Fisica | PHYSICS OF CONDENSED STATES

cod. 0522600006

PHYSICS OF CONDENSED STATES

	0522600006
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"
	EQF7
	PHYSICS
	2016/2017

PERCORSO COMUNE Cohort 2015/2016

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2014
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	FIS/03	6	48	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	THE COURSE HAS THE OBJECTIVE OF INTRODUCING THE STUDENTS TO THE USE OF THE BASIC THEORETICAL TOOLS NEEDED TO STUDY FROM THE SIMPLEST TO THE MOST COMPLEX SOLID STATE SYSTEMS AND, IN PARTICULAR, THE EMERGENCE IN THESE LATTER OF NEW ELEMENTARY EXCITATIONS. 1. KNOWLEDGE AND UNDERSTANDING: THE AIM IS TO PROVIDE THEORETICAL KNOWLEDGES OF THE PHYSICS OF CONDENSED MATTER, WITH SPECIAL REFERENCE TO THE MICROSCOPIC THEORY OF SUPERCONDUCTIVITY AND TO THE BOSE-EINSTEIN CONDENSATION. 2. APPLYING KNOWLEDGE AND UNDERSTANDING: THE APPLICATION OF KNOWLEDGE AND UNDERSTANDING WILL BE DEVELOPED THROUGH PROBLEM SOLVING ABILITIES ALSO IN NEW OR UNFAMILIAR ENVIRONMENTS.

THE COURSE HAS THE OBJECTIVE OF INTRODUCING THE STUDENTS TO THE USE OF THE BASIC THEORETICAL TOOLS NEEDED TO STUDY FROM THE SIMPLEST TO THE MOST COMPLEX SOLID STATE SYSTEMS AND, IN PARTICULAR, THE EMERGENCE IN THESE LATTER OF NEW ELEMENTARY EXCITATIONS.

1. KNOWLEDGE AND UNDERSTANDING: THE AIM IS TO PROVIDE THEORETICAL KNOWLEDGES OF THE PHYSICS OF CONDENSED MATTER, WITH SPECIAL REFERENCE TO THE MICROSCOPIC THEORY OF SUPERCONDUCTIVITY AND TO THE BOSE-EINSTEIN CONDENSATION.

2. APPLYING KNOWLEDGE AND UNDERSTANDING: THE APPLICATION OF KNOWLEDGE AND UNDERSTANDING WILL BE DEVELOPED THROUGH PROBLEM SOLVING ABILITIES ALSO IN NEW OR UNFAMILIAR ENVIRONMENTS.

	Prerequisites
	QUANTUM MECHANICS, CONDENSED MATTER PHYSICS.

	Contents
	FORMALISM OF SECOND QUANTIZATION. CANONICAL QUANTIZATION OF CLASSIC FIELDS. BOSONIC AND FERMIONIC FIELDS. QUANTIZATION OF THE HARMONIC FILED. PHONONS. ELECTRON-HOLE INTERACTION. WANNIER EXCITONS. EXCITON WAVE FUNCTION AND ITS SPECTRUM. EXCITON CONDENSATION AND EXCITON MATTER. QUANTIZATION OF THE ELECTROMAGNETIC FIELD. ELECTRON-PHOTON INTERACTIONS. FRENKEL EXCITONS. ELECTRON-EXCITON. EXCITONIC OPERATORS AND COMMUTATION RULES. EXCITON POLARITONS. POLARIZATION WAVES IN POLAR CYSTALS. ELECTRON-PHONON INTERACTION. FROHLICH HAMILTONIAN FOR POLAR CRYSTALS AND FOR METALS. INTERACTION PICTURE AND PERTURBATION THEORY. FEYNMAN GRAPHS. ELECTRON-PHONON SCATTERING AMPLITUDES. SPONTANEOUS AND STIMULATED EMISSION OF PHONONS. CALCULATION OF THE SELF ENERGY AND EFFECTIVE MASS OF AN ELECTRON IN INTERACTION WITH A PHONON FIELD. ELECTRON-PHONON INTERACTION IN IONIC CRYSTALS. POLARON. GENERALIZATION OF BLOCH THEOREM FOR NON RIGID CRYSTALS. THE POLARON WAVE FUNCTION OF LOW-LEE-PINES. WEAK COUPLING LIMIT. EXTENSION TO THE LIMIT OF STRONG COUPLING (LANDAU-PEKAR). EFFECTIVE INTERACTION AMONG POLARONS. BIPOLARONS. ELECTRON-ELECTRON EFFECTIVE INTERACTION IN METALS. PAIRING HAMILTONIAN. BCS THEORY OF SUPERCONDUCTIVITY. THE PROBLEM OF COOPER. INSTABILITY OF THE FERMI SEA. WAVE FUNCTION OF THE SUPERCONDUCTING STATE. SOLUTION AT A TEMPERATURE OF ZERO. EQUATION OF GAP. ELEMENTARY EXCITATIONS AND BOGOLIUBOV TRANSFORMATION. GAP EQUATION AT FINITE TEMPERATURE. EXPERIMENTAL EVIDENCES OF THE EXISTENCE OF THE ENERGY GAP. CALCULATION OF THE SPECIFIC HEAT OF A SUPERCONDUCTOR. BOSE-EINSTEIN CONDENSATION OF ULTRACOLD ATOMIC GASES. MEAN FIELD EQUATION OF GROSS-PITAEVSKII. BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES. BLOCH OSCILLATIONS AND JOSEPHSON EFFECT BETWEEN CONDENSATES IN OPTICAL LATTICES. MULTICOMPONENT CONDENSATES AND MIXTURES OF BOSE-FERMI.

Contents

FORMALISM OF SECOND QUANTIZATION. CANONICAL QUANTIZATION OF CLASSIC FIELDS. BOSONIC AND FERMIONIC FIELDS. QUANTIZATION OF THE HARMONIC FILED. PHONONS.

ELECTRON-HOLE INTERACTION. WANNIER EXCITONS. EXCITON WAVE FUNCTION AND ITS SPECTRUM. EXCITON CONDENSATION AND EXCITON MATTER.

QUANTIZATION OF THE ELECTROMAGNETIC FIELD. ELECTRON-PHOTON INTERACTIONS. FRENKEL EXCITONS. ELECTRON-EXCITON. EXCITONIC OPERATORS AND COMMUTATION RULES.
EXCITON POLARITONS. POLARIZATION WAVES IN POLAR CYSTALS.

ELECTRON-PHONON INTERACTION. FROHLICH HAMILTONIAN FOR POLAR CRYSTALS AND FOR METALS. INTERACTION PICTURE AND PERTURBATION THEORY. FEYNMAN GRAPHS. ELECTRON-PHONON SCATTERING AMPLITUDES. SPONTANEOUS AND STIMULATED EMISSION OF PHONONS. CALCULATION OF THE SELF ENERGY AND EFFECTIVE MASS OF AN ELECTRON IN INTERACTION WITH A PHONON FIELD.

ELECTRON-PHONON INTERACTION IN IONIC CRYSTALS. POLARON. GENERALIZATION OF BLOCH THEOREM FOR NON RIGID CRYSTALS. THE POLARON WAVE FUNCTION OF LOW-LEE-PINES. WEAK COUPLING LIMIT. EXTENSION TO THE LIMIT OF STRONG COUPLING (LANDAU-PEKAR). EFFECTIVE INTERACTION AMONG POLARONS. BIPOLARONS.

ELECTRON-ELECTRON EFFECTIVE INTERACTION IN METALS. PAIRING HAMILTONIAN. BCS THEORY OF SUPERCONDUCTIVITY. THE PROBLEM OF COOPER. INSTABILITY OF THE FERMI SEA. WAVE FUNCTION OF THE SUPERCONDUCTING STATE. SOLUTION AT A TEMPERATURE OF ZERO. EQUATION OF GAP. ELEMENTARY EXCITATIONS AND BOGOLIUBOV TRANSFORMATION. GAP EQUATION AT FINITE TEMPERATURE. EXPERIMENTAL EVIDENCES OF THE EXISTENCE OF THE ENERGY GAP. CALCULATION OF THE SPECIFIC HEAT OF A SUPERCONDUCTOR.

BOSE-EINSTEIN CONDENSATION OF ULTRACOLD ATOMIC GASES. MEAN FIELD EQUATION OF GROSS-PITAEVSKII. BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES. BLOCH OSCILLATIONS AND JOSEPHSON EFFECT BETWEEN CONDENSATES IN OPTICAL LATTICES. MULTICOMPONENT CONDENSATES AND MIXTURES OF BOSE-FERMI.

	Teaching Methods
	THE COURSE HAS A DOMINANT THEORETICAL CHARACTER WITH STRESS TO PHENOMENOLOGICAL PARTS DEVOTED TO POSSIBILE APPLICATIONS.

	Verification of learning
	THE EVALUATION WILL CONSIST OF A FINAL ORAL EXAMINATION PLUS A SEMINAR ON AN ARGUMENT CHOSEN BY THE STUDENT AND RELATED TO THE TOPICS STUDIED IN THE COURSE.

	Texts
	H. HAKEN, QUANTUM FIELD THEORY OF SOLIDS, NORTH-HOLLAND, AMSTERDAM, 1976. R. P. FEYNMAN STATISTICAL MECHANICS: A SET OF LECTURES, BENJAMIN, 1972. L. PITAEVSKII, S. STRINGARI, BOSE-EINSTEIN CONDENSATION, OXFORD SCIENCE PUBLICATIONS, 2003

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2019-03-11]