Quantum Mechanics and Band Theory

J. Žák

de Bianchi, Massimiliano Sassoli de Bianchi

Francesco Giacosa, A. Kolbus, Krzysztof Kyzioł +4 more

Quantum mechanics predicts deviations from exponential decay at short and long times, yet experimental evidence is limited. We report a power-law tail after $\sim$10 lifetimes in two fluorescent compounds (erythrosine~B and eosine Y), confirmed by two detectors probing distinct bands but yielding different power coefficients. The data match a divergent but normalizable spectral density, and theory predicts oscillations as a future test. A novel and general result is that in multichannel QM (and QFT) decay, the lifetime is universal, but the late-time deviations are channel- (or band-) dependent, a feature consistent with our data.

Miguel Gonçalves, Sarang Gopalakrishnan

We present a mechanism for ferromagnetism in narrow bands consisting of Anderson-localized states. We exploit single-particle localization to derive a controlled theory of exchange interactions within the narrow band. For quasiperiodic systems with a half-filled moiré band, we show that the critical interaction strength for ferromagnetism is highly sensitive to the geometry of real-space overlaps between localized orbitals: we find well-defined resonances at which ferromagnetism sets in for interaction energies that are far lower than the gap to other bands. Near these resonances, all the approximations in our theory are controlled, so our critical point predictions are quantitative. We show examples both in one and two dimensions. Our work identifies a route to ferromagnetism based on the geometry of real-space wavefunctions, distinct from previously found mechanisms based on the quantum geometry of Bloch bands.

Jochen Vogt

J. S. Faulkner

Modern Quantum Mechanics and Quantum Information surveys the fundamental aspects of quantum mechanics against the backdrop of its use in modern science applications. The book covers several topics in modern quantum mechanics and quantum information that do not appear in older texts. These include a mathematically sound treatment of delta functions and the rigged Hilbert space, an exposition of many-body theory including density functional theory and Feynman diagrams, and an explanation of chemical bonds and energy band theory. It also contains expansive chapters on relativistic Dirac theory, group theory including Lie groups, exotic quantum phenomena, interpretations of quantum theory, quantum computers and quantum cryptography. Each chapter ends with a set of questions and exercises for the student. This authoritative and expansive survey of the field is ideal for advanced researchers, upper undergraduate and graduate studentss, with a main purpose as a text for a graduate course in quantum mechanics. Key features • Provides a thorough review of the basics • Discusses the philosophical questions of quantum theory • Includes the concepts used in quantum condensed matter physics and quantum chemistry in detail • Presents quantum information • Discusses the density functional and the diagrammatic approaches to many-body theory