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OsloMet: Mathematics 4000 and Quantum Information Technology
Augsburg University (2012-2018):

WS12/13, WS13/14, SS16 Dynamics of Nonlinear and Chaotic systems

(note that the transparencies are mere illustrations; most of the lectures went on the blackboard)

  • [Lecture1]: Introduction, Baker's map, periodic orbits, stability

  • [Lecture3]: Maps
  • [add. to Lecture3]

  • [Lecture5]: Stable and unstable manifolds (Henon map); Lyapunov exponents for maps (I)
  • [add. to Lecture5]

  • [Lecture6]: Lyapunov exponents for maps (II)

  • [Lecture7]: Fractals and fractal dimension
  • [add. to Lecture7]

  • [Lecture8]: Fractals in dynamics
  • [add. to Lecture8]

  • [Lecture9]: Fractals in dynamics (part2)

  • [Lecture10]: Two-dimensional nonlinear dynamics: fixed points and limit cycles

  • [Lecture11]: Andronov-Hopf bifurcations

  • [Lecture12]: Lyapunov exponents for continuous-time systems

  • [Lecture13]: (Unstable) periodic orbits of continuous-time systems

  • [Lecture14]: Control of chaos (part I)

  • [Lecture11old]: Controlling chaos: the OGY-method

  • [Projects]
  • ["Chaos in learning a simple two-person game", PNAS 99, 4748 (2002)]
  • ["Evolutionary dynamics for bimatrix games: A Hamiltonian system?", J. Math. Biol. 34, 675 (1996)]
  • ["Generalized synchronization of chaos in directionally coupled chaotic systems", Phys. Rev. E 51, 980 (1995)]
  • ["Detecting unstable periodic orbits in chaotic continuous-time dynamical systems", Phys. Rev. E 64, 026214 (2001)]
  • ["Leaping into Lyapunov space", SciAm, September 1991, p. 178]
  • ["Non-linear autonomous systems of differential equations and Carleman linearization procedure", J. Math. Anal. Appl. 2, 601 (1980)]

    SS15 Theoretical concepts and simulations in material science

  • [Lecture1]: Course description, numerical precision

  • [Lecture2]: Numerical precision and scaling of errors in computations
  • [Nice reading after lecture2]: David Goldberg, What Every Computer Scientist Should Know About Floating Point Arithmetic (1991)

  • [Lecture3]: Random numbers in computer simullations
  • [Addendum to Lecture3]: Transformation of random variables
  • [Nice reading after lecture3]: A. Leike, Demonstration of the Exponential Decay Law using Beer Froth (2002)

  • [Lecture4]: Simulations of random walks, Numerical integration: Trapezoid & Simpson's rules
  • [Addendum to Lecture4]: Error analysis of trapezoid & Simpson's rules

  • [Lecture5]: Gaussian quadratures

  • [Lecture6]: Differentiation, polynimial interpolation

  • [Lecture7]: Least squares method, Newton & Newton-Raphson methods

  • [Lecture8]: Integration of ODEs, Euler & RK methods

  • [Lecture9]: Integration of ODEs: advanced methods
  • [Addendum to Lecture 9]

  • [Lecture10]: Partial differential equations: Part I

  • [Lecture11]: Partial differential equations: Part II
  • [Addendum to Lecture11]: Illustrations

  • [Lecture12]: Partial differential equations: Part III
  • [Addendum to Lecture12]: Illustrations

  • [Lecture13]: Monte-Carlo methods: Metropolis algorithm
  • [Addendum to Lecture13]

  • [Lecture14]: Monte-Carlo methods, deposition models

  • [Lecture15]: Wang-Landau sampling
  • [Addendum to Lecture15]

    (the rest went on the blackboard)

    SS15, WS17, SS18 Basics of Quantum Information and Computation

  • [Lecture1]: Classical Information (part 1)
  • [Sup. to Lecture1]

  • [Lecture2]: Classical Information (part 2)

  • [Exercises1] [Solution to Exercises1]

  • [Lecture3 (first part)]: Classical Information (part 3, final)
  • [Lecture3 (second part)]: Qbit
  • [Sup. to Lecture3]

  • [Lecture4]: Single-bit gates, two-bits states & gates

  • [Exercises2] [Solution to Exercises2]

  • [Lecture5]: Cotrolled-U gates, No-cloning theorem & quantum teleportation

  • [Lecture6]: Quantum teleportation, ebit, & clasical simulations with quantum circuits

  • [Lecture7]: Quantum parallelism, Deutsch's & the Deutsch-Jozsa algorithms, the Fourier transform with a quantum circuit (brief discussion)

  • [Exercises3] [Solution to Exercises3] [Addendum to Exercises3]: The CHSH game

  • [Lecture8]: Crash course on quantum mechanics (math. foundation) (part 1)

  • [Lecture9]: Crash course on quantum mechanics (math. foundation) (part 2)

  • [Lecture10]: POVM measurements

  • [Lecture11]: Density matrix
  • [Addendum to Lecture11]: Schmidt decomposition

  • [Exercises5] [Solution to Exercises1]

  • [Lecture12]: Bell's inequality, local realism

  • [Lecture13]: Intro to computer science: I. Turing machine and circuits
  • [Sup. to Lecture13: See the Turing machine at work]

  • [Exercises6] [Solution to Exercises6]

  • [Lecture14]: Intro to computer science: II. Complexity classes, reversible computations, & back to quantum gates

  • [Exercises7] [Solution to Exercises7]

  • [Lecture15]: Universal quantum gates
  • [Addendum to Lecture15]: Transformation of SU(2) to a controlled single-qubit unitary

  • [Exercises8] [Solution to Exercises8]

  • [Lecture16]: Approximation of single-qubit unitaries with a universal set of gates
  • [see also a relevant discussion here]

  • [Lecture17]: Propagation of quantum systems on quantum computers (Trotter decomposition)

  • [Lecture18]: Quantum Fourier transform

  • [Lecture19]: Phase estimator (a step toward Schor's algorithm); Grover's algorithm

  • [Lecture20]: Quantum search as quantum simulation

  • [Exercises10] [Solution to Exercises10]

  • [Lecture21]: Quantum operations and channels

  • [Projects (2018)]

  • "Quantum teleportation" by Farzad Schafighpur

  • "Coin flipping by telephone: A protocol for solving impossible problems" by Milan Harth

  • "Quantum random access memory" by Carsten Neumann

  • "Matrix prodcut states" by Jakob Bonart

  • "An adaptive attack on Wiesners quantum money" by Thomas Gimpel and Marius Gebhardt

  • "Zero knowledge proofs" by Sebastian Angermann

    WS12/13, WS14/15 Non-equlibrium Statistical Physics

  • [Lecture1]: Mathematical foundations of statistical physics: Hamiltonian dynamics (Liouvilles's, Birkhoff-Khinchin's, & Gromov's "Non-Squeezing" theorems)

  • [Lecture2]: Mathematical foundations of statistical physics: Measure on a surface of constant energy, structure functions, ergodicity, & reduction to probailities

  • [Lecture3]: Mathematical foundations of statistical physics: Classical canonical typicality by Khinchin

  • [Lecture4]: Mathematical foundations of statistical physics: Quantum canonical typicality & eigenstates thermalization hypothesis (ETH)
  • [addendum to Lecture4]: Shnirelman's theorem & a billiard with a needle

  • [Lecture5]: Mathematical foundations of statistical physics: Forces, thermodynamical functions and the Second Law by Khinchin

  • [Lecture6]: 'Linear' non-equlibrium statistical mechanics: fluxes, affinities, & phenomenological coefficients
  • [addendum to Lecture6]

  • [Lecture7]: 'Linear' non-equlibrium statistical mechanics: Onsager's reciprocal relations (part I)

  • [Lecture8]: 'Linear' non-equlibrium statistical mechanics: Onsager's reciprocal relations (part II), thermoelectrical effects

  • [Lecture9]: 'Linear' non-equlibrium statistical mechanics: Minimal-entropy-production states, stability of states

  • [Lecture10]: Stability of non-equlibrium states (part I)

  • [Lecture11]: Stability of non-equlibrium states (part II). Chemical systems (part I)

  • [Lecture12]: Chemical systems (part II)

  • [Lecture13]: Chemical systems far from equlibrium (Schogl model, Lottka-Volterra model)

  • [Lecture14]: Periodic chemical reactions (BZ-reaction, glycolisis in yeasts)

  • [Lecture15]: Periodic chemical reactions: Hopf bifurcation

  • [Lecture16]: Evolutionary games

  • [Lecture17]: Stochastic kinetics of finite checmical systems: Ideology

  • [Lecture18]: Stochastic kinetics of finite checmical systems: Master equation (part I)
  • [addendum to Lecture18]: Radioactive decay with the Master equation

  • [Lecture19]: Brusselator with the Master equation. Gillespie's algorithm (part I)

  • [Lecture20]: Gillespie's algorithm (part II)
  • [addendum to Lecture20]: Brusselator with Gillespie's algorithm

  • [Lecture21]: Evolutionary games in finite populations: Master equation approach

  • [Lecture22]: Evolutionary games in finite populations: selection-imitation process (Moran and the likes)

  • [Lecture23]: Gene transcriptional regulators: repressilator and the likes

  • [Student projects (2016)]

  • "Why Imitate, and If So, How?" by Manuel Milling and Severin Wunsch

  • "Stochastic Simulations of the Oregonator:The Gillespie-Algorithm" by Marco Bussolera and Christoph Appel

  • "Evolutionary games of condensates in coupled birth-death processes" by Simon Kirschler and Asmar Nayis

  • "Generalized Nyquist theorem" by Stefan Gorol and Dominikus Zielke

    SS16 Seminar "Quantum channels & open quantum systems: a mathematical foundation"

  • [Lecture1]: Observables, density matrix, measurements (projective & POVMs)

  • [Lecture2]: Density matrix, bipartite systems, entanglement

  • [Lecture3]: Evolution, completely positive maps and quantum channels

  • [Lecture4]: Representations of quantum channels
  • [Problems to solve]

    (then went on a blackboard)

    [Oslo Metropolitan University] [TKD] [Department of Computer Science]
    last modified on Sunday, 25-Sep-2022 14:03:22 UTC by Sergey Denisov