## 20410434 - FS450 - Elements of Statistical Mechanics

Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.

RAIMONDI ROBERTO

teacher profile | teaching materials

Fruizione: 20401806 ELEMENTI DI MECCANICA STATISTICA in Fisica L-30 N0 RAIMONDI ROBERTO

Programme

CONTENTS OF THE LECTURES: the numbers in round brackets refer to the chapter and section of the textbook adopted.
Kinetic theory of gases. Boltzmann equation and H theorem. (1, Par.2.1,2.2,2.3,2.4)
Maxwell-Boltzmann distribution. (1, Par. 2.5)
Phase space and Liouville theorem. (1, Par. 3.1,3.2)
Gibbs ensembles. Micro canonical ensemble. Definition of entropy. (1, Par. 3.3,3.4)
The ideal gas in the micro canonical ensemble. (1, Par. 3.6)
The equipartition theorem. (1, Par. 3.5)
The canonical ensemble. (1, Par.4.1).
The partition function and the free energy. Fluctuations of energy in the canonical ensemble. (1 Par. 4.4)
The grand canonical ensemble. The grand potential. The ideal gas in the grand canonical ensemble. (1 Par. 4.3).
Fluctuations of the particle number. (1 Par. 4.4)
Classical theory of the linear response and fluctuation-dissipation theorem. (1, Par. 8.4).
Einstein and Langevin theories of the Brownian motion. (Par. 1 par. 11.1,11.2).
Johnson-Nyqvist theory of thermal noise. (1 Par. 11.3).
Quantum statistical mechanics and the density matrix. (1, Par. 6.2,6.3,6.4)
Fermi-Dirac and Bose-einstein quantum statistics. ( 1, Par. 7.1)
The Fermi gas. The Sommerfeld expansion and the electron specific heat. (1, Par. 7.2)
The Bose gas. The Bose-Einstein condensation. (1, Par. 7.3)
Quantum theory of black-body radiation. (1, Par. 7.5)

e-Learning Moodle Platform with Supplementary Material

Core Documentation

Suggested textbook:
1) C. Di Castro and R. Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press, 2015.

2) K. Huang, Meccanica Statistica, Zanichelli, 1997.
3) L. Peliti, Appunti di Meccanica Statistica, Bollati Boringhieri, 2003.
4) Joel L. Lebowitz, Statistical mechanics: A selective review of two central issues, Reviews of Modern Physics, 71, S346 (1999).

Type of delivery of the course

The course offers both theory lectures and exercise classes. During the latter, paradigmatic problems are presented and solved, with the interactive participation of the students present in the classroom.

Type of evaluation

The written exam is about solving two problems, one dedicated to the statistical mechanics of classical systems and one dedicated to the statistical mechanics of quantum systems. The exam problems are of the typeof those illustrated during the exercises class. The oral exam is made of two questions, concerning classical and quantum systems respectively. The final mark combines the mark of the written examination and of the oral one and is given as a fraction of 30 (maximum score).

RAIMONDI ROBERTO

teacher profile | teaching materials

Fruizione: 20401806 ELEMENTI DI MECCANICA STATISTICA in Fisica L-30 N0 RAIMONDI ROBERTO

Programme

CONTENTS OF THE LECTURES: the numbers in round brackets refer to the chapter and section of the textbook adopted.
Kinetic theory of gases. Boltzmann equation and H theorem. (1, Par.2.1,2.2,2.3,2.4)
Maxwell-Boltzmann distribution. (1, Par. 2.5)
Phase space and Liouville theorem. (1, Par. 3.1,3.2)
Gibbs ensembles. Micro canonical ensemble. Definition of entropy. (1, Par. 3.3,3.4)
The ideal gas in the micro canonical ensemble. (1, Par. 3.6)
The equipartition theorem. (1, Par. 3.5)
The canonical ensemble. (1, Par.4.1).
The partition function and the free energy. Fluctuations of energy in the canonical ensemble. (1 Par. 4.4)
The grand canonical ensemble. The grand potential. The ideal gas in the grand canonical ensemble. (1 Par. 4.3).
Fluctuations of the particle number. (1 Par. 4.4)
Classical theory of the linear response and fluctuation-dissipation theorem. (1, Par. 8.4).
Einstein and Langevin theories of the Brownian motion. (Par. 1 par. 11.1,11.2).
Johnson-Nyqvist theory of thermal noise. (1 Par. 11.3).
Quantum statistical mechanics and the density matrix. (1, Par. 6.2,6.3,6.4)
Fermi-Dirac and Bose-einstein quantum statistics. ( 1, Par. 7.1)
The Fermi gas. The Sommerfeld expansion and the electron specific heat. (1, Par. 7.2)
The Bose gas. The Bose-Einstein condensation. (1, Par. 7.3)
Quantum theory of black-body radiation. (1, Par. 7.5)

e-Learning Moodle Platform with Supplementary Material

Core Documentation

Suggested textbook:
1) C. Di Castro and R. Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press, 2015.
{"ft_lang_label":"__label__en","ft_lang_prob":0.76321465,"math_prob":0.88274205,"size":5580,"snap":"2022-05-2022-21","text_gpt3_token_len":1508,"char_repetition_ratio":0.14472741,"word_repetition_ratio":0.97893435,"special_character_ratio":0.25250897,"punctuation_ratio":0.23162393,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9749346,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-19T18:08:08Z\",\"WARC-Record-ID\":\"<urn:uuid:d966e783-4eed-4ac2-983a-d3f9e6c5672c>\",\"Content-Length\":\"91605\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:824a2b25-3982-4f62-919c-8f54c5f5cd41>\",\"WARC-Concurrent-To\":\"<urn:uuid:fa98894e-5f76-4d47-a79d-468ca742a72d>\",\"WARC-IP-Address\":\"193.205.143.192\",\"WARC-Target-URI\":\"https://www.uniroma3.it/en/insegnamento-erogato/dipartimento-di-matematica-e-fisica/l/2021-2022/matematica-0580706203500001/60740dd8-44c8-44a0-bd26-15faf036d5bc--20410434/\",\"WARC-Payload-Digest\":\"sha1:UZSBCPFMTWNKK6QJHLEWW5ESPR6L6HW2\",\"WARC-Block-Digest\":\"sha1:5VHABMYDS2P2QSHYJZPBSXXVEFJIUW6A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662529658.48_warc_CC-MAIN-20220519172853-20220519202853-00403.warc.gz\"}"}