Efficient Diagonalization of Kicked Quantum Systems
arXiv:cond-mat/9712209 · doi:10.1016/S0167-2789(98)00230-9
Abstract
We show that the time evolution operator of kicked quantum systems, although a full matrix of size NxN, can be diagonalized with the help of a new method based on a suitable combination of fast Fourier transform and Lanczos algorithm in just N^2 ln(N) operations. It allows the diagonalization of matrizes of sizes up to N\approx 10^6 going far beyond the possibilities of standard diagonalization techniques which need O(N^3) operations. We have applied this method to the kicked Harper model revealing its intricate spectral properties.
Text reorganized; part on the kicked Harper model extended. 13 pages RevTex, 1 figure
References in corpus (6)
- Fractal Conductance Fluctuations in Generic Chaotic Cavities
- Fractal Conductance Fluctuations in a Soft Wall Stadium and a Sinai Billiard
- Field theory of the quantum kicked rotor
- Fractal Conductance Fluctuations in Gold--Nanowires
- Tunneling and the Band Structure of Chaotic Systems
- Avoided Band Crossings: Tuning Metal-Insulator Transitions in Chaotic Systems
Cited by in corpus (18)
- Gauging classical and quantum integrability through out-of-time ordered correlators
- Quantum Hall effect in a one-dimensional dynamical system
- Visualization and comparison of classical structures and quantum states of 4D maps
- Quantum-to-classical correspondence in open chaotic systems
- Dynamical model for the quantum-to-classical crossover of shot noise
- Quantum Andreev map: A paradigm of quantum chaos in superconductivity
- Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics
- Quantum Computation of a Complex System : the Kicked Harper Model
- Non-universal level statistics in a chaotic quantum spin chain
- Classical limit of transport in quantum kicked maps
- Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
- Quantum-to-classical crossover for Andreev billiards in a magnetic field
- Freed by interaction kinetic states in the Harper model
- Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
- First verification of generic fidelity recovery in a dynamical system
- Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator
- Macroscopic Resonant Tunneling through Andreev Interferometers
- Chaotic delocalization of two interacting particles in the classical Harper model