Power-law bounds on transfer matrices and quantum dynamics in one dimension

We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the Fibonacci Hamilto...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 236; no. 3; pp. 513 - 534
Main Authors DAMANIK, David, TCHEREMCHANTSEV, Serguei
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.06.2003
Springer Verlag
Subjects
Classical and quantum physics: mechanics and fields
Dynamical Systems
Exact sciences and technology
Functional analytical methods
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Ordinary differential equations
Physics
Quantum ensemble theory
Quantum mechanics
Quantum statistical mechanics
Sciences and techniques of general use
Statistical physics, thermodynamics, and nonlinear dynamical systems
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Lower bound
Transfer matrix
Thue Morse model
Quantum mechanics
Fibonacci sequence
One dimensional model
Schrödinger operator
Hamiltonian
Self adjoint operator
Mathematical physics
Power law bound
Quantum Dynamics
Fibonacci Potential
Schrödinger Operators
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Summary:We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the Fibonacci Hamiltonian.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-003-0824-6