Semiclassical States of Quantum Systems  

In General > s.a. coherent states; mixed states; quantum field theory states; quantum locality.
* Idea: With respect to correlations, a bipartite state is called classical if it is left undisturbed by a certain local von Neumann measurement.
* Idea: Semiclassical states are states with a classical interpretation, in which the probability distributions for a chosen set of observables are narrowly peaked around classical values; Common examples are coherent and squeezed states.
$ Def: A set of semiclassical states is a collection {|ω\(\rangle\)} of states labelled by points ω in Γ in phase space, together with a set {(Fi, εi, δi)} of observables and tolerances, such that |\(\langle\)ω|Fi|ω\(\rangle\) – Fi(ω )| ≤ εi and (ΔFi)ω2δi, for all ω and i.
@ General references: Solovej & Spitzer CMP(03) [semiclassical calculus]; Genoni et al PRA(07)-a0704 [departure from Gaussianity]; Badziag et al PRL(09) [there are no "classical" states].
@ Minimum uncertainty: Trifonov et al PRL(01) [discrete-valued observables]; Detournay et al PRD(02) [with gup]; de Gosson PLA(04) [optimal]; Al-Hashimi & Wiese AP(09)-a0907 [relativistic and non-relativistic]; Hagedorn a1301 [minimal-uncertainty product for complex Gaussian wave packets]; Kisil ch(15)-a1312 [minimal-uncertainty states and holomorphy-type conditions on the images of the respective wavelet transform]; Korzekwa & Lostaglio a1602 [and classical noise]; > s.a. coherent and Squeezed States.
@ With classical behavior: Davidovic & Lalovic JPA(98); Kuś & Bengtsson PRA(09)-a0905 [most-classical states]; Koide PLA(15)-a1412 [extracting classical degrees of freedom, and hybrid systems]; > s.a. macroscopic quantum systems.
@ Non-classical states: Vogel PRL(00) [sho]; Foldi PhD(03)qp/04 [and decoherence]; Hammerer et al a1211-ch; Szymusiak a1701 [states that are "most" quantum with respect to a given measurement]; > s.a. mesoscopic systems.
@ Related topics: Senitzky PRL(81) [statistics]; Shvedov AP(02)mp/01 [symmetries], mp/01 [group actions]; de Gosson mp/02 [symplectic area]; Hájíček FP(09)-a0901 [maximum-entropy states]; Ishikawa & Tobita PTP(09)-a0906 [wave-packet coherent length]; Budiyono PRA(09)-a0907 ["most probable wave function", and finite-size progressing solution]; Nicacio et al PLA(10) [generalized Gaussian cat states]; Luis PRA(11) [classicality and probabilities of non-commuting observables]; Olivares EPJST(12)-a1111 [Gaussian Wigner functions]; de Gosson a1204 [optimal Gaussian states for joint position-momentum measurements], a1205; Tsobanjan JMP(15)-a1410 [on finite-dimensional Lie algebras]; Buono et al a1609 [quantum coherence of Gaussian states].
> Related topics: see complex structure; conservation laws [and symmetries]; dirac fields [wave packets]; entanglement; wigner functions; Explanation; fluctuation; quantum effects.

blue bullet Related pages: see quantum state evolution; relationship classical-quantum theory; semiclassical effects and degree of quantumness; semiclassical limit.

Special Types of Systems > s.a. phase transition.
* Issue: Is environmental decoherence required to prevent classically chaotic systems (e.g., tumbling satellites such as Hyperion) from exhibiting non-classical behavior within a short time span?
@ General references: Arsenović et al PRA(99) [spin-1/2]; Blanchard & Olkiewicz PLA(00) [open systems]; Yang & Kellman PRA(02) [EBK wave function near resonance]; Schulman PRL(04) [particles, evolution of spreads]; Giraud et al PRA(08) [spin states]; Pedram EPL(10)-a1001 [1D]; > s.a. oscillators; photon; semiclassical quantum gravity [including non-classical]; thermal radiation.
@ Constrained systems: Shvedov ht/01 [first-class], mp/05-conf [linear C, quadratic H]; Dell'Antonio & Tenuta JPA(04)mp/03 [with constraining potential]; Ashtekar et al PRD(05)gq [kinematical and physical states]; Gambini & Pullin a1207 [totally constrained, self-adjointness of the Hamiltonian].
@ Chaotic systems: Eckhardt PRP(88); Ballentine PRA(01), PRA(02); Kaplan NJP(02); Gong & Brumer PRA(03); Schomerus & Jacquod JPA(05); Wiebe & Ballentine PRA(05) [classical Hyperion tumbling and decoherence], comment Schlosshauer FP(08)qp/06, reply Ballentine FP(08); Everitt NJP(09)-a0712 [SQUID ring]; Paul a0901; Goletz et al PRE(09)-a0904 [semiclassical, long-time quantum transport]; Wisniacki et al PRL(10)-a0911 [quantum perturbations]; Giller & Janiak a1108 [classically chaotic, Maslov-Fedoriuk approach].


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