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];
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.

@ __Gaussian states__: Nicacio et al PLA(10) [generalized Gaussian cat states];
Olivares EPJST(12)-a1111 [Gaussian Wigner functions];
de Gosson a1204
[optimal Gaussian states for joint position-momentum measurements];
Hagedorn a1301
[minimal-uncertainty product for complex Gaussian wave packets];
Buono et al a1609 [quantum coherence of Gaussian states];
de Gosson a1809
[separability of bipartite Gaussian mixed states]

@ __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];
Adhikary et al a1710 [framework];
> 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];
Luis PRA(11) [classicality and probabilities of non-commuting observables];
de Gosson a1205;
Tsobanjan JMP(15)-a1410 [on finite-dimensional Lie algebras].

> __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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