大学院
過去（2016年度）の授業の情報です
学内のオンライン授業の情報漏洩防止のため，URLやアカウント、教室の記載は削除しております。
最終更新日：2024年4月22日
授業計画や教室は変更となる可能性があるため、必ずUTASで最新の情報を確認して下さい。
UTASにアクセスできない方は、担当教員または部局教務へお問い合わせ下さい。
最終更新日：2024年4月22日
授業計画や教室は変更となる可能性があるため、必ずUTASで最新の情報を確認して下さい。
UTASにアクセスできない方は、担当教員または部局教務へお問い合わせ下さい。
物理学特別講義BI
Hard Disks: A Window into the World of Statistical Physics
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
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
時間割／共通科目コード
コース名
教員
学期
時限
35603-1060
物理学特別講義BI
Werner KRAUTH
集中
マイリストに追加
マイリストから削除
講義使用言語
英語
単位
2
実務経験のある教員による授業科目
NO
他学部履修
可
開講所属
理学系研究科
授業計画
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)
授業の方法
Blackboard lectures (website-supported for additional literature, algorithms and problem sets).
成績評価方法
Active participation in the course, brief report and/or short seminar.
教科書
The course will be entirely self-contained.
参考書
The course will be entirely self-contained.
履修上の注意
Lecture notes will (it is hoped) be created by participants of the course, together with the Professor.
