Nonequilibrium Quantum Matter
This course introduces theoretical ideas and toolkits for understanding quantum matter away from equilibrium, with a focus on quantum transport, driven quantum dynamics, and open quantum systems.
Students will learn a compact set of theoretical tools for describing quantum systems away from equilibrium. By the end of the course, students should be able to:
1. Identify the physical mechanism driving a quantum system out of equilibrium.
2. Analyze simple coherent quantum transport and understand quantum noise and current fluctuations at a basic level.
3. Use Floquet theory to describe periodically driven quantum systems and construct simple effective Hamiltonians for high-frequency driving.
4. Explain Floquet engineering, topological pumping, and parametric driving at the model level.
5. Use density matrices and Lindblad master equations to describe decoherence and dissipation.
Modern research in condensed matter physics, AMO physics, and quantum technology increasingly deals with quantum systems beyond thermal equilibrium. They may be driven by external fields, connected to reservoirs, subjected to measurement, or influenced by noise and dissipation. This course introduces key theoretical ideas for understanding quantum matter away from equilibrium. It is organized around three broad routes to nonequilibrium behavior: transport generated by thermodynamic bias, coherent evolution under time-dependent Hamiltonians, and irreversible dynamics due to dissipation, decoherence, or measurement. Through model-based descriptions of coherent quantum transport, Floquet dynamics, parametric driving, and open quantum systems, students will develop physical intuition for both theoretical and experimental setups. The course is designed as a bridge between standard graduate quantum mechanics and the modern research literature, preparing students for research in nonequilibrium quantum physics, condensed matter physics, and quantum dynamics.
Introduction to concepts
Block I: Quantum Transport (3 weeks)
- Coherent transport, scattering approach, and Landauer formula
- Quantum noise in mesoscopic transport
- Introduction to nonequilibrium Green’s functions, Keldysh formalism
Block II: Driven quantum dynamics (5 weeks)
- Time-dependent Hamiltonians, Rabi oscillation, Landau-Zener transition
- Floquet theorem, Magnus expansion, stroboscopic dynamics and micromotion
- Floquet engineering of quantum matter and Floquet control of collective modes
- Parametric driving, resonance, and amplification
- Introduction to quantum thermal machines and quantum batteries
Block III: Open quantum systems (3 weeks)
- Reduced density matrices, quantum channels, Lidbladian dynamics
- Quantum trajectories, monitored quantum systems, non-Hermitian dynamics
- Dissipative state preparation and reservoir engineering
- Non-Markovian dynamics, Caldeira-Leggett model, structured reservoir and memory effects
Student presentations on research topics
40% Homework
30% Progress tests
30% Final presentation
Quantum mechanics (including second quantization), statistical mechanics, and condensed matter physics
The students are encouraged to take in parallel A229: Statistical Fluctuations and Elements of Physical Kinetics or A230: Quantum Optics for Qubits
- Nazarov and Blanter. Quantum Transport: Introduction to Nanoscience. Cambridge University Press; 2009.
- Review papers: Oka and Kitamura, “Floquet engineering of quantum materials,” Annual Review of Condensed Matter Physics 10, 387, 2019; Eckardt, “Colloquium: Atomic quantum gases in periodically driven optical lattices,” Reviews of Modern Physics 89, 011004, 2017.
-Breuer and Petruccione, The Theory of Open Quantum Systems (Oxford, 2007; online edn, Oxford Academic, 1 Feb. 2010).
New for AY2026