Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian

DOI10.1016/j.jfa.2008.08.010zbMath1153.81011arXiv0801.3399OpenAlexW2962826225MaRDI QIDQ960552

Serguei Tcheremchantsev, David Damanik

Publication date: 22 December 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3399

zbMATH Keywords

Schrödinger operatorsquantum dynamicsFibonacci potential

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items

Power law logarithmic bounds of moments for long range operators in arbitrary dimension, Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy, ON- AND OFF-DIAGONAL STURMIAN OPERATORS: DYNAMIC AND SPECTRAL DIMENSION, Upper bounds on quantum dynamics in arbitrary dimension, Schrödinger operators with dynamically defined potentials, Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian, The density of states measure of the weakly coupled Fibonacci Hamiltonian, Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schrödinger operators, Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices, The Fibonacci Hamiltonian, Transport exponents of states with large support, Upper bounds on transport exponents for long-range operators, Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian, Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian, Transport exponents of Sturmian Hamiltonians

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