Instructor: Manas Kulkarni,

TA:  Sparsh Gupta,

Prerequisites: Quantum Mechanics, Statistical Physics

Day/Time: Tuesday and Thursday, 2pm - 3:30pm

Venue: Emmy Noether Room


1. General theory for Open Quantum systems

2. Exactly solvable / quantum integrable systems

3. Damped Quantum Harmonic Oscillator and multi-level systems

4. Matrix Product States for open quantum systems

5. Driven-Dissipative Quantum Systems and applications 

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

Floquet states in open quantum systems

- Mori, T., 2023. Floquet states in open quantum systems. Annual Review of Condensed Matter Physics, 14, pp.35-56.
- Schnell, A., Eckardt, A. and Denisov, S., 2020. Is there a floquet lindbladian?. Physical Review B, 101(10), p.100301.
- Schnell, A., Denisov, S. and Eckardt, A., 2021. High-frequency expansions for time-periodic Lindblad generators. Physical Review B, 104(16), p.165414.

 Matrix Product States for Open Quantum Systems

- 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)
- Schollwöck, Ulrich. "The density-matrix renormalization group in the age of matrix product states." Annals of physics 326.1 (2011): 96-192.
- Prosen, T. and Žnidarič, M., 2009. Matrix product simulations of non-equilibrium steady states of quantum spin chains. Journal of Statistical Mechanics: Theory and Experiment, 2009(02), p.P02035.

Quantum circuits and Measurement-Induced Phase Transitions

- Li, Yaodong. Measurement-Induced Phase Transitions in Quantum Circuits. eScholarship, University of California, 2022.
- 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 %