Master
2021/2022
Statistical Mechanics: Algorithms and Computations
Type:
Elective course (Materials. Devices. Nanotechnology)
Area of studies:
Electronics and Nanoelectronics
Delivered by:
School of Electronic Engineering
When:
2 year, 3 module
Mode of studies:
distance learning
Online hours:
53
Open to:
students of all HSE University campuses
Instructors:
Renat Ikhsanov
Master’s programme:
Материалы. Приборы. Нанотехнологии
Language:
English
ECTS credits:
3
Contact hours:
3
Course Syllabus
Abstract
In this course a student 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. A student will find out about algorithms, and about the deep insights into science that one can obtain by the algorithmic approach. It is expected that applicants to the discipline should be able to demonstrate knowledge of the following topics: general physics and higher mathematics (calculus and linear algebra) at least in the scope of a technical university program
Learning Objectives
- Objectives of mastering the discipline "Statistical Mechanics: Algorithms and Computations": • give students an idea of modern physics (classical and quantum) from basic computer programs that you will download, generalize, or write from scratch, discuss, and then hand in;
- • give students an understanding of the essential concepts of Monte Carlo techniques (detailed balance, irreducibility, and a-periodicity), and Metropolis algorithm.
Expected Learning Outcomes
- Knowledge: - hard-disk model; - difference between direct sampling and Markov-chain sampling.
- Knowledge: - the local algorithm; - the heat-bath algorithm.
- Knowledge: a dynamic Monte Carlo algorithm.
- Knowledge: entropic interactions concept.
- Knowledge: quantum mechanics.
- Knowledge: sampling, and its connection with integration.
- Knowledge: the Bose-Einstein condensation phenomenon.
- Knowledge: the central limit theorem.
- Knowledge: the essential concepts of Monte Carlo techniques.
- Knowledge: the properties of bosons.
- Possess: density matrices and path integrals techniques.
- Possess: Newtonian mechanics and statistical mechanics.
- Possess: python programming.
- Possess: the Lévy construction.
- Possess: the path-integral technique.
- Skills: to do standard sampling techniques.
- Skills: to make perfect algorithm to sample configurations.
- Skills: to make the connection of Monte Carlo and Molecular Dynamics algorithms.
- Skills: to program Metropolis algorithm.
- Skills: to program the Ising model.
- Skills: to program the sampling algorithm.
- Skills: to use the Maxwell and Boltzmann distributions of velocities and energies.
- Skills: to use the Trotter approximation.
Course Contents
- Topic 1. Monte Carlo algorithms (Direct sampling, Markov-chain sampling).
- Topic 2. Hard disks: From Classical Mechanics to Statistical Mechanics
- Topic 3. Entropic interactions and phase transitions
- Topic 4. Sampling and integration
- Topic 5. Density matrices and Path integrals (Quantum Statistical mechanics 1/3)
- Topic 6. Lévy Quantum Paths (Quantum Statistical mechanics 2/3).
- Topic 7. Bose-Einstein condensation (Quantum Statistical mechanics 3/3)
- Topic 8. Ising model - Enumerations and Monte Carlo algorithms.
- Topic 9. Dynamic Monte Carlo, simulated annealing.
- Topic 10. The Alpha and the Omega of Monte Carlo, Review, Party.
Assessment Elements
- Экзамен (тест)If a student misses the exam because of some valid reason, s/he receives «absence» grade. The grade for the course is calculated on the course page on the basis of the student’s number of points that are awarded to the student for answering questions of the proposed tests. Контрольные работы и экзамен по курсу проводятся в письменной форме на платформе Coursera (https://www.coursera.org/learn/statistical-mechanics). Во время написания контрольных и экзаменационных работ студентам запрещено: общаться с кем-либо, пользоваться конспектами и подсказками. Кратковременным нарушением связи во время контрольной работы или экзамена считается нарушение связи менее часа. Долговременным нарушением связи считается нарушение связи в течение часа и более. При долговременном нарушении связи студент не может продолжить участие в контрольной или экзамене. Процедура пересдачи аналогична процедуре сдачи.
- Самостоятельная работа
Bibliography
Recommended Core Bibliography
- Baxter, R. J. (2007). Exactly Solved Models in Statistical Mechanics (Vol. Dover ed). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1152951
- Ландау Л.Д., Лифшиц Е.М. - Курс теоретической физики. Статистическая физика - Издательство "Физматлит" - 2001 - ISBN: 978-5-9221-0054-0 - Текст электронный // ЭБС ЛАНЬ - URL: https://e.lanbook.com/book/2230
- Теоретическая физика. Т.5, Ч. 1: Статистическая физика, Ландау, Л. Д., 2005
Recommended Additional Bibliography
- Statistical physics of particles, Kardar, M., 2017