2, organic systems, and Fe-based pnictides, continue to offer challenges. The technical applications grow steadily. What the temperature and field limits are remains illusive. Atomic nuclei, neutron stars and the Universe itself all involve various aspects of superfluidity, and the lessons learned have had a broad impact on physics as a whole.

Proposes a new way of understanding and interpreting the fundamental laws of science that will open up human thinking to the vast possibilities of the universe.

This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Its intended audience is students of mathematics at the senor university level and beginning graduate students in mathematics and physics. Early chapters address such topics as the Fourier transform, the spectral theorem for bounded self-joint operators, and unbounded operators and semigroups. Subsequent topics include a discussion of Weyl's theorem on the essential spectrum and some of its applications, the Rayleigh-Ritz method, one-dimensional quantum mechanics, Ruelle's theorem, scattering theory, Huygens' principle, and many other subjects.