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