The Mathematical Physics at Leeds (MaPLe) seminar series is aimed at bringing together researchers at any level from across the University of Leeds — from both mathematics and physics departments alike — to give talks on themes in mathematical physics, broadly construed. On occasion, we also host seminars by researchers from outside the University of Leeds.
The current organisers are Cas Chaudhuri (mmgch[at]leeds.ac.uk) and Nora Gavrea (lxgz1729[at]leeds.ac.uk). If you would like to give a seminar or want to be added to the chat and the mailing list, please get in touch.
The seminar takes place every other Tuesday at 10:00 AM in the MALL.
Talks from the 2024 series can be found at: https://anupanand.space/maple/.
The induced connection is a natural connection on a subbundle of a vector bundle. In physics, it is known as the Berry connection, and its parallel transport operators give rise to the Berry phase. In this talk I will explain exactly what the Berry/induced connection is and present some work I have done on finding numerical approximations to its parallel transport. This will lead to some interesting(?) questions for the algebraists in the audience!
The quest to understand out-of-equilibrium behaviour of complex quantum systems represents one of the frontiers of contemporary quantum science. For a long time, the prevailing belief has been that complex quantum systems, comprising many interacting degrees of freedom, all suffer the same inevitable fate: that of thermalisation, whereby the system relaxes towards a featureless thermal state, completely "forgetting" its initial condition. However, a flurry of recent works has unearthed a new paradigm of behaviour in many well-known physical systems, including Rydberg atoms, lattice gauge theories, and certain kinds of frustrated magnets. Such systems have been understood to possess a subtle breakdown of ergodicity, now commonly known as "quantum many-body scars". Quantum many-body scars exhibit fascinating properties, such as extreme sensitivity to initial conditions: while a system initialised randomly undergoes chaotic dynamics and thermalisation, specific initial conditions can result in persistent dynamical revivals, surpassing native thermalisation timescales. The discovery of quantum many-body scars has not only deepened our understanding of many-body quantum mechanics, but it also has direct practical relevance for improving the control over the delicate physical phenomena underpinning quantum technologies. In this talk, I will present a pedagogical overview of this fascinating new field of physics, highlighting a few of the remaining mysteries for theory and future experiments.
We take a look at several random geometric graphs (RGG) with increasing levels of complexity, starting from the classical Gilbert disc model with fixed radius and up to the weight-dependent random connection model. At each step, we discuss the heuristics of what the newly added complexity changes in the behaviour of the models and how it affects the criticality of the largest connected component and the typical distance between two points of this component.
