84543 - QUANTUM THEORY OF MATTER

Learning outcomes

At the end of the course the student acquires theoretical tools for the modelling of quantum states of matter and radiation. In particular he/she learns the phenomenology and the models related to: i) genuine quantum phenomena of interaction of matter with radiation and quantum theory of radiation; ii) second quantization of fermions and applications to some interacting systems, such as superconductors.

Course contents

MODULE 1

Photons as quantized modes of the electromagnetic field.

Typical states of single-mode fields: Fock states and coherent states. Quantum fluctuations.

Multi-mode states. Casimir effect.

Basic theory of second quantization for boson and fermions: states in Fock space, representation of one-body and two-body operators.

Minimal models of radiation-matter interaction: Rabi model and Jaynes-Cummings model. Emission and quantum revivals.

Tight-binding approach for electrons in solids: the example of graphene. Effective Dirac fermions, Klein paradox, Landauer formula and minimal conductivity.

 

MODULE 2

Phonons

1D examples. Acoustic and optical phonons. Basics of continuum dynamics: strain and stress tensors. Longitudinal and transversal phonons. The dilation operator in 2nd quantization representation.

Electron-phonon interaction

The electron-phonon interaction operator. Perturbative theory for the single electron. The polaron.

Polaron-Polaron interaction

Effective interaction between two polarons via lattice deformation. Deduction of the effective electron-electron interaction via phonon exchanges. Effective BCS Hamiltonian.

BCS Superconductivity

Phenomenology and thermodynamics of metal superconductivity. Cooper pairs. Application of the effective BCS Hamiltonian and BCS supercondutivity. Isotopic effect.

Readings/Bibliography

MODULE 1

C. C. Gerry and P. L. Knight: Introductory Quantum Optics,
Cambridge University Press (2005)

A. Altland and B. Simons: Condensed Matter Field Theory, Cambridge University Press (2010), chap. 2

J. W. Negele and H. Orland: Quantum Many-Particle Systems, Addison-Wesley (1988)

A. H. Castro Neto et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109, 2009

A. J. Leggett, Graphene: Electronic Band Structure and Dirac Fermions, 2010

 

MODULE 2

C. Kittel, Quantum Theory of Solids (John Wiley Sons), chap. 10; p. 195-197

J. M. Ziman Princioles of the Theory of Solids, Cambridge University Press (1964) chap. 1.

B. H. Brandsen and C. J. Joachain, Physics of Atoms and Molecules, Longman (1983), p. 116-122; 227; 512; 529

A. L. Fetter and J. D. Walecka, Quaum Theory of Many Particle Systems, McGraw-Hill Book company, p. 3-33

L. Landau et L. Lifschitz, Théorie de l'élasticité, Editions MIR, Moscou (1967)

 

Lecture Notes, F. Ortolani

Teaching methods

Front lectures.

Assessment methods

Oral exam, with both professors of the two modules.

Questions on topics from both modules.

The final mark reflects the overall performance and it is assigned jointly by the two teachers.

Office hours

See the website of Cristian Degli Esposti Boschi

See the website of Loris Ferrari