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This site has been supported by the NSF-CAREER award grant DMR-1147430, the NSF-RUI award grant DMR-1603418, the BSF-NSF grant DMR-1936006. Its purpose is to make available tutorials and computer codes developed with students and postdocs.
**) Floquet systems, quasienergies, quantum chaos (file) (2022-2023)
Look also at the excellent tutorial by Holthaus.
J. Phys. B: At. Mol. Opt. Phys. 49, 013001 (2016).
It is available in the arXiv here.
**) Some of the codes used in the 2nd International Summer School on Advanced Quantum Mechanics, Sep/02-11, 2021, Prague.
Slides about STATIC properties
Slides about DYNAMICS
Fortran code for GOE matrices
Figures for the results for the GOE code
Fortran code for spin-1/2 models
Figures for the results of the spin-1/2 model with a single-defect
Figures for the results of the spin-1/2 model with couplings between 2nd neighbors
**) Notes and codes developed for the International Summer School on Exact and Numerical Methods for Low-Dimensional Quantum Structures that took place at the Izmir Institute of Technology, Turkey, from August 23 to August 31, 2014. The tutorial teaches how to exactly diagonalize one-dimensional spin-1/2 models. In hands of the eigenvalues and eigenstates, we: (i) analyze signatures of quantum phase transition, localization, and quantum chaos; (ii) investigate the dynamics of the system by studying the survival probability and the evolution of various few-body observables; (iii) compare the infinite-time averages of observables with thermal averages and identify conditions that can lead to the thermalization of isolated quantum systems. Computer programs in Mathematica and Fortran 90 are provided.
EXERCISES (Fortran Codes)
Fortran_Exercise01
Fortran_Exercise02
Fortran_Exercise03
Fortran_Exercise04
Fortran_Exercise06
Fortran_Exercise07
Fortran_Exercise09
Fortran_Exercise12
Fortran_Exercise16
Fortran_Exercise17
Fortran_Exercise20
EXERCISES (Mathematica Codes)
Mathematica_Exercise01
Mathematica_Exercise02
Mathematica_Exercise03
Mathematica_Exercise04
Mathematica_Exercise05
Mathematica_Exercise06
Mathematica_Exercise07
Mathematica_Exercise09
Mathematica_Exercise11
**) An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains (paper)
American Journal of Physics 81, 450 (2013)
Codes developed with undergraduate students Kira Joel and Davida Kollmar. They can be used to:
(i) Diagonalize the Hamiltonian matrix.
(ii) Find the density of states and Inverse Participation Ratio for all eigenstates.
(iii) Study the time evolution of different initial states.
(iv) Analyze the effects of the symmetries of the system.
**) Quantum chaos: an introduction via chains of interacting spins-1/2 (paper)
American Journal of Physics 80, 246 (2012)
Codes developed with undergraduate student Aviva Gubin.
(i) Density of states, level spacing distribution and NPC for spin-1/2 chain.
(spin-1/2 chain Mathematica code)
(ii) Density of states, level spacing distribution, and NPC for Gaussian Orthogonal Ensembles.
(GOE Mathematica code)
(iii) Suggestions for exercises.
(Extra Exercises)