Nonequilibrium mesoscopic transport: a genealogy

Models of nonequilibrium quantum transport underpin all modern electronic devices, from the largest scales to the smallest. Past simplifications such as coarse graining and bulk self-averaging served well to understand electronic materials. Such particular notions become inapplicable at mesoscopic dimensions, edging towards the truly quantum regime. Nevertheless a unifying thread continues to run through transport physics, animating the design of small-scale electronic technology: microscopic conservation and nonequilibrium dissipation. These fundamentals are inherent in quantum transport and gain even greater and more explicit experimental meaning in the passage to atomic-sized devices. We review their genesis, their theoretical context, and their governing role in the electronic response of meso- and nanoscopic systems.Comment: 21p

Quantum trajectories and open many-body quantum systems

The study of open quantum systems has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This was developed as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. We review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.Comment: 66 pages, 29 figures, review article submitted to Advances in Physics - comments and suggestions are welcom

Quantum-memory-enhanced dissipative entanglement creation in nonequilibrium steady states

This article investigates dissipative preparation of entangled nonequilibrium steady states (NESS). We construct a collision model where the open system consists of two qubits which are coupled to heat reservoirs with different temperatures. The baths are modeled by sequences of qubits interacting with the open system. The model can be studied in different dynamical regimes: with and without environmental memory effects. We report that only a certain bath temperature range allows for entangled NESS. Furthermore, we obtain minimal and maximal critical values for the heat current through the system. Surprisingly, quantum memory effects play a crucial role in the long-time limit. First, memory effects broaden the parameter region where quantum correlated NESS may be dissipatively prepared and, second, they increase the attainable concurrence. Most remarkably, we find a heat current range that does not only allow, but even guarantees that the NESS is entangled. Thus, the heat current can witness entanglement of nonequilibrium steady states.</p

Thermalization of finite many-body systems by a collision model

We construct a collision model description of the thermalization of a finite many-body system by using careful derivation of the corresponding Lindblad-type master equation in the weak coupling regime. Using the example of two level target system, we show that collision model thermalization is crucially dependent on the various relevant system and bath timescales and on ensuring that the environment is composed of ancillae which are resonant with the system transition frequencies. Using this we extend our analysis to show that our collision model can lead to thermalisation for certain classes of many-body systems. We establish that for classically correlated systems our approach is effective, while we also highlight its shortcomings, in particular with regards to reaching entangled thermal states

Ten reasons why a thermalized system cannot be described by a many-particle wave function

It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of statistical mechanics. The usual attempts to resolve this conflict for instance by appealing to decoherence or eigenstate thermalization are riddled with problems. This paper considers theoretical physics of thermalized systems as it is done in practise and shows that all approaches to thermalized systems presuppose in some form limits to linear superposition and deterministic time evolution. These considerations include, among others, the classical limit, extensivity, the concepts of entropy and equilibrium, and symmetry breaking in phase transitions and quantum measurement. As a conclusion, the paper argues that the irreversibility and stochasticity of statistical mechanics should be taken as a true property of nature. It follows that a gas of a macroscopic number $N$ of atoms in thermal equilibrium is best represented by a collection of $N$ wave packets of a size of the order of the thermal de Broglie wave length, which behave quantum mechanically below this scale but classically sufficiently far beyond this scale. In particular, these wave packets must localize again after scattering events, which requires stochasticity and indicates a connection to the measurement process.Comment: Drastically rewritten version, with more explanations, with three new reasons added and three old ones merged with other parts of the tex

Fluctuations and Noise: A General Model with Applications

A wide variety of dissipative and fluctuation problems involving a quantum system in a heat bath can be described by the independent-oscillator (IO) model Hamiltonian. Using Heisenberg equations of motion, this leads to a generalized quantum Langevin equation (QLE) for the quantum system involving two quantities which encapsulate the properties of the heat bath. Applications include: atomic energy shifts in a blackbody radiation heat bath; solution of the problem of runaway solutions in QED; electrical circuits (resistively shunted Josephson barrier, microscopic tunnel junction, etc.); conductivity calculations (since the QLE gives a natural separation between dissipative and fluctuation forces); dissipative quantum tunneling; noise effects in gravitational wave detectors; anomalous diffusion; strongly driven quantum systems; decoherence phenomena; analysis of Unruh radiation and entropy for a dissipative system.Comment: Presented at the SPIE International Symposium on Fluctuations and Noise in Photonics and Quantum Optics (Austin, May 2005

Conformal field theory out of equilibrium: a review

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.Comment: 50 pages + 10 pages of references, 5 figures. v2: minor modifications. Review article for special issue of JSTAT on nonequilibrium dynamics in integrable quantum system