Publications

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• Ambitions for theory in the physics of life

  William Bialek

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

• Topological insulators and geometry of vector bundles

  Alexander S. Sergeev

  SciPost Phys. Lect. Notes 67 (2023) · published 12 April 2023 | Toggle abstract · pdf

  For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of eigenspaces determines the electric polarization, while their global twisting gives rise to the metallic surface states in topological insulators. These phenomena are central topics of the present notes. The shape of eigenspaces is also responsible for many intriguing physical analogies, which have their roots in the theory of vector bundles. We give an informal introduction to the geometry and topology of vector bundles and describe various physical models from this mathematical perspective.

• Normative approaches to neural coding and behavior

  Ann Hermundstad

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

• 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 | Toggle abstract · 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.

• The Higgs mechanism with diagrams: A didactic approach

  Jochem Kip, Ronald Kleiss

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

• Dark matter effective theory

  Joachim Brod

  SciPost Phys. Lect. Notes 38 (2022) · published 31 January 2022 | Toggle abstract · pdf

  Les Houches 2021 lectures on dark matter effective field theory (short course). The aim of these two lectures is to calculate the DM-nucleus cross section for a simple example, and then generalize to the treatment of general effective interactions of spin-1/2 DM. Relativistic local operators, the heavy-DM effective theory, the chiral effective Lagrangian, and nuclear effective operators are briefly discussed.

• Field theory of collinear and noncollinear magnetic order

  Oleg Tchernyshyov

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

• A brief tutorial on information theory

  Tarek Tohme, William Bialek

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