The Theory of Open Quantum Systems

Book•

The Theory of Open Quantum Systems

Heinz-Peter Breuer, Francesco Petruccione

29 Aug 2002-

TL;DR: Probability in classical and quantum physics has been studied in this article, where classical probability theory and stochastic processes have been applied to quantum optical systems and non-Markovian dynamics in physical systems.

read less

Abstract: PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics

...read moreread less

Content maybe subject to copyright Report

Citations

PDF

Open Access

More filters

Journal Article•DOI•

Theory of open quantum systems

[...]

Rui-Xue Xu, YiJing Yan¹•Institutions (1)

Hong Kong University of Science and Technology¹

09 May 2002-Journal of Chemical Physics

TL;DR: In this paper, a quantum dissipation theory is constructed with the system-bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition.

...read moreread less

Abstract: A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.

...read moreread less

1,731 citations

Cites background or methods from "The Theory of Open Quantum Systems"

...[2] and more physically minded books of Breuer-Petruccione [5], Alicki-Lendi [1]....
[...]
...I used several textbooks [8, 12, 5, 2, 16, 14, 1] during the preparation for the class and I often refer to these textbooks instead of rewriting the same material here....
[...]

Journal Article•DOI•

Quantum fluids of light

[...]

Iacopo Carusotto¹, Cristiano Ciuti²•Institutions (2)

University of Trento¹, Paris Diderot University²

21 Feb 2013-Reviews of Modern Physics

TL;DR: In this paper, a review of recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems is presented, from the superfluid flow around a defect at low speeds to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles.

...read moreread less

Abstract: This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

...read moreread less

1,469 citations

Cites background from "The Theory of Open Quantum Systems"

...Tracing out the radiative modes of the eld outside the cavity, dissipation results in additional terms to be included in the master equation for the evolution of the density matrix of the cavity eld (Breuer and Petruccione, 2002; Gardiner and Zoller, 2004; Walls and Milburn, 2006), dˆ dt = 1 i~ [H;ˆ] + L[ˆ]: (16) Under the assumptions that the temperature of the radiative modes outside the cavity is much lower than the frequ...
[...]

Journal Article•DOI•

QuTiP: An open-source Python framework for the dynamics of open quantum systems !

[...]

J. R. Johansson, P. D. Nation¹, Franco Nori¹•Institutions (1)

University of Michigan¹

01 Aug 2012-Computer Physics Communications

TL;DR: An object-oriented open-source framework for solving the dynamics of open quantum systems written in Python that is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.

...read moreread less

1,430 citations

Journal Article•DOI•

Colloquium: quantum coherence as a resource

[...]

Alexander Streltsov¹, Gerardo Adesso², Martin B. Plenio³•Institutions (3)

Gdańsk University of Technology¹, University of Nottingham², University of Ulm³

30 Oct 2017-Reviews of Modern Physics

TL;DR: In this article, the authors discuss and review the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

...read moreread less

Abstract: The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted a considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has only been initiated recently. In this Colloquium we discuss and review the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

...read moreread less

1,392 citations

Journal Article•DOI•

Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems

[...]

Massimiliano Esposito¹, Upendra Harbola², Shaul Mukamel²•Institutions (2)

University of California, San Diego¹, University of California, Irvine²

02 Dec 2009-Reviews of Modern Physics

TL;DR: Fluctuation theorems (FTs) as discussed by the authors describe some universal properties of nonequilibrium fluctuations and are derived from a quantum perspective by introducing a two-point measurement on the system.

...read moreread less

Abstract: Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Green's functions techniques for computing the energy and particle statistics are presented.

...read moreread less

1,203 citations

Cites background or methods from "The Theory of Open Quantum Systems"

...The rotating wave approximation (RWA) [23, 76] (also known as secular approximation [39, 156] or Davis procedure [103, 166]) is often used to impose a Lindblad form [23, 123, 166] to the Markovian QME generator in order to guaranty the complete positivity of the subsystem density matrix time evolution....
[...]
...This means that the QME is interpreted as resulting from a continuous positive operator-valued measurement [23, 141] on the system by the leads....
[...]
...(130) is extended to infinity), we perform the RWA approximation which is equivalent to assume that the lead correlation functions are diagonal in s [88]....
[...]
...It can be shown that performing the RWA on the GQME is equivalent to assume from the beginning that the coupling term is of the simplified form V̂X = ∑ i∈X J X i0 (â † i â0 + â † 0âi)....
[...]
...Such interpretation allows to construct a trajectory picture of the system dynamics, where each realization of the continuous measurement leads to a given system trajectory [23, 24, 25, 76, 141]....
[...]

Collapse

The Theory of Open Quantum Systems

Citations

Cites background or methods from "The Theory of Open Quantum Systems"

Cites background from "The Theory of Open Quantum Systems"

Cites background or methods from "The Theory of Open Quantum Systems"

Related Papers (5)