**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

**Language**: English

**Course Plan**:

**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:**

**Oral exam: **

Structure of the oral exam depends on the actual COVID situation.

**Problem solving:**

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.

**Term paper: **

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

**Additional material:**

**List of subjects for oral exam: **