Open Quantum Systems  

In General > s.a. deformation quantization; path integrals; quantum systems; modified quantum theory [non-Hamiltonian systems].
* Goal: Provide conceptual and theoretical tools for the description of the reduced dynamics of a system interacting with an external environment.
* Idea: They are usually described by mixed states of the type ρ(t) = trbath whole\(\rangle\)\(\langle\)Ψwhole|, and linear quantum state diffusion (LQSD) stochastic Schrödinger equations; The interaction with the environment can lead to decoherence.
* Markovian systems: In 1992 the idea was introduced that a Markovian open quantum system, such as a laser-driven atom, evolving deterministically as a mixed state because of coupling to its environment, could be fruitfully modelled as a stochastically evolving pure state, e.g., using quantum state diffusion.
* Non-Markovian systems: While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects as key property.
@ Books and reviews: Klimontovich PS(00); Breuer & Petruccione 02; Rotter & Bird RPP(15)-a1507; Lidar a1902-ln; Vacchini a1907.
@ General references: Isar et al IJMPE(94)qp/04; Calzetta et al PhyA(03)qp/00 [stochastic description]; Gambetta & Wiseman PRA(01)qp; Štelmachovič & Bužek PRA(01)qp [entangled with the environment]; Okołowicz et al PRP(03); Ollivier et al PRL(04)qp/03, PRA(05)qp/04 [environment and objective properties]; Nicolosi OSID(05)qp; Jordan et al PRA(06)qp/05 [Schrödinger picture]; Vol PRA(06)qp/05 [semiclassical quantization]; Bodor & Diósi PRA(06) [conserved current]; Crooks PRA(08)-a0706 [time reversal of a quantum operation]; Pérez PRA(09) [Hilbert-space average method]; Vogl et al PRA(10)-a0908 [relaxation towards the ground state]; Bolivar AP(12) [dynamical-quantization approach]; Triana a1508-MS [at low temperatures]; Wiseman JPA(16)-a1609 [Gisin and Percival's quantum state diffusion]; Kheirandish a1903, Karve & Loganayagam a2011 [Heisenberg picture]; > s.a. types of quantum field theories.
@ States: Klimontovich PS(98) [information]; Isar RJP(98)qp/06 [pure states]; Gardas & Puchała JPA(11)-a1006 [stationary states]; Goldstein et al CMP(16)-a1104 [conditional wave function]; Iles-Smith et al PRA(14)-a1311 [non-canonical equilibrium states]; Eleuch & Rotter a1511 [interaction between states via the environment]; Macieszczak et al PRL(16)-a1512 [theory of metastability]; Amato et al PRA(19)-a1903 [microscopic modeling]; > s.a. generalized coherent states.
@ Phase transitions: Nesterov & Ovchinnikov PRE(08)-a0806 [and geometric phases]; Jo et al a2004 [non-equilibrium, neural network approach].
@ Non-Markovian systems: Strunz et al PRL(99) [stochastic Schrödinger equation]; Breuer LNP-a0707; Fischer & Breuer PRA(07)-a0708 [spin + spin-bath]; Rodríguez-Rosario & Sudarshan a0803; Piilo et al PRL(08), PRA(09)-a0902 [in terms of quantum jumps]; Emary PRA(08) [in non-equilibrium environment]; Breuer et al PRL(09)-a0908, Rivas et al PRL(10)-a0911, Laine et al PRA(10) [degree of non-Markovian behavior of quantum evolution]; Chruściński et al PRA(10) [long-time memory]; Fleming & Hu AP(12) [stochastic equations and their perturbative solutions]; Breuer JPB(12)-a1206; De Santis et al a1903 [witnessing non-Markovian dynamics]; Vacchini a1907-in [overview]; Li et al EPL(19)-a2001 [meaning].
@ Related topics: Xu et al PRE(14)-a1403 [back-action on the bath, and non-canonical statistics]; Jordan a1408, Jordan & Seo a1408 [symmetries].
> Examples: see random walk.

Dynamics > s.a. effects [decay]; entanglement; networks [neural networks]; wigner function.
@ General references: Mensky PLA(03)qp/02 [evolution as measurement]; Mohseni & Lidar PRL(06)qp; Kuzovlev a0903 [Schrödinger equation]; Attal & Pellegrini a1004 [thermal environment, stochastic master equation]; Chruściński & Kossakowski a1006; Rivas & Huelga 11-a1104 [introduction]; Monnai JPA(12) [microscopic reversibility]; Gessner & Breuer PRE(13)-a1301 [dynamics of complex open quantum systems]; Cubitt et al CMP(15)-a1303 [local quantum dissipative systems, stability]; Giorgi et al PRA(05)-a1305 [2 spins interacting via an environment, spontaneous synchronization]; Mori PRA(14)-a1310 [non-Markovian corrections]; Gough et al Dokl(14)-a1403 [methods for describing the dynamics]; Overbeck & Weimer PRA(16)-a1510 [many-body systems]; Maziero RBEF(16)-a1510 [Kraus representation, and two-level atom interacting with the electromagnetic vacuum]; Pigeon & Xuereb JSM(16)-a1602 [thermodynamics of trajectories]; Reimer et al JChemP(19)-a1903 [five approaches]; Alba & Carollo a2002 [spreading of correlations]; Merkli a2105, a2105.
@ Hamiltonian: Huang et al PRA(08)-a0810 [effective Hamiltonian approach]; Rotter JPA(09) [non-Hermitian Hamiltonian operator]; Lucia a1101 [thermodynamic Hamiltonian]; Reiter & Sørensen PRA(12)-a1112 [effective operator formalism]; Maksimov et al a1501 [effective non-Hermitian Hamiltonian]; Layden et al PRA(16)-a1506 [emergent unitarity].
@ Decoherence: Dugić & Jeknić IJTP(06)qp/99; Monteoliva & Paz PRA(01)qp [classically chaotic]; Alicki qp/02, et al JPA(04)qp/03; Pepe et al PSSB(12)-a1110 [and energy dissipation]; Bellomo et al a1206 [quantum-to-classical limit]; Vacchini FNL(16)-a1605 [and noise].
@ With classical environment: Kapral a1611 [rev, Liouville dynamics].
@ Entropy production: Yu PLA(08) [and environment]; Deffner & Lutz PRL(11)-a1103 [non-equilibrium].
@ Evolution speed limits: del Campo et al PRL(13); Taddei PhD(14)-a1407; Uzdin & Kosloff EPL(16)-a1607 [rate of purity change]; Funo et al NJP(19)-a1810.
@ Fluctuation-dissipation theorem: Campisi et al PRL(09) + Ritort Phy(09); Fleming et al PRE(13)-a1012; Kawamoto & Hatano PRE(11)-a1105; Hsiang & Hu a2007 [in non-equilibrium steady state].
> Related topics: see Anderson Localization; arrow of time [irreversibility]; geometric phase; lorentz transformations; noether's theorem.

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