Advanced Topics in Theoretical Physics (Spring 2025)


It is a pleasure to announce this spring's Advanced Topics in Theoretical Physics course on Many-body physics. The course is divided into three 5-week modules, which will cover Lattice gauge theories, Density Functional Theory, and Active Matter. As always, the emphasis is on methods that can be used across all fields of physics.

Each module consists of four lectures and exercise sessions. Lectures will take place on Mondays at 11:15 - 13:00, followed by a study/exercise session from 13:45 - end. At the end of each module there is an exam. All exams are pass/fail, and you need to pass all three exams to receive credit (6EC) for the course.

Teaching is on location in person, with the location of this course rotating between the three institutes. The first module is in Amsterdam. Directions to the institutes can be found here: Amsterdam, Utrecht, Leiden. Students who do not have an OV-card from the Dutch government can have their travel costs reimbursed. Please contact the local coordinator (below) for details.

Please register here before the course begins, even if you do not take the course for credit. We cannot process your grade or send important notices if you do not register.

  • MODULE 1:

    Module 1: Symmetry, duality, and topology in lattice gauge theories
    Jasper van Wezel (Amsterdam)
    Lectures and exercises: Feb 3, 10, 17, 24
    Exam: March 3

    Location: Science Park G3.10, Amsterdam

    Abstract:
    Lattice gauge theories are prevalent both in high and low energy physics, either as discrete approximations to a continuous field theory, or as a direct implementation of lattice models. Besides their inherent interest, lattice gauge theories also provide a particularly nice background for illustrating the correspondence between quantum dynamics and classical equilibrium descriptions, the presence or absence of symmetry breaking phase transitions, the use of duality transformations, and the role of topological defects in mediating phase transitions.
    In this lecture series, we will follow one of the classic texts on lattice gauge theory and discover how all these aspects emerge from very simple building blocks. We will start from the famous Kramers-Wannier duality in the Ising model and, time permitting, end up with accessible lattice descriptions of confinement and the Kosterlitz-Thouless phase transition.

    Recommended prior knowledge:
    — [Necessary] Working knowledge of basic Quantum Field Theory.
    — [Useful] Some familiarity with spin systems in condensed matter theory.

  • MODULE 2:

    Module 2: Density Functional Theory
    Matthieu Verstraete (Utrecht)
    Lectures and exercises: Mar 10, 17, 24, 31
    Exam: Apr 7

    Location: TBA (Utrecht)

    Abstract: Density functional theory (DFT) is one of the most successful and widely used methods to explain and predict the physical properties of matter. It has enabled the discovery, e.g., of exotic high pressure phase transitions and new superconductors, and ushered in a new era of data-driven discovery of novel functional materials.

    DFT is based on standard quantum mechanics and classical electromagnetism, but attacks the many-body problem in an original and in principle exact way, through an (unknown but approximable) energy functional of the electronic density. It strikes an excellent balance between accuracy and computational cost, avoiding the exponential explosion with size of the “naïve” Schrödinger equation.

    We will introduce the basic theoretical foundations, and see which approximations are needed to use DFT for realistic crystals and molecules (up to 100s or 1000s of atoms). The lectures will be followed by conceptual exercises and a hands-on introduction to a DFT simulation software, on a Utrecht teaching computer cluster, or on your laptops if they have a working compiler suite (C, Fortran, C++).

    Prerequisites: — Quantum Mechanics — Basic Solid state Physics Useful: — Familiarity with command line software (e.g. linux or MacOS/Windows terminal shells)

  • MODULE 3:

    Module 3: Active Matter
    Yann-Edwin Keta (Leiden)
    Lectures and exercises: Apr 14, May 12, 19, 26
    Exam: June 2
    (No class: April 21 is Easter holiday, April 28 is UvA holiday, May 5 is Liberation day)

    Location: TBA (Leiden)

    Abstract:
    Active matter has emerged as an important class of materials composed of active particles.
    These particles are self-driven units, individually capable of using available energy to generate forces.
    This broad definition applies to a wide array of synthetic and living elements at all scales, from subcellular elements, to self-driven colloids, to birds and humans.
    Due to their continual generation of forces, these elements escape the rules of equilibrium statistical mechanics, and display a wealth of surprising phenomena which challenge our conceptions of equilibrium phases and dynamics [1].
    This lecture introduces analytical and numerical tools, rooted in nonequilibrium statistical mechanics, to describe and understand the structural and dynamical features of these systems.
    We will first study stochastic differential equations as the natural framework to describe systems subject to fluctuations, with a specific focus on Langevin-like equations, and their representation as Fokker-Planck equations [2].
    This will enable to introduce active Brownian particles (ABPs) which is a widely used model to represent crawling living cells and self-propelled synthetic colloids.
    We will first explore its properties numerically by integrating the stochastic dynamics of this model using molecular dynamics tools [3].
    We will focus on two emergent features: velocity correlations and spontaneous motility-induced phase separation (MIPS).
    We will rationalise the former feature with a theory based on linear elasticity [4], and the latter with a mean-field active field theory [5].
    Finally we will study large deviation theory and how this provides a natural framework for both equilibrium and nonequilibrium statistical mechanics [6].
    Within this framework we will study the concept of dynamical phase transitions in biased ensembles of trajectories, and will characterise one of these in ABPs [7].

    [1] Active Matter and Nonequilibrium Statistical Physics. (Oxford University Press, 2022).
    [2] Gardiner, C. W. Handbook of Stochastic Methods: For Physics, Chemistry, and the Natural Sciences. (Springer, 2004).
    [3] Mannella, R. Integration of stochastic differential equations on a computer. Int. J. Mod. Phys. C 13, 1177 (2002).
    [4] Henkes, S., Kostanjevec, K., Collinson, J. M., Sknepnek, R. & Bertin, E. Dense active matter model of motion patterns in confluent cell monolayers. Nat. Commun. 11, 1405 (2020).
    [5] Cates, M. E. & Tailleur, J. Motility-Induced Phase Separation. Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
    [6] Touchette, H. The large deviation approach to statistical mechanics. Physics Reports 478, 1 (2009).
    [7] Keta, Y.-E., Fodor, É., van Wijland, F., Cates, M. E. & Jack, R. L. Collective motion in large deviations of active particles. Phys. Rev. E 103, 022603 (2021).

     

  • CONTACT:

    Dr. Lars Fritz
    Institute for Theoretical Physics
    Utrecht University
    Princetonplein 5
    3584 CC Utrecht
    tel: +31 30 253 3880
    e-mail: l.fritz@uu.nl

    Prof. Koenraad Schalm
    Instituut-Lorentz for Theoretical Physics
    Leiden University
    Niels Bohrweg 2
    2335 CA Leiden
    email: kschalm@lorentz.leidenuniv.nl

    Dr. Clelia de Mulatier
    Institute for Theoretical Physics
    University of Amsterdam
    Science Park 904
    1098 XH Amsterdam
    e-mail: c.m.c.demulatier@uva.nl