Publications

Order by: publication date number of citations

• Useful relations among the generators in the defining and adjoint representations of SU(N)

  Howard E. Haber

  SciPost Phys. Lect. Notes 21 (2021) · published 20 January 2021 | Toggle abstract · pdf

  There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc. Due to the existence of the completely symmetric tensor $d_{abc}$ that arises in the study of the SU(N) Lie algebra, one can also consider relations that involve the adjoint representation matrix, $(D^a)_{bc}=d_{abc}$. In this review, we summarize many useful relations satisfied by the defining and adjoint representation matrices of SU(N). A few relations special to the case of N=3 are highlighted.

  18 citations

• On model selection in cosmology

  Martin Kerscher, Jochen Weller

  SciPost Phys. Lect. Notes 9 (2019) · published 19 June 2019 | Toggle abstract · pdf

  We review some of the common methods for model selection: the goodness of fit, the likelihood ratio test, Bayesian model selection using Bayes factors, and the classical as well as the Bayesian information theoretic approaches. We illustrate these different approaches by comparing models for the expansion history of the Universe. In the discussion we highlight the premises and objectives entering these different approaches to model selection and finally recommend the information theoretic approach.

  18 citations

• Quantum computation with cat qubits

  Jérémie Guillaud, Joachim Cohen, Mazyar Mirrahimi

  SciPost Phys. Lect. Notes 72 (2023) · published 16 June 2023 | Toggle abstract · pdf

  These are the lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines". After a brief introduction to quantum error correction and bosonic codes, we focus on the case of cat qubits stabilized by a nonlinear multi-photon driven dissipation process. We argue that such a system can be seen as a self-correcting qubit where bit-flip errors are robustly and exponentially suppressed. Next, we provide some experimental directions to engineer such a multi-photon driven dissipation process with superconducting circuits. Finally, we analyze various logical gates that can be implemented without re-introducing bit-flip errors. This set of bias-preserving gates pave the way towards a hardware-efficient and fault-tolerant quantum processor.

  17 citations

• Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories

  Patrick Emonts, Erez Zohar

  SciPost Phys. Lect. Notes 12 (2020) · published 17 January 2020 | Toggle abstract · pdf

  In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced, by looking at the Gauss law from two different points of view: for the gauge field it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

  16 citations

• Many-body open quantum systems

  Rosario Fazio, Jonathan Keeling, Leonardo Mazza, Marco Schirò

  SciPost Phys. Lect. Notes 99 (2025) · published 14 August 2025 | Toggle abstract · pdf

  These lecture notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by reviewing the theoretical frameworks and methods used to describe and tackle open quantum many-body systems. We then discuss the use of dissipative processes to engineer many-body stationary states with desired properties and the emergence of dissipative phase transitions arising out of the competition between coherent evolution and dissipation. We review the dynamics of open quantum many body systems in the presence of correlated many-body dissipative processes, such as heating and many-body losses. Finally we provide a different perspective on open quantum many-body systems by looking at stochastic quantum trajectories, relevant for the case in which the environment represents a monitoring device, and the associated measurement-induced phase transitions.

  16 citations

• Lecture notes on Berry phases and topology

  Barry Bradlyn, Mikel Iraola

  SciPost Phys. Lect. Notes 51 (2022) · published 11 May 2022 | Toggle abstract · pdf

  In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to topological insulators.

  16 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 | Toggle abstract · 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.

  16 citations

• An introduction to axions and their detection

  Igor García Irastorza

  SciPost Phys. Lect. Notes 45 (2022) · published 29 March 2022 | Toggle abstract · pdf

  In these notes I try to introduce the reader to the topic of axions: their theoretical motivation and expected phenomenology, their role in astrophysics and as dark matter candidate, and the experimental techniques to detect them. Special emphasis is made in this last point, for which a relatively updated review of worldwide efforts and future prospects is made. The material is intended as an introduction to the topic, and it was prepared as lecture notes for Les Houches summer school 2021. Abundant references are included to direct the reader to deeper insight on the different aspects of axion physics.

  15 citations

• Dark Matter direct detection of classical WIMPs

  Jodi Cooley

  SciPost Phys. Lect. Notes 55 (2022) · published 20 May 2022 | Toggle abstract · pdf

  One of the highest priorities in particle physics today is the identification of the constituents of dark matter. This manuscript is a supplement to pedagogical lectures given at the 2021 Les Houches Summer School on Dark Matter. The lectures cover topics related to the direct detection of WIMP dark matter, including the distribution of dark matter, nuclear scattering, backgrounds, planning and designing of experiments, and a sampling of planned and ongoing experiments.

  15 citations

• Magnetisation and Mean Field Theory in the Ising Model

  Dalton A R Sakthivadivel

  SciPost Phys. Lect. Notes 35 (2022) · published 19 January 2022 | Toggle abstract · pdf

  In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

  14 citations