Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect

We analyse the noise of the edge current of a generic fractional quantum Hall state in a tunnelling point contact system. We show that the non-symmetrized noise in the edge current for the system out-of-equilibrium is completely determined by the noise in the tunnelling current and the Nyquist-Johnson (equilibrium) noise of the edge current. Simply put, the noise in the tunnelling current does not simply add up the equilibrium noise of the edge current. A correction term arises associated with the correlation between the tunnelling current and the edge current. We show, using a non-equilibrium Ward identity, that this correction term is determined by the anti-symmetric part of the noise in the tunnelling current. This leads to a non-equilibrium fluctuation-dissipation theorem and related expressions for the excess and shot noise of the noise in the edge current. Our approach makes use of simple properties of the edge, such as charge conservation and chirality, and applies to generic constructions of the edge theory which includes edges of non-Abelian states and edges with multiple charged channels. Two important tools we make use of are the non-equilibrium Kubo formula and the non-equilibrium Ward identity. We discuss these identities in the appendix.Comment: 20 pages, 5 figure

Non-Equilibrium Quantum Dissipation

Dissipative processes in non-equilibrium many-body systems are fundamentally different than their equilibrium counterparts. Such processes are of great importance for the understanding of relaxation in single molecule devices. As a detailed case study, we investigate here a generic spin-fermion model, where a two-level system couples to two metallic leads with different chemical potentials. We present results for the spin relaxation rate in the nonadiabatic limit for an arbitrary coupling to the leads, using both analytical and exact numerical methods. The non-equilibrium dynamics is reflected by an exponential relaxation at long times and via complex phase shifts, leading in some cases to an "anti-orthogonality" effect. In the limit of strong system-lead coupling at zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with {\it voltage difference} activation. This is analogous to the equilibrium spin-boson model, where at strong coupling and high temperatures the spin excitation rate manifests temperature activated Gaussian behavior. We find that there is no simple linear relationship between the role of the temperature in the bosonic system and a voltage drop in a non-equilibrium electronic case. The two models also differ by the orthogonality-catastrophe factor existing in a fermionic system, which modifies the resulting lineshapes. Implications for current characteristics are discussed. We demonstrate the violation of pair-wise Coulomb gas behavior for strong coupling to the leads. The results presented in this paper form the basis of an exact, non-perturbative description of steady-state quantum dissipative systems

Non-equilibrium field theory

I discuss various topics in relativistic non-equilibrium field theory related to high energy physics and cosmology. I focus on non-perturbative problems and how they can be treated on the lattice.Comment: Plenary talk given at the 18th International Symposium on Lattice Field Theory (Lattice 2000), Bangalore, India, 17-22 Aug 200

Holographic Non-equilibrium Heating

We study the holographic entanglement entropy evolution after a global sharp quench of thermal state. After the quench, the system comes to equilibrium and the temperature increases from $T_i$ to $T_f$. Holographic dual of this process is provided by an injection of a thin shell of matter in the black hole background. The quantitative characteristics of the evolution depend substantially on the size of the initial black hole. We show that characteristic regimes during non-equilibrium heating do not depend on the initial temperature and are the same as in thermalization. Namely these regimes are pre-local-equilibration quadratic growth, linear growth and saturation regimes of the time evolution of the holographic entanglement entropy. We study the initial temperature dependence of quantitative characteristics of these regimes and find that the critical exponents do not depend on the temperature, meanwhile the prefactors are the functions on the temperature.Comment: v1:12 pages, 9 figures; v2:The title and abstract are slightly changed, the discussion is enlarged, the pictures are changed to make presentation more clear and refs. added , 22 pages, 4 figures; v3: typos correcte

Non-Equilibrium Quantum Electrodynamics

We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator for the spinor field is then constructed. We discuss the role of time-dependent renormalization in the propagator and focus on the possibility of obtaining dynamically induced superselection rules. Finally, we derive the master equation for the case of the field being in an one-particle state in a non-relativistic regime and discuss whether EM vacuumm fluctuations are sufficient to produce decoherence in the position basis.Comment: 28 pages, 2 figures. Substantially revised, one important mistake corrected; discussion on decoherence upgraded, section 4 essentially rewritte

Non-equilibrium work relations

This is a brief review of recently derived relations describing the behaviour of systems far from equilibrium. They include the Fluctuation Theorem, Jarzynski's and Crooks' equalities, and an extended form of the Second Principle for general steady states. They are very general and their proofs are, in most cases, disconcertingly simple.Comment: Brief Summer School Lecture Note