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Statistical Mechanics: Algorithms and Computations
  • Level Foundation
  • Duration 16 hours
  • Course by École normale supérieure
  • Offered by

About

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.

Modules

Lecture 1: Introduction to Monte Carlo algorithms

    • 1 Videos
    • 2 Readings
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1 Videos

  • Lecture 1: Introduction to Monte Carlo algorithms

2 Readings

  • Python programs and references
  • Errata (Lecture 1)

Tutorial 1: Exponential convergence and the 3x3 pebble game

    • 1 Videos
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1 Videos

  • Tutorial 1: Exponential convergence and the 3x3 pebble game

Homework Session 1: From the one-half rule to the bunching method

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 1: spotting a correct algorithm

1 Peer Review

  • From the one-half rule to the bunching method

1 Videos

  • Homework Session 1: From the one-half rule to the bunching method

Lecture 2: Hard disks: from Classical Mechanics to Statistical Mechanics

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 2: Hard disks: from Classical Mechanics to Statistical Mechanics

1 Readings

  • Python programs and references

Tutorial 2: Equiprobability, partition functions, and virial expansions for hard disks

    • 1 Videos
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1 Videos

  • Tutorial 2: Equiprobability, partition functions, and virial expansions for hard disks

Homework Session 2: Paradoxes of hard-disk simulations in a box

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 2: spotting a correct algorithm (continued)

1 Peer Review

  • Paradoxes of hard-disk simulations in a box

1 Videos

  • Homework Session 2: Paradoxes of hard-disk simulations in a box

Lecture 3: Entropic interactions, phase transitions

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 3: Entropic interactions, phase transitions

1 Readings

  • Python programs and references

Tutorial 3: Algorithms, exact solutions, thermodynamic limit

    • 1 Videos
    • 1 Readings
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1 Videos

  • Tutorial 3: Algorithms, exact solutions, thermodynamic limit

1 Readings

  • Errata (Tutorial 3)

Homework Session 3: Two-dimensional liquids and solids

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 3: Spotting a correct algorithm (continued)

1 Peer Review

  • Two-dimensional liquids and solids

1 Videos

  • Homework Session 3: Two-dimensional liquids and solids

Lecture 4: Sampling and Integration - From Gaussians to the Maxwell and Boltzmann distributions

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 4: Sampling and Integration - From Gaussians to the Maxwell and Boltzmann distributions

1 Readings

  • Python programs and references

Tutorial 4: Sampling discrete and one-dimensional distributions

    • 1 Videos
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1 Videos

  • Tutorial 4: Sampling discrete and one-dimensional distributions

Homework Session 4: Sampling and integration in high dimensions

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 4: four disks in a box

1 Peer Review

  • Sampling and integration in high dimensions

1 Videos

  • Homework Session 4: Sampling and integration in high dimensions

Lecture 5: Density matrices and path integrals

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 5: Density matrices and path integrals

1 Readings

  • Python programs and references

Tutorial 5: Trotter decomposition and quantum time-evolution

    • 1 Videos
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1 Videos

  • Tutorial 5: Trotter decomposition and quantum time-evolution

Homework session 5: Quantum statistical mechanics and Quantum Monte Carlo

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 5: Four disks in a box (continued)

1 Peer Review

  • Quantum statistical mechanics and Quantum Monte Carlo

1 Videos

  • Homework session 5: Quantum statistical mechanics and Quantum Monte Carlo

Lecture 6: Lévy sampling of quantum paths

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 6: Lévy sampling of quantum paths

1 Readings

  • Python programs and references

Tutorial 6: Bosonic statistics (with wave functions)

    • 1 Videos
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1 Videos

  • Tutorial 6: Bosonic statistics (with wave functions)

Homework session 6: Path sampling: A firework of algorithms

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 6: Path integrals

1 Peer Review

  • Path sampling: A firework of algorithms

1 Videos

  • Homework session 6: Path sampling: A firework of algorithms

Lecture 7: Quantum indiscernability and Bose-Einstein condensation

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 7: Quantum indiscernability and Bose-Einstein condensation

1 Readings

  • Python programs and references

Tutorial 7: Permutation cycles and ideal Bosons

    • 1 Videos
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1 Videos

  • Tutorial 7: Permutation cycles and ideal Bosons

Homework session 7: Bosons in a trap - Bose-Einstein condensation

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 7: BEC

1 Peer Review

  • Bosons in a trap - Bose-Einstein condensation

1 Videos

  • Homework session 7: Bosons in a trap - Bose-Einstein condensation

Lecture 8: Ising model - From enumeration to Cluster Monte Carlo Simulations

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 8: Ising model - From enumeration to Cluster Monte Carlo Simulations

1 Readings

  • Python programs and references

Tutorial 8: Ising model - Heat bath algorithm, coupling of Markov chains

    • 1 Videos
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1 Videos

  • Tutorial 8: Ising model - Heat bath algorithm, coupling of Markov chains

Homework session 8: Cluster sampling, perfect sampling in the Ising model

    • 1 Videos
    • 1 PeerReview
    • 1 Assignment
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1 Assignment

  • Practice quiz 8: Spins and Ising model

1 Peer Review

  • Cluster sampling, perfect sampling in the Ising model

1 Videos

  • Homework session 8: Cluster sampling, perfect sampling in the Ising model

Lecture 9: Dynamical Monte Carlo and the Faster-than-the-Clock approach

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 9: Dynamical Monte Carlo and the Faster-than-the-Clock approach

1 Readings

  • Python programs and references

Tutorial 9: Simulated Annealing and the 13-sphere problem

    • 1 Videos
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1 Videos

  • Tutorial 9: Simulated Annealing and the 13-sphere problem

Homework session 9: Simulated Annealing for sphere packings and the travelling salesman problem

    • 1 Videos
    • 1 PeerReview
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1 Peer Review

  • Simulated Annealing for sphere packings and the travelling salesman problem

1 Videos

  • Homework session 9: Simulated Annealing for sphere packings and the travelling salesman problem

Lecture 10: The Alpha and the Omega of Monte Carlo

    • 1 Videos
    • 1 Readings
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1 Videos

  • Lecture 10: The Alpha and the Omega of Monte Carlo

1 Readings

  • Python programs and references

Tutorial 10: Review - Party - Best of

    • 1 Videos
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1 Videos

  • Tutorial 10: Review - Party - Best of

Final Exam

    • 1 Assignment
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1 Assignment

  • Final Exam 2016

Auto Summary

Explore the intriguing world of modern physics through "Statistical Mechanics: Algorithms and Computations." Designed for curious minds, this foundational course delves into classical and quantum physics using basic computer programs. Taught by Coursera, learners will write, generalize, and discuss algorithms to gain deep scientific insights. With a duration of 960 minutes, the course is accessible via a Starter subscription, making it ideal for those eager to understand physics algorithmically.

Werner Krauth
Instructor

Werner Krauth