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
{(*F*_{i},
*ε*_{i},
*δ*_{i})}
of observables and tolerances, such that |\(\langle\)*ω*|*F*_{i}|*ω*\(\rangle\) – *F*_{i}(*ω* )| ≤ *ε*_{i} and
(Δ*F*_{i})_{ω}^{2} ≤ *δ*_{i},
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.

__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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