# PHYSICS OF MATTER 1

OVERVIEW

This is a basic course of classical and quantum statistical physics, with applications to gases, liquids and solids.

## AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

Basic knowledge about the principles of statisticall mechanics. Basic knowledge about the physical properties of gases, liquids and solids. Ability to solve simple exercises about the different topics of the course.

Teaching methods

Standard lectures and exercises.

SYLLABUS/CONTENT

Quotations of thermodynamics Classical Statistical Mechanics - Phase space. Macrostates and microstates. Liouville equation. Statistical ensembles. Microcanonical ensemble. Entropy and temperature in the microcanonical ensemble. Counting microstates and the Gibbs Paradox. Ideal gas equation and internal energy. Canonical ensemble. Partition function and its relationship with Hehlmoltz free energy. Energy fluctuations and thermal capacity. Energy equipartition theorem. Examples of partition functions: harmonic oscillator, rigid rotator, ideal gas. Law of Dulong and Petit. Quantum statistical mechanics - Density matrix. Microcanonical ensemble. Canonical ensemble. Partition function of the harmonic oscillator and of the quantum rigid rotator. Einstein model for the specific heat of the solids. Particle with spin 1/2. Grancanonical ensemble. Density fluctuations and isothermal compressibility. Quantum perfect gas (monoatomic) - Bose-Einstein and Fermi-Dirac statistics. Density of states in energy. Classical limit: the ideal gas. Strongly degenerate Bose gas and Bose-Einstein condensation. Strongly degenerate Fermi gas and electronic specific heat of metals. Weakly degenerate perfect gas. Photon gas and black body radiation. Perfect Polyatomic Gases - Born-Oppenheimer approximation. Biatomic molecules: translational, vibrational and rotational partition functions. Heteronuclear biatomic molecules. Homonuclear biatomic molecules: ortho- and para-hydrogen. Examples of triatomic molecules. Crystal Lattices - Bravais lattices and crystals. Primitive and conventional unit cells. Wigner-Seitz cell. Reciprocal lattice and first Brillouin zone. Examples of 2D and 3D crystal lattices. Lattice vibrations in Solids - Small oscillations of a linear chain with one atom per cell. Normal vibrational modes of a crystal: general treatment. Example: linear chain with two atoms per cell. Phonons. Vibrational free energy of a solid. Thermal capacity of a solid in Debye approximation. Lattice vibrations of three-dimensional solids and measurement of dispersion curves. Interacting gases and liquds - Pair correlation function g(r) and potential of the mean force. Calculation of pressure and g(r) for a diluted interacting gas by the virial expansion.

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes.

## TEACHERS AND EXAM BOARD

Exam Board

RICCARDO FERRANDO (President)

GIULIA ROSSI

FRANCESCO BUATIER DE MONGEOT

CORRADO BORAGNO

## LESSONS

Teaching methods

Standard lectures and exercises.

ORARI

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