Semester: 2020/21, SPRING SEMESTER
Time, location: Tuesdays, 16:15-17:45, online course
to join the course via Teams, use the code: evqa8kx
Lecturers: Gergely Zaránd and András Pályi
Principles of Random Matrix Theory
Disordered systems and random Hamiltonians, symmetries and invariant measures, metric tensor and distances, maximum entropy principle, and joint energy distributions, GOE, GUE and GSE
Transmission through mesoscopic conductors
Landauer-Büttiker formula, and circular ensembles, universal conductance fluctuations;weak localization correctiondistribution of transmissions.
Classical and quantum noise
Classical noise, Fano factors (determination of charge); Scattering states and current operator; rigorous derivation of Landauer-Büttiker;quantum noise through a scattering region
Coulomb blockade of grains
Hartree terms and classical Coulomb energy; Effective Hamiltonian for grains, energy of a grain embedded into a circuit; Quantum fluctuatons and Coulomb blockade conditions; Coulomb blockade of superconducting grains (Richardson model, even-odd effect etc.)
Transport through grains and QD's
Anderson model and sequential tunneling through grains and/or QDs; Quantum fluctuations and Kondo effect; Kondo resonance, Fermi liquid theory
Possible additional subjects:
Dynamical Coulomb blockade and P(E) theory;
DMPK theory of a 1D conductor
Properties of Carbon nanotubes
Phase description of superconducting grains
Requirements and grading:
Structure of the oral exam depends on the actual COVID situation.
You can obtain a grade through problem solving, too.
You will recieve 2 problem sets.
You can select problems from each set to collect 50 points at maximum (i.e. max. 100 points).
To pass (grade 2) you need to reach 50% (from each set), for grade 3 you need 60points, for grade 4 you need to reach 70points, and for grade 5, you must score above 80points.
You may discuss with the others (or with us), give hints to each-other, but we request independent work: you may help each-other but you are not allowed to copy
Deadlines will be specified in the problem sets.
Instead of problem solving, you can pass by handing in a 15 page long term paper, too. To do that you must paricipate in / watch each lecture. The term paper is supposed to start with a 8-10 pages introduction, putting your subject into context and revising the relevant material of the course, and the last 8-10 pages are supposed to discuss a hand-out (publication or book chapter). You do not need to understand all details of the handout, but the text must be clear and logical, reflecting your clear understanding.
Handouts: to be posted via Teams
Handouts for term paper: to be posted via Teams
Lecture notes (for personal use, only, no responsibility for mistakes, typos etc.):
to be posted via Teams
List of subjects for oral exam: