Alex Kamenev

QUASIPARTICLE LIFETIME IN A FINITE SYSTEM : A NONPERTURBATIVE APPROACH

The problem of electron-electron lifetime in a quantum dot is studied beyond perturbation theory by mapping onto the problem of localization in the Fock space. Localized and delocalized regimes are identified, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are single-particle-like. In the delocalized regime, each eigenstate is a superposition of states with very different quasiparticle content. The transition energy is

Keldysh technique and non-linear σ-model: basic principles and applications

{\ensuremath{\epsilon}}_{c}\ensuremath{\simeq}\ensuremath{\Delta}(g/\mathrm{ln}g{)}^{1/2}

Sachdev–Ye–Kitaev model as Liouville quantum mechanics

, where

Electron-electron interactions in disordered metals: Keldysh formalism

\ensuremath{\Delta}

Coulomb drag in normal metals and superconductors: Diagrammatic approach.

is mean level spacing, and

Extinction of an infectious disease: a large fluctuation in a nonequilibrium system.

g

Dynamic Response of One-Dimensional Interacting Fermions

is the dimensionless conductance. Near

Power-law out of time order correlation functions in the SYK model

{\ensuremath{\epsilon}}_{c}

Wigner-Dyson Statistics from the Replica Method

there is a broad critical region not described by the golden rule.

Switching rates of multistep reactions

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg–Landau theory, proximity and Josephson effects, etc.