Dissipative Systems  

In General > s.a. fluctuations; Kinetic Theory; specific heat.
* Idea: A dissipative system (also called damped system) is one subject to a non-conservative force that dissipates energy.
* Description: As a dynamical system, time evolution is described by a semigroup of transformations, rather than a group, since it is associated with a preferred time direction, and using contact structures; Dissipative processes contract volumes in phase space.
@ General references: Bimonte et al PLA(03)ht, MPLA(03)ht-conf [Peierls-type brackets for Langevin equation]; Chruściński RPMP(06) [Koopman's operator and role of resonant states]; Kawai et al PRL(07) [average dissipation in a transition between equilibria]; Sonnino & Evslin PLA(07) [relaxation, minimum rate of dissipation principle]; Ichinose a1305 [renormalization-group approach]; Razavy 17 [classical and quantum].
@ Variational principles: Patiño & Rago NCB(01); Luo & Guo a1102 [new variational principle]; Kraus & Osborne PRA(12)-a1206 [time-dependent]; Taverna & Torres MMAS(15)-a1404 [generalized fractional operators and non-standard Lagrangians]; Lazo & Krumreich JMP(14)-a1412 [action principle]; Martínez-Pérez & Ramírez JMP(18)-a1708 [Lagrangian, and Noether's theorem].
@ Hamiltonian formulation: Rajeev AP(07) [complex Hamiltonian and quantization]; Luo & Guo a0803; Fröhlich et al CMP(12)-a1110 [friction from Cerenkov radiation in a model for a heavy particle in a medium]; Schuch et al a1306 [relations between approaches]; de León & Sardón a1607 [geometric Hamilton-Jacobi theory]; Gaset et al a1907 [Hamiltonian and Lagrangian contact formalisms, symmetries]; > s.a. hamiltonian systems.

Types of Systems > s.a. classical systems; fluids [non-perfect]; Friction; open systems; oscillators; wave phenomena [attenuation].
@ Relativistic mechanics: González IJTP(07)qp/05, IJTP(07) [1D system Lagrangian and Hamiltonian]; Tarasov AP(10).
@ Constrained: Nguyen & Turski JPA(01) [Dirac-like brackets].
@ Chaotic: Bag et al JPA(00) [entropy production]; Motter et al PRL(13) + news PhysOrg(13)nov [doubly transient chaos].
@ Non-Markovian: Koch et al PRL(08) [semiclassical]; > s.a. brownian motion.
@ Field theories: Vitela AJP(04)mar [electromagnetic waves in dissipative media]; Gaset et al a1905 [contact geometry framework].
@ Dissipative subsystem of conservative system: Wesz RPMP(06) [perturbation theory].
@ Related topics: Romano PhD(02)hp/03 [in particle physics]; Krechetnikov & Marsden RMP(07) [dissipation-induced instabilities]; Herrera et al PLA(12)-a1201 [reversible dissipative processes]; Bardyn et al NJP(13) [dissipation as a resource for many-body dynamics, and topological phases].

Quantum Dissipative Systems > s.a. modified quantum mechanics [non-Hamiltonian]; quantum systems; spin systems.
* Idea: Phenomena of decoherence and dissipation in quantum mechanics arise from the interaction with the environment.
* And quantum foundations: A deterministic, dissipative classical model is used in a proposal by 't Hooft for obtaining quantum mechanics; > s.a. origin of quantum mechanics.
@ General references: Feynman & Vernon AP(63), reprint AP(00) [and influence functionals]; Rajagopal & Rendell PhyA(02)qp/01; Rau & Wendell PRL(02)qp; Tarasov PLA(02)-a1107 [stationary states]; Richardson AP(06); Tsekov NAP(09)-a0903; Öttinger EPL(11)-a1002 [geometry and thermodynamics]; Chruściński et al OSID(12)-a1102 [observables]; Abreu & Godinho PRE(11)-a1102 [using fractional calculus]; Weiss 12; Sanz et al AP(14)-a1306 [Bohmian analysis]; Aivazian a1702 [extended Hilbert phase space formalism]; Anuar a1705 [canonical quantization].
@ Path-integral approach: Jain et al AJP(07)mar [evolution, types of damping]; Barth et al PRA(16)-a1607 [combined Hamiltonian and non-Hamiltonian dynamics].
@ And decoherence: Retamal & Zagury PRA(01) [and pure states]; Ambegaokar JSP(06)qp/05 [quantum oscillator]; Mousavi & Miret-Artés JPcomm(18)-a1711.
@ Chaos, stability: Cohen AP(00); Cubitt et al CMP(15)-a1303; Lucia et al PRA(15)-a1409 [rapid mixing and stability]; Brandão et al JMP(15)-a1505 [rapidly mixing, area law for the mutual information for fixed points].
@ Types of systems: Senitzky PR(60) [damped oscillator]; Hakim & Ambegaokar PRA(85) [free particle in dissipative environment]; Ozorio de Almeida et al JPA(09)-a0708 [Markovian, semiclassical]; Poletti et al proc(13)-a1212 [many-atom systems and the effect of interactions on the rate of decoherence]; Polonyi PRA-a1502 [test particle interacting with an ideal gas]; > s.a. quantum oscillators [damped].
@ Special topics: Blasone et al PLA(01) [and quantum zero-point energy]; Moshinsky & Schuch JPA(01) [and diffraction in time]; Mensky & Stenholm PLA(03) [and continuous measurement]; Sivasubramanian et al PLA(03) [induced non-commutative geometry]; Terra Cunha et al qp/04 [time scale]; López et al qp/05 [position-dependent coefficient and ambiguity]; García-Mata et al PRA(05)qp [quantum phase space contraction rate]; Wysocki PRA(05) [hydrodynamic quantization]; Khademi & Nasiri qp/05 [extended phase space]; Urasaki qp/07 [and reality].
@ Field theories: Calzetta & Hu PRD(89) [dissipation from particle creation]; Zhong et al ChPB(14)-a1212 [condensate + continuum, effects of dissipation and non-linearity]; > s.a. quantum field theory in curved spacetime.
> Gravitational: see approaches to quantum gravity; minisuperspace quantum cosmology.
> Related topics: see deformation quantization; entanglement; Lindblad Equation; quantum phase transitions; vacuum; zeno effect.

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