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
|Ψwhole\(\rangle\)\(\langle\)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.
main page
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