科目名

Course Title

統計物理学3(Statistical Physics III)
学科・専攻

Department/Program

G30 Physics

受講年次Grade

授業形態

3rdClass style

必修・選択の別講義

Compulsory or Elective* See "Remarks"

時間割コードRegistration code

0680180

開講期・曜日・時限

Semester,Day & Period

単位数

春学期 木：5Credit

科目区分

2

Course typeSpecialized Course

担当教員

Instructor

所属研究室
連絡先

WOJDYLO John Andrew(WOJDYLO John Andrew)

Laboratory

居室

Contact

john.wojdylo@s.phys.nagoya-u.ac.jp

Room

講義の目的とねらい

S-Lab

ES035

Course purpose

This is an intermediate-advanced course in statistical mechanics and thermodynamics. Students learn quantum
statistics of ideal gases, introductory statistical mechanics of systems of interacting particles and introductory theoryof phase transitions and critical phenomena, and some modern theory such as the scaling hypothesis, an introduction
to renormalization group theory (the spatial renormalization group), and the Bogolyubov Variational Theorem and its
application to constructing an optimal Mean Field Theory. If time permits, we will also cover Callen Ch 14 onirreversible thermodynamics, including the Onsager Reciprocity, with an application to thermoelectricity: the Seebeck
Effect, Peltier Effect and Thomson Effect.
In this unit applications are considered in condensed matter physics, solid state physics, cosmology, chemistry,materials science and biology. For chemistry majors, this course together with Statistical Physics II provides a
powerful boost to your skills set and can open many doors.
履修要件

Prerequisite

Statistical Physics II; or Consent of Instructor• Students must have passed Statistical Physics II to take Statistical Physics III.
履修取り下げの方法について

How to Apply for Course Withdrawal<「履修取り下げ届」提出の要・不要 Necessity/Unnecessity to submit "Course Withdrawal Request Form">
Necessary<条件等 Conditions>
A formal withdrawal form must be signed by the lecturer and submitted to the Student Office by the official
withdrawal date around mid-May.
成績評価

GradingAttendance: 5%; Weekly quizzes or other written assessment: 30%; Mid-term exam: 32.5%; Final Exam: 32.5%

不可（F）と欠席（W）の基準

Criteria for "Absent(W)" &"Fail" grades

The Absent grade is reserved for students who withdraw by the official deadline in May. After that day, a letter
grade will be awarded based on marks earned from all assessment during the semester.
関連する科目

Related courses

It is strongly advised that students concurrently register for Physics Tutorial IVa.
教室Class room

Check the Course Timetable.
ES035 or online using MS Teams. (To be advised.)

到達目標

Goal

At the end of this course, students will have mastered basic aspects of quantum statistics of ideal gases, statisticalmechanics of systems of interacting particles, and the theory of phase transitions and critical phenomena, including
modern topics such as the scaling hypothesis, an introduction to renormalization group theory (the spatialrenormalization group), and the Bogolyubov Variational Theorem and its application to constructing an optimal Mean
Field Theory.

授業内容ContentSome topics are covered in assignments. The precise order and content of the lectures might vary slightly.
Lecture 1. Revision of quantum statistical mechanics. Quantum states of a single particle. Reflecting boundary
conditions, periodic boundary conditions. Density of states in 3, 2 and 1 dimensions, for linear and quadratic
dispersion relations. Turning sums into integrals. Example: EM radiation. The quantum distribution functions:Fermi-Dirac, Bose-Einstein distributions. Photon statistics: Planck distribution. Systems with varying number ofparticles: the Grand Canonical ensemble and partition function. Occupation number formalism: mean occupation
number and dispersion. Role of the chemical potential.
Lecture 2. Examples. Vapour pressure of a solid. Diatomic molecules. Black body radiation: Stefan-Boltzmann Law;
Wien s Displacement Law; radiation pressure; Grand Canonical partition function and probability of a many-bodystate at temperature T. Example: adsorption of a gas onto a 2D surface.
Lecture 3. The ideal Fermi fluid: conduction electrons in metals. Specific heat and ground state energy in 3D, 2D, 1D.
Sommerfeld expansion.
Lecture 4. The ideal Bose fluid: Bose-Einstein condensation in 3D. What about in 2D or 1D? Critical temperature.
Mean energy, specific heat. The possibility of BEC in a photon gas. Breakdown of the Grand Canonical description.
Lecture 5. Systems of interacting particles (1). The Debye Model of solids. Normal modes. Specific heat.
Lecture 6. Systems of interacting particles (2). Weakly nonideal gases: virial expansion. Derivations of the Van derWaals equation of state for a weakly non-ideal gas, as well as for a fluid using a self-consistent mean field approach.
Lecture 7. Irreversible Thermodynamics. Entropy production. Onsager Reciprocity; Thermoelectric Effect; Seebeck
Effect; Peltier Effect.
Lecture 8. Stability of thermodynamic systems. Concavity/convexity of thermodynamic potentials. Le Chatelier sPrinciple. First Order phase transitions, features of the free energy. Discontinuity in the entropy: latent heat. Slope ofthe coexistence curves: Clausius-Clapeyron Equation.
Lecture 9. Van der Waals fluid: unstable isotherms, physical isotherm, Maxwell equal-area rule. Multicomponent
systems: Gibbs phase rule. Why does the phase diagram of water not have more than three phases coexisting at thesame point?
Lecture 10. The Fluctuation-Dissipation Theorem. Response functions and correlations. Quantitative explanation ofcritical opalescence.
Lecture 11. Examples of phase transitions (order-disorder transition, which is a structural phase transition). Why dofluctuations get out of control near the critical point? Alben s Model. Landau Theory: classical theory in the criticalregion. Order parameter and the critical exponents α,β,γ,δ; their classical values.
Lecture 12. Magnetic systems: ferromagnetism and models for it. Ising model. Mean field theory treatment of the 1D
Ising chain. Critical exponents.
Lecture 13. Ising model continued. No phase transition in the 1D Ising chain: proof by a simple argument; and bysolving the model exactly ‒ no phase transition but at any finite field, magnetisation gets saturated if temperature is
low enough. Ising model in 2D (just mention): critical exponents, behaviour of the specific heat. Spin correlation
function: exact calculation for the 1D Ising chain. Phase diagram of ferromagnetic systems. Cause of the breakdownof the classical theory (qualitative).
Lecture 14. Breakdown of the classical theory and advent of the modern theory. Derivation of an inequality involving
critical exponents ‒ but all experiments suggest equality holds. Scaling hypothesis: ad hoc argument. Justification of
the scaling hypothesis using Kadanoff s block spins. Spatial renormalization group theory and sample calculation for
the 1D Ising chain.
Lecture 15. Bogolyubov Variational Theorem. Order-Disorder Transition: constructing the Hamiltonian and deriving
the optimal Mean Field Theory for its solution. Mean Field Theory for 1D Ising Model revisited.

教科書Textbook

1. Callen, Herbert, Thermodynamics and an Introduction to Thermostatistics, 2nd Ed., Wiley.
translation has fewer misprints.)(The Japanese

2. Reif, F., Fundamentals of Statistical and Thermal Physics, McGraw-Hill, 1965.
3. Plischke, M. & Bergersen, B., Equilibrium Statistical Mechanics, 3rd Ed., World Scientific, 2006.
参考書

Recommended reading

1. Hill, T., An Introduction to Statistical Thermodynamics, Dover, 1986. (Excellent introduction to Statistical
Mechanics at Year 3 level. Alternative textbook. Highly recommended. Cheap to buy.)
2. Kittel, C., Elementary Statistical Physics, Dover, 2004. (Highly recommended. Cheap to buy.)
3. Kubo R., Statistical Mechanics, North Holland, 1965. (More of a second course on Stat Mech, but contains many
examples and worked solutions.)
4. Huang, K., Statistical Mechanics, Wiley. (Advanced reference.)
5. Kittel, C. and Kroemer, H., Thermal Physics, W.H. Freeman. (Try as alternative.)
6. Landau, L.D. and Lifshitz, E.M., Statistical Physics, Part I, by E.M. Lifshitz and L.P. Pitaevskii, Pergamon Press. (Aclassic book: thorough, advanced treatment.)

連絡方法

Contact method

Consultation or help is available at anytime online using MS Teams.
I can also be contacted by email.
その他

Remarks*See Course List and Graduation Requirements for your program for your enrollment year.
Students taking Statistical Physics III should also take Physics Tutorial IVa. No solutions are handed out in class: youmust obtain any solutions during the tutorial. It pays to come prepared and pay attention during the tutorial!

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