Lectures
Summer Term 2024:
Summer Term 2023:
Winter Term 2022:
Advanced Student Seminar: Nonequilibrium Field Theory
Primary Areas of Specialization: Solid State Theory / QFT and General Relativity
The goal of the seminar is to get familiar with an advanced topic in nonequilibrium field theory. Under guidance provided by the lecturers, the students learn to :
survey the literature on a current topic of research,
extract the central message of a publication and relevant background information,
present scientific results in front of a general audience.
Seminar:
The seminar is jointly organized by Prof. Dr. Sebastian Diehl and Priv.-Doz. Dr. Michael Buchhold. The topics will be discussed and handed out at the beginnig of the semester. We will meet on October 18 at 10AM in lecture hall E0.03 in the Institute for Theoretical Physics.
The seminar talks will take place in a conference like atmosphere on February 6 - 8 2023 between 9AM and 2PM.
Topics:
Part I: Theory background
A -- Langevin equation and Martin-Siggia-Rose functional integral
B -- Rare trajectories, noise activation and escape problems
C -- Keldysh functional integral for nonequilibrium quantum systems
Part II: Application to nonequilibrium criticality
A -- Dynamics at equilibrium critical phenomena
B -- Directed percolation and Rydberg gases
C -- Kardar-Parisi-Zhang universality in cold atoms
Part III: Special topics
A -- Floquet formalism
B -- Fluctuation-dissipation relations out of equilibrium
Literature:
A. Altland, B. Simons, "Condensed Matter Field Theory", Cambridge University Press (2010)
A. Kamenev "Field Theory of Non-Equilibrium Systems" Cambridge University Press (2011)
Summer Term 2022:
Nonunitary Quantum Many-Body Dynamics: Quantum Circuits and Quantum Error Correcting Codes
Primary Areas of Specialization: Solid State Theory / Quantum Information Science and Technology / Elective
The goal of the course is to get familiar with the interplay of unitary time evolution, measurements and decoherence in elementary quantum circuits (bosonic and fermionic Gaussian states and Clifford circuits). These represent the basic building blocks for many modern applications in quantum computing and quantum error correction.
Lectures:
The lecture will be held in presence and will be broadcasted live via zoom. The time for the lectures is Monday 4PM and the first appointment for the summer term is on April 04. Interactions among the students and with the lecturer/tutor will be facilitated via a Slack workspace. The details will be provided in our first lecture (both in presence or zoom) .
Practice groups:
The topic of the lecture provides a great opportunity to design students projects, which are close to current research and applications. The projects will be handed out to groups of students and may include analytical approaches (e.g. quantum Kalman filter, Weingarten calculus), numerical simulations (Clifford circuits, Gaussian fermions) or experiments on commercial quantum computers. The project tasks will be worked out by the students during the semester and be presented towards the end of the term. We will discuss this opportunity, and the corresponding dates for the presentation, in the first lecture.
Contents:
Basics of quantum circuits
Gaussian states of fermions and bosons, qubits, stabilizer states, pure and mixed quantum states, representations of pure and mixed states, entanglement entropy, mutual information, correlation functions
Dynamics in quantum circuits
Unitary time-evolution, discrete and continuous Hamiltonian evolution, unitary quantum gates, projective measurements, weak continuous measurements, imperfect measurements, environmental decoherence
Applications
Digital and analog quantum computers, quantum error correcting codes, entanglement phase transitions, information scrambling
Literature:
M. A. Nielsen, I. L. Chuang, "Quantum Computation and Quantum Information", Cambridge University Press (2010)
X.-G. Wen, D.-L. Zhou, X. Chen, "Quantum Information meets Quantum Matter" Springer (2019)
Summer Term 2021:
Nonequilibrium Field Theory
Primary Areas of Specialization: GR/QFT and Solid State Theory
The course extends classical and quantum field theory to nonequilibrium settings, focussing on collective phenomena in systems of many degrees of freedom.
Online lectures:
The lecture will be broadcasted live via zoom. The time for the lectures is Monday 2:00 PM and the first appointment for the summer term is on April 12. Interactions among the students and with the lecturer/tutor will be facilitated via a Slack workspace. The details will be provided in our first zoom meeting via this link.
Practice groups:
The content of the lecture provides a opportunity to hand out individual projects in both quantum and classical nonequilibrium physics, which are worked out by the students and presented towards the end of the term. We will discuss this opportunity, and the corresponding dates for the presentation, in the first lecture.
Contents:
Classical Nonequilibrium Systems
Langevin equation, Martin-Siggia-Rose functional, rare fluctuations, noise activation, nonequilibrium phase transitions, directed percolation, Kardar-Parisi-Zhang equation, perturbation theory and renormalization group approach
Quantum Nonequilibrium Systems
stochastic Schrödinger equation (SSE), quantum master equation, Keldysh path integral, Floquet formalism, driven-dissipative quantum systems, measurement-induced dynamics
Literature:
A. Altland, B. Simons, "Condensed Matter Field Theory", Cambridge University Press (2010)
A. Kamenev "Field Theory of Non-Equilibrium Systems" Cambridge University Press (2011)