Publications

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The Higgs mechanism with diagrams: A didactic approach

Jochem Kip, Ronald Kleiss

SciPost Phys. Lect. Notes 88 (2024) · published 14 October 2024 | · pdf

We present a paedagogical treatment of the electroweak Higgs mechanism based solely on Feynman diagrams and S-matrix elements, without recourse to (gauge) symmetry arguments. Throughout, the emphasis is on Feynman rules and the Schwinger-Dyson equations; it is pointed out that particular care is needed in the treatment of tadpole diagrams and their symmetry factors.
A brief tutorial on information theory

Tarek Tohme, William Bialek

SciPost Phys. Lect. Notes 87 (2024) · published 23 September 2024 | · pdf

At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial, lightly edited. It covers basic definitions and context rather than detailed calculations. We hope to have maintained the informality of the presentation, including exchanges with the students, while still being useful.
An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation

Jan Naumann, Erik Lennart Weerda, Matteo Rizzi, Jens Eisert, Philipp Schmoll

SciPost Phys. Lect. Notes 86 (2024) · published 10 September 2024 | · pdf

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results.
Field theory of collinear and noncollinear magnetic order

Oleg Tchernyshyov

SciPost Phys. Lect. Notes 85 (2024) · published 5 September 2024 | · pdf

These lecture notes from the 2023 Summer School "Principles and applications of symmetry in magnetism" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.
Ambitions for theory in the physics of life

William Bialek

SciPost Phys. Lect. Notes 84 (2024) · published 15 August 2024 | · pdf

Theoretical physicists have been fascinated by the phenomena of life for more than a century. As we engage with more realistic descriptions of living systems, however, things get complicated. After reviewing different reactions to this complexity, I explore the optimization of information flow as a potentially general theoretical principle. The primary example is a genetic network guiding development of the fly embryo, but each idea also is illustrated by examples from neural systems. In each case, optimization makes detailed, largely parameter-free predictions that connect quantitatively with experiment.

1 citation
Normative approaches to neural coding and behavior

Ann Hermundstad

SciPost Phys. Lect. Notes 83 (2024) · published 13 August 2024 | · pdf

These are a brief set of lectures notes for lectures given at the Les Houches Summer School in Theoretical Biological Physics in July 2023. In these notes, I provide an introduction to some of the theoretical frameworks that are used to understand how the brain makes sense of incoming signals from the environment to ultimately guide effective behavior. I then discuss how we can apply these frameworks to understand the structure and function of real brains.
The quantum Ising chain for beginners

Glen Bigan Mbeng, Angelo Russomanno, Giuseppe E. Santoro

SciPost Phys. Lect. Notes 82 (2024) · published 14 June 2024 | · pdf

We present here various techniques to work with clean and disordered quantum Ising chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. In particular, we analyze the form of the ground state and excitations of the model, relating them to the symmetry-breaking physics, and illustrate aspects connected to calculating dynamical quantities, thermal averages, correlation functions, and entanglement entropy. A few problems provide simple applications of the techniques.

7 citations
KPZ fluctuations in finite volume

Sylvain Prolhac

SciPost Phys. Lect. Notes 81 (2024) · published 12 June 2024 | · pdf

These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects describing the relaxation to its stationary state of a finite system starting from a given initial condition. The second part is more specifically devoted to an approach allowing to express in a simple way the statistics of the current in the totally asymmetric simple exclusion process in terms of a contour integral on a compact Riemann surface, whose infinite genus limit leads to KPZ fluctuations in finite volume.

2 citations
Methods and conversations in (post)modern thermodynamics

Francesco Avanzini, Massimo Bilancioni, Vasco Cavina, Sara Dal Cengio, Massimiliano Esposito, Gianmaria Falasco, Danilo Forastiere, Nahuel Freitas, Alberto Garilli, Pedro E. Harunari, Vivien Lecomte, Alexandre Lazarescu, Shesha G. Marehalli Srinivas, Charles Moslonka, Izaak Neri, Emanuele Penocchio, William D. Piñeros, Matteo Polettini, Adarsh Raghu, Paul Raux, Ken Sekimoto, Ariane Soret

SciPost Phys. Lect. Notes 80 (2024) · published 20 March 2024 | · pdf

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues.

7 citations
Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings

Wenxuan Zou, Haiping Huang

SciPost Phys. Lect. Notes 79 (2024) · published 20 February 2024 | · pdf

Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners to access the essence of this tool and the underlying physics. Here, we give a pedagogical introduction of this method in a particular example of random neural networks, where neurons are randomly and fully connected by correlated synapses and therefore the network exhibits rich emergent collective dynamics. We also review related past and recent important works applying this tool. In addition, a physically transparent and alternative method, namely the dynamical cavity method, is also introduced to derive exactly the same results. The numerical implementation of solving the integro-differential mean-field equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem.

2 citations

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