Instructor: Manas Kulkarni,

TA: Tamoghna Ray,

Prerequisites: Quantum Mechanics, Statistical Physics

Day/Time: Tuesday and Thursday, 4pm - 5:30pm


1.    General theory for Open Quantum systems
2.    Exactly solvable / quantum integrable systems
3.    Damped Quantum Harmonic Oscillator and multi-level systems
4.    Non-Hermitian Random Matrix Theory and Quantum Chaos
5.    Driven-Dissipative Quantum Systems and applications
6.    Matrix Product States for open quantum systems



Below are some suggested references. I will also be making additional notes.

1. Howard Carmichael, Statistical Methods in Quantum Optics 1. Master Equations and Fokker-Planck Equations (Springer)
2. Girish S. Agarwal, Quantum Optics (Cambridge University Press)
3. Heinz-Peter Breuer and Francesco Petruccione, The theory of open quantum systems (Oxford University Press)
4. Marlan O. Scully and M. Suhail Zubairy, Quantum optics (Cambridge University Press)
5. Fritz Haake, Sven Gnutzmann, Marek Kuś, Quantum signatures of chaos (Springer)
6. Simulation methods for open quantum many-body systems, Hendrik Weimer, Augustine Kshetrimayum, and Román Orús, Rev. Mod. Phys. 93, 015008  (2021)

Term paper (report + presentation) topics

Non-Markovian Open Quantum systems:

- Colloquium: Non-Markovian dynamics in open quantum systems, Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo, and Bassano Vacchini, Rev. Mod. Phys. 88, 021002  (2016)
- Dynamics of non-Markovian open quantum systems, Inés de Vega and Daniel Alonso, Rev. Mod. Phys. 89, 015001 (2017)

Matrix Product States for Lindblad Master Equations:

- Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems, F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004)
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems, Jian Cui, J. Ignacio Cirac, and Mari Carmen Bañuls, Phys. Rev. Lett. 114, 220601 (2015)

Measurement-Induced Phase Transitions

- Measurement-driven entanglement transition in hybrid quantum circuits, Yaodong Li, Xiao Chen, and Matthew P. A. Fisher, Phys. Rev. B 100, 134306 (2019)

- Measurement-Induced Phase Transitions in the Dynamics of Entanglement, Brian Skinner, Jonathan Ruhman, and Adam Nahum, Phys. Rev. X 9, 031009 (2019)

- Dynamical Purification Phase Transition Induced by Quantum Measurements, Michael J. Gullans and David A. Huse, Phys. Rev. X 10, 041020  (2020)


Grading Policy

Homework – 40 %
Term paper (report and presentation) – 30 %
Final Exam – 30 %