list 10 sequencias
assignment Nível: Introdutório
label Física
chat_bubble_outline Idioma: Inglês
card_giftcard 320 pontos
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Informações principais

credit_card Free accesso
verified_user Certificado pago
timer 40 total de horas

Sobre o conteúdo

In this course you will learn a whole lot of modern physics (classical and quantum) from basic computer programs that you will download, generalize, or write from scratch, discuss, and then hand in. Join in if you are curious (but not necessarily knowledgeable) about algorithms, and about the deep insights into science that you can obtain by the algorithmic approach.

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Programa de estudos

  • Week 1 - Monte Carlo algorithms (Direct sampling, Markov-chain sampling)
    Dear students, welcome to the first week of Statistical Mechanics: Algorithms and Computations!
    Here are a few details about the structure of the course: For each week, a lecture and a tutorial videos will be presented, together with a downloadable copy o...
  • Week 2 - Hard disks: From Classical Mechanics to Statistical Mechanics
    In Week 2, you will get in touch with the hard-disk model, which was first simulated by Molecular Dynamics in the 1950's. We will describe the difference between direct sampling and Markov-chain sampling, and also study the connection of Monte Carlo and Molecu...
  • Week 3 - Entropic interactions and phase transitions
    After the hard disks of Week 2, in Week 3 we switch to clothe-pins aligned on a washing line. This is a great model to learn about the entropic interactions, coming only from statistical-mechanics considerations. In the tutorial you will see an example of a ty...
  • Week 4 - Sampling and integration
    In Week 4 we will deepen our understanding of sampling, and its connection with integration, and this will allow us to introduce another pillar of statistical mechanics (after the equiprobability principle): the Maxwell and Boltzmann distributions of velocitie...
  • Week 5 - Density matrices and Path integrals (Quantum Statistical mechanics 1/3)
    Week 5 is the first episode of a three-weeks journey through quantum statistical mechanics. We will start by learning about density matrices and path integrals, fascinating tools to study quantum systems. In many cases, the Trotter approximation will be useful...
  • Week 6 - Lévy Quantum Paths (Quantum Statistical mechanics 2/3)
    In Week 6, the second quantum week, we will introduce the properties of bosons, indistinguishable particles with peculiar statistics. At the same time, we will also go further by learning a powerful sampling algorithm, the Lévy construction, and in the homewor...
  • Week 7 - Bose-Einstein condensation (Quantum Statistical mechanics 3/3)
    At the end of our quantum journey, in Week 7, we discuss the Bose-Einstein condensation phenomenon, theoretically predicted in the 1920's and observed in the 1990's in experiments with ultracold atoms. In the path-integral framework, an elegant description of ...
  • Week 8 - Ising model - Enumerations and Monte Carlo algorithms
    In Week 8 we come back to classical physics, and in particular to the Ising model, which captures the essential physics of a set of magnetic spins. This is also a fundamental model for the development of sampling algorithms, and we will see different approache...
  • Week 9 - Dynamic Monte Carlo, simulated annealing
    Continuing with simple models for spins, in Week 9 we start by learning about a dynamic Monte Carlo algorithm which runs faster than the clock. This is easily devised for a single-spin system, and can also be generalized to the full Ising model from Week 8. In...
  • Week 10 - The Alpha and the Omega of Monte Carlo, Review, Party
    The lecture of Week 10 includes the alpha and the omega of our course. First we repeat the experiment of Buffon's needle, already performed in the 18th century, and then we touch the sophisticated theory of Lévy stable distributions, and their connection with ...
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Instrutores

Werner Krauth
Directeur de recherches au CNRS
Department of physics

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Criador do conteúdo

École normale supérieure

L’École normale supérieure (ENS) est un établissement d'enseignement supérieur pour les études prédoctorales et doctorales (graduate school) et un haut lieu de la recherche française. L'ENS offre à 300 nouveaux étudiants et 200 doctorants chaque année une formation de haut niveau, largement pluridisciplinaire, des humanités et sciences sociales aux sciences dures. Régulièrement distinguée au niveau international, l'ENS a formé 10 médailles Fields et 13 prix Nobel.

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Plataforma

Coursera

A Coursera é uma empresa digital que oferece um curso on-line massivo e aberto, fundado pelos professores de computação Andrew Ng e Daphne Koller Stanford University, localizado em Mountain View, Califórnia.

O Coursera trabalha com as melhores universidades e organizações para disponibilizar alguns dos seus cursos on-line e oferece cursos em várias disciplinas, incluindo: física, engenharia, humanidades, medicina, biologia, ciências sociais, matemática, negócios, ciência da computação, marketing digital, ciência de dados. e outros assuntos.Cours

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