Hard disks: A Window into the World of Stat Physics
From Werner KRAUTH
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| ==Keywords of the Course== | ==Keywords of the Course== | ||
| Statistical mechanics, computational physics, phase transitions, colloids, melting transition, Monte Carlo algorithms, Molecular dynamics, Kosterlitz-Thouless transition. | Statistical mechanics, computational physics, phase transitions, colloids, melting transition, Monte Carlo algorithms, Molecular dynamics, Kosterlitz-Thouless transition. | ||
| - | |||
| - | ! Teaching Methods | ||
| - | Blackboard lectures (website-supported for additional literature, algorithms and problem sets). | ||
| - | |||
| - | ! Method of Evaluation | ||
| - | Active participation in the course, brief report and/or short seminar. | ||
| - | |||
| - | ! Notes on Taking the Course | ||
| - | Lecture notes will (it is hoped) be created by participants of the course, together with the Professor. | ||
| - | |||
| - | !Schedule | ||
| - | January 24th, 2017: 10:25 - 16:40 (periods 2,3,4) | ||
| - | January 26th, 2017: 10:25 - 18:35 (periods 2,3,4,5) | ||
| - | January 31st, 2017: 10:25 - 16:40 (periods 2,3,4) | ||
| - | February 2nd, 2017: 10:25 - 18:35 (periods 2,3,4,5) | ||
| - | |||
| - | ! Course Title | ||
| - | Hard Disks: A Window into the World of Statistical Physics | ||
| - | |||
| - | ! Course Objectives/Overview | ||
| - | The hard-disk model has exerted outstanding influence on statistical physics, starting with the first ever N-body calculation in science, by D. Bernoulli (1738), and leading up to its role in the very definition of statistical mechanics, by Maxwell and Boltzmann, and to the formal proof of the validity of statistical mechanics, by Sinai (1970). | ||
| - | Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods (Metropolis et al, 1953) and by molecular dynamics (Alder and Wainwright, 1957). Up to the present day, the model has continued to drive the development of algorithms (Bernard et al, 2009), including the "Beyond-Metropolis" approach (Michel et al, 2014). | ||
| - | It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur (Alder and Wainwright, 1962) even though such systems cannot develop long-range crystalline order (Mermin and Wagner, 1966). This provided the starting point for the Kosterlitz-Thouless theory (1973), although the hard-disk phase diagram was established only recently (Bernard and Krauth, 2011), thus providing a clear view on the physics of phase transitions in two dimensions. | ||
| - | |||
| - | The objective of this course will thus be to discuss the aforementioned central topics of statistical physics from the unique vantage point of the hard-disk model, and in a self-contained way that will be accessible to a wide audience. Overall, the course will introduce to a variety of approaches, from rigorous mathematics to statistics, and from algorithm design and numerical simulations to theoretical modeling and to the interpretation of experiment. | ||
| - | It is intended to show how the hard-disk model has continued to shape our view of the physical world, to teach us key aspects, and to prepare for general progress in science. | ||
| - | |||
| - | First part of the course (January 24 and January 26, 2017): | ||
| - | * Hard disks in classical and statistical mechanics | ||
| - | * Hard disks and thermodynamical phases | ||
| - | Second part of the course (January 31 and February 2, 2017): | ||
| - | * Hard disks and Markov chains | ||
| - | * Hard disks and two-dimensional melting | ||
| - | |||
| - | ! Keywords of the Course (Japanese/English) | ||
| - | Statistical mechanics, computational physics, phase transitions, colloids, melting transition, Monte Carlo algorithms, Molecular dynamics, Kosterlitz-Thouless transition. | ||
| - | |||
| - | ! Teaching Methods | ||
| - | Blackboard lectures (website-supported for additional literature, algorithms and problem sets). | ||
| - | |||
| - | ! Method of Evaluation | ||
| - | Active participation in the course, brief report and/or short seminar. | ||
| - | |||
| - | ! Required Textbook | ||
| - | N/A: The course will be entirely self-contained. | ||
| - | |||
| - | ! Reference Books | ||
| - | N/A: The course will be entirely self-contained. | ||
| - | |||
| - | ! Notes on Taking the Course | ||
| - | Lecture notes will (it is hoped) be created by participants of the course, together with the Professor. | ||
| - | |||
| - | ! Course-Related Websites | ||
| - | http://www.lps.ens.fr/~krauth/index.php/Hard_disks:_A_Window_into_the_World_of_Stat_Physics | ||
| - | |||
| - | |||
| - | |||
| - | ! Language used in class | ||
| - | English | ||
| - | s.fr/~krauth/index.php/Hard_disks:_A_Window_into_the_World_of_Stat_Physics | ||
| - | |||
| - | ! E-mail Address | ||
| - | werner.krauth@ens.fr | ||
| - | |||
| - | ! Laboratory room phone no. | ||
| - | N/A | ||
| - | |||
| - | ! Language used in class | ||
| - | English | ||
Revision as of 10:48, 4 December 2016
This is the homepage for the Lecture series on Hard disks: A Window into the World of Statistical Physics, that I will give in January and February 2017 at the University of Tokyo, where I will be invited Professor at the Department of Physics.
Look here for practical information
!Schedule January 24th, 2017: 10:25 - 16:40 (periods 2,3,4) January 26th, 2017: 10:25 - 18:35 (periods 2,3,4,5) January 31st, 2017: 10:25 - 16:40 (periods 2,3,4) February 2nd, 2017: 10:25 - 18:35 (periods 2,3,4,5)
Course Title
Hard Disks: A Window into the World of Statistical Physics
Course Objectives/Overview
The hard-disk model has exerted outstanding influence on statistical physics, starting with the first ever N-body calculation in science, by D. Bernoulli (1738), and leading up to its role in the very definition of statistical mechanics, by Maxwell and Boltzmann, and to the formal proof of the validity of statistical mechanics, by Sinai (1970). Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods (Metropolis et al, 1953) and by molecular dynamics (Alder and Wainwright, 1957). Up to the present day, the model has continued to drive the development of algorithms (Bernard et al, 2009), including the "Beyond-Metropolis" approach (Michel et al, 2014). It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur (Alder and Wainwright, 1962) even though such systems cannot develop long-range crystalline order (Mermin and Wagner, 1966). This provided the starting point for the Kosterlitz-Thouless theory (1973), although the hard-disk phase diagram was established only recently (Bernard and Krauth, 2011), thus providing a clear view on the physics of phase transitions in two dimensions.
The objective of this course will thus be to discuss the aforementioned central topics of statistical physics from the unique vantage point of the hard-disk model, and in a self-contained way that will be accessible to a wide audience. Overall, the course will introduce to a variety of approaches, from rigorous mathematics to statistics, and from algorithm design and numerical simulations to theoretical modeling and to the interpretation of experiment. It is intended to show how the hard-disk model has continued to shape our view of the physical world, to teach us key aspects, and to prepare for general progress in science.
First part of the course (January 24 and January 26, 2017):
- Hard disks in classical and statistical mechanics
- Hard disks and thermodynamical phases
Second part of the course (January 31 and February 2, 2017):
- Hard disks and Markov chains
- Hard disks and two-dimensional melting
Keywords of the Course
Statistical mechanics, computational physics, phase transitions, colloids, melting transition, Monte Carlo algorithms, Molecular dynamics, Kosterlitz-Thouless transition.
