PHYSICS OF CONDENSED STATES

International Teaching PHYSICS OF CONDENSED STATES

0522600006
DEPARTMENT OF PHYSICS "E. R. CAIANIELLO"
EQF7
PHYSICS
2021/2022

YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2017
PRIMO SEMESTRE
CFUHOURSACTIVITY
648LESSONS
Objectives
THE TEACHING AIM WILL BE FOCUSED ON:
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.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE APPLICATION OF KNOWLEDGE AND UNDERSTANDING WILL BE DEVELOPED THROUGH PROBLEM SOLVING ABILITIES ALSO IN NEW OR UNFAMILIAR ENVIRONMENTS. IN PARTICULAR, STUDENTS WILL BE STIMULATED TO INTEGRATE KNOWLEDGE AND HANDLE COMPLEXITY AND TO COMMUNICATE CONCLUSIONS AND KNOWLEDGE TO SPECIALIST AND NON SPECIALIST AUDIENCES.
Prerequisites
QUANTUM MECHANICS, CONDENSED MATTER PHYSICS.
Contents
OPERATOR ALGEBRAS AND COMMUTATION RELATIONS (LECT. 2H). CREATION AND ANNICHILATION OPERATORS. FUNCTIONS OF OPERATORS. COMMUTATION RELATIONS. DEFORMATIONS OF THE HEISENBERG ALGEBRA. THE SHIFTED HARMONIC OSCILLATOR. COHERENT STATES.
CANONICAL QUANTIZATION OF CLASSIC FIELDS (LECT. 2H). BOSONIC AND FERMIONIC FIELDS AND COMMUTATION RELATIONS. QUANTIZATION OF THE FIELD OF THE HARMONIC CRYSTAL. PHONONS. OPERATORS IN THE FORMALISM OF SECOND QUANTIZATION. THE MANY BODY PROBLEM.
ELECTRON-HOLE INTERACTION (LECT. 6H). EXCITONS OF LARGE RADIUS. THE WANNIER EXCITON. EXCITON WAVE FUNCTION AND ENERGY SPECTRUM. EXCITON CONDENSATION AND EXCITON MATTER. SNAL RADIUS EXCITONS. THE FRENKEL EXCITON. ELECTRON-EXCITON INTERACTION. POLARIZATION WAVES IN POLAR CRYSTALS.
ELECTRON-PHONON INTERACTION IN POLAR CRYSTALS AND IN METALS (LECT. 6H). ELECTRON-PHONON INTERACTION. DERIVATION OF THE FROHLICH HAMILTONIAN FOR POLAR CRYSTALS AND FOR METALS. ELECTRON COUPLING WITH ACUSTIC AND OPTICAL PHONONS. FROLICH HAMILTONIAN IN THE INTERACTION PICTURE.
PERTURBATION THEORY AND FEYNMAN GRAPHS (LECT. 6H). CALCULATIONS OF 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 (LECT. 6H). THE POLARON PROBLEM. GENERALIZATION OF BLOCH THEOREM FOR DEFORMABLE CRYSTALS. THE WEAK COUPLING LIMIT AND THE POLARON WAVE FUNCTION OF LOW-LEE-PINES. EFFECTIVE INTERACTION BETWEEN POLARONS. BIPOLARONS.
THE BCS MICROSCOPIC THEORY OF SUPERCONDUCTIVITY (LECT. 8H). THE BCS THEORY OF THE SUPERCONDUCTIVITY. FROHLICH EFFECTIVE ELECTRON-ELECTRON INTERACTION IN METALS AND PAIRING HAMILTONIAN. INSTABILITY OF THE FERMI SPHERE AND THE COOPER PAIR PROBLEM. WAVE FUNCTION OF THE SUPERCONDUCTING STATE. SOLUTION AT A TEMPERATURE OF ZERO. EQUATION OF GAP. BOGOLIUBOV TRANSFORMATION EXCITED STATES OF A SUPERCONDUCTOR.
BCS AT FINITE TEMPERATURE (LECT. 4H). THE GAP EQUATION AT FINITE TEMPERATURE. THE CRITICAL TEMPERATURE. EXPERIMENTAL EVIDENCES OF THE EXISTENCE OF THE ENERGY GAP. SPECIFIC HEAT OF A SUPERCONDUCTOR. DENSITY OF THE STATES AND DIFFERENTIAL CONDUCTANCE.
TUNNELING PHENOMENA IN SUPERCONDUCTORS (LECT. 3H). TUNNELING HAMILTONIAN. TUNNELING OF QUASI-PARTICLES AND OF COOPER PAIRS. THE JOSEPHSON EFFECT. DERIVATION OF THE JOSEPHSON EQUATIONS FOR CURRENT AND VOLTAGE. LONG JOSEPHSON JUNCTIONS ELECTRODYNAMICS. THE SINE-GORDON EQUATION. FLUXONS AND SOLITONS.
BOSE-EINSTEIN CONDENSATION (LECT. 5H). MEAN FIELD THEORY AND GROSS-PITAEVSKII EQUATION. BOGOLIUBOV THEORY FOR THE WEAKLY INTERACTING BOSE GAS. GROUND STATE ENERGY AND QUASI-PARTICLE SPECTRUM. BOSE-EINSTEIN CONDENSATES OF ULTRACOLD ATOMIC GASES IN OPTICAL LATTICES.
Teaching Methods
A COURSE WITH THEORETICAL CHARACTER DEVOTED TO THE STUDY OF THE PHYSICS OF SEVERAL CONDENSATE STATES,
Verification of learning
THE LEVEL OF LEARNING WILL BE EVALUATED WITH THE DISCUSSION OF A REPORT/PRESENTATION ON AN IN-DEPTH TOPIC CHOSEN BY THE STUDENT AND AN ORAL EXAMINATION WITH A SET OF QUESTIONS ON THE CONTENT OF THE COURSE . IN PARTICULAR, IT WILL BE VERIFIED THE ABILITY OF A) KNOWING AND UNDERSTANDING: CORRECTLY EXPOSING THE COURSE TOPICS; SHOWING ABILITY TO REPORT AND TO CITE MODELS, INTERPRETING WHAT LEARNED AND EXPLAINING, GETTING IMPLICATIONS AND SIMPLIFICATIONS. (RANGE IN THE EXAM ASSESSMENT: 18-26). B) IDENTIFY RELATIONSHIPS, MODELS AND HYPOTIZE ALTERNATIVES, EXPRESS SCIENTIFIC SUPPORTED OPINIONS, AGREE OR DISAGREE USING SCIENTIFIC ARGUMENTS, AND INDEPENDENT LERNING SKILLS (RANGE IN THE EXAM ASSESSMENT: 27-30) . THE PRAISE WILL BE GIVEN TO STUDENTS SHOWING A SIGNIFICATIVE ABILITY OF MASTERING, UNDERSTANDING AND REWORKING SKILLS WITH APPROPRIATE SCIENTIFIC LANGUAGE.
Texts
H. HAKEN, QUANTUM FIELD THEORY OF SOLIDS, NORTH-HOLLAND, AMSTERDAM, 1976.
PHILIP PHILLIPS, ADVANCED SOLID STATE PHYSICS, CAMBRIDGE UNIVERSITY PRESS, 2012.
L. PITAEVSKII, S. STRINGARI, BOSE-EINSTEIN CONDENSATION, OXFORD SCIENCE PUBLICATIONS, 2003.
R. P. FEYNMAN STATISTICAL MECHANICS: A SET OF LECTURES, BENJAMIN, 1972.
LECTURE NOTES.
More Information
THE COURSE WILL BE GIVEN IN THE SECOND SEMESTER.
  BETA VERSION Data source ESSE3