Introduction to Open Quantum Systems

Last modified by muratore@helsinki_fi on 2024/03/27 10:50

Introduction to Open Quantum Systems

Schedule

Location

Format

Scope

Tue. + Thu., 10–12

B322, Exactum building (Kumpula)

Lecture + Exercise

10 cr

The course addresses physicists and mathematicians at advanced undergraduate or graduate level. For physics students the course will provide an introduction to theory and examples of quantum systems interacting with their environment. For students of mathematics the course will provide an introduction into to an algebraic treatment of probability and Markov processes.

Content

  • probabilistic foundations of quantum mechanics
  • composite systems, entanglement
  • quantum channels alias completely positive maps
  • quantum Markov processes
  • Lindblad equation
  • repeated interaction systems
  • stochastic Schrödinger equation

Requirements

The course requires linear algebra and differential calculus as discussed in the basic courses. In addition, some very basic understanding of probability is needed. For physicists we recommend some pre-knowledge in quantum mechanics.

Literature

The main part of the course will rely on the following books:

  1. Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems, Oxford University Press, 2002
  2. Wiseman, H. M., Milburn, G. J.: Quantum Measurement and Control, Cambridge University Press, 2009

Course Organization

Lectures

06.09.2016–15.12.2016, weeks 36–42 and 44–50
every Tuesday and Thursday, 10–12,
room B322 in Exactum (Kumpula)

Exercises

every Tuesday, 09-10, room B321
 every Thursday, 09-10, room B322

Lecturers

Dmitry Golubev (Aalto),
Paolo Muratore-Ginanneschi (Helsinki),
Kay Schwieger (Helsinki) 

Presemo

The course as a dedicated presemo room (web space). To access this web space just follow the foregoing link.  Students are encouraged to use the presemo room for any civilized activity pertaining the course.

Lecture Notes

The lecture notes are grouped not in correspondence to actual lectures but by topics

Lecture 01: The Postulates of Quantum Mechanics 

Lecture 11: Completely Positive Semigroups and the Lindblad Equation

Lecture 02: Probability & Measurements

Lecture 12: Dynamics and the time asymptotic behavior of the evolution operator

Lecture 03: Dynamics by examples

Lecture 13: van Hove's weak coupling scaling limit

Lecture 04: Hilbert Spaces, Operators, and Tensor Products

Lecture 14: the Born approximation

Lecture 05: Subsystems, Commutants, Independence

Lecture 15: the Markov approximation and the Lindbladian

Lecture 06: Purification, Entanglement

Lecture 16: Linbladian dynamics of the Qubit

Lecture 07: Jaynes Cummings Hamiltonian I

Lecture 17: Linbladian dynamics of the Caldeira-Leggett model

Lecture 08: Jaynes Cummings Hamiltonian II

Lecture 18: Quantum jumps

Lecture 09: Completely Positive Maps, No-Cloning Theorem

Lecture 19: An overview of (Poisson) stochastic differential equations

Lecture 10: Kraus-Stinespring Representation, Indirect Measurement, Markov Processes

Lecture 20:

Exercises

 

 

 

 

 

 

 

 

 

 

 

News

CHANGE OF PLAN:

  • On 20.09 we will have exercise session as usual 09-10 (Kay Schwieger) and main lecture 10-12 (Paolo Muratore-Ginanneschi)
  • 22, 27, 29.09 lectures will be as follows: 09-11 main lecture (lecturer Kay Schwieger) 11-12 exercises and complements

Starting from the week of Monday 31/10 the exercises are on Tuesdays from 14:15-16:00 in room B119.

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