Dissipative Systems| 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.
main page
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send feedback and suggestions to bombelli at olemiss.edu – modified 2 aug 2019