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

• 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

• 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.

  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

• 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

• 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

• 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

• 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.

  15 citations

• Dark matter in astrophysics/cosmology

  Anne M. Green

  SciPost Phys. Lect. Notes 37 (2022) · published 25 January 2022 | Toggle abstract · pdf

  These lecture notes aim to provide an introduction to dark matter from the perspective of astrophysics/cosmology. We start with a rapid overview of cosmology, including the evolution of the Universe, its thermal history and structure formation. Then we look at the observational evidence for dark matter, from observations of galaxies, galaxy clusters, the anisotropies in the cosmic microwave background radiation and large scale structure. To detect dark matter we need to know how it's distributed, in particular in the Milky Way, so next we overview relevant results from numerical simulations and observations. Finally, we conclude by looking at what astrophysical and cosmological observations can tell us about the nature of dark matter, focusing on two particular cases: warm and self-interacting dark matter.

  14 citations

• The WIMP paradigm: Theme and variations

  Jonathan L. Feng

  SciPost Phys. Lect. Notes 71 (2023) · published 13 June 2023 | Toggle abstract · pdf

  WIMPs, ↑ weakly-interacting massive particles, have been leading candidates for particle dark matter for decades, and they remain a viable and highly motivated possibility. In these lectures, I describe the basic motivations for WIMPs, beginning with the WIMP miracle and its under-appreciated cousin, the discrete WIMP miracle. I then give an overview of some of the basic features of WIMPs and how to find them. These lectures conclude with some variations on the WIMP theme that have by now become significant topics in their own right and illustrate the richness of the WIMP paradigm.

  14 citations