In General > s.a. [quantum states]; entanglement; locality; mixed
states; pilot-wave theory ["non-quantum"]; schrödinger
equation.
$ Pure states: A state
s is pure if there are no two distinct states s1 and s2 and positive c1 and
c2 such that s = c1s1 + c2s2.
$ Separable states:
If A and B are two subsystems, separable states are the non-entangled ones,
convex combinations of
product states
=
k
k
Ak
Bk , where
k
k =
1 .
* Unstable / decaying states:
Can be associated with resonances, and described by a Rigged Hilbert space.
* Schrödinger cat states: Superpositions
of well-separated coherent states.
@ Separable states: Peres PRL(96)qp [necessary
condition]; Sanpera et al qp/97 [characterization];
Zyczkowski et al PRA(98)
[volume]; Majewski OSID(99)qp/97 [rigorous
description]; Lockhart et al QIC(02)qp/00 [product
states]; Shi & Du qp/01 [boundary];
Wu & Anandan PLA(02),
Rudolph PLA(04)
[criteria]; Albeverio et al PRA(03)qp [reduction
criterion]; Wu PLA(04)
[as convex sum]; Timpson & Brown IJQI(05)qp/04 [proper
vs improper]; Raggio qp/05 [spectral
conditions]; Khasin et al PRA(07)qp [negativity
as measure of non-separability]; Li & Luo PRA(08)
[intrinsic characterization]; Jakubczyk & Pietrzkowski RPMP(09) [integral representations].
@ Energy eigenstates: Halliwell & Thorwart PRD(02)gq [and
dynamics]; Moriconi AJP(07)mar-qp [number
of nodes].
@ Ground state: Mouchet JPA(05)qp/04 [energy
estimation method]; > s.a. schrödinger equation [bounds].
@ Bound states: Chadan et al JMP(96)
[bound on number]; Chadan & Kobayashi JMP(97)
[sufficient condition]; Aktosun et al JMP(98)
[number, 1D]; Chadan et al JMP(99)
[number]; Brau & Calogero JPA(03)mp/04,
Brau JPA(03)mp/04,
JPA(04)mp [central V,
conditions and bounds]; Chadan et al JMP(03)
[number, 1D and 2D]; Ritchie PLA(06)
[relativistic]; > s.a. atomic physics, oscillators, quantum
systems.
@ Unstable states: Ordonez et al PRA(01)
[dressed]; Chruscinski mp/02 [Wigner
functions for damped systems]; Castagnino et al PLA(01)qp/02;
Kielanowski qp/03-in; > s.a. resonance.
@ Metastable states: Davies JFA(82) [dynamical stability].
@ Bipartite states: Yu et al RPMP(07)-a0711 [differential geometry];
> s.a. entanglement.
@ In atoms: Bialynicka-Birula & Bialynicki-Birula PRA(97)
+ pn(97)nov
[Trojan states]; Calsamiglia et al PRL(01)cm [macroscopic
superpositions].
@ Other states: Mould FPL(01)qp, qp/01,
Ferrero et al FP(04)
[physical vs subjective]; in Sanz JPA(05)qp/04 [nowhere
differentiable]; Jeong & Ralph qp/05-in
[Schrödinger cat states, application]; de Oliveira et al PhyA(05),
Malbouisson
et
al PhyA(07)
[displaced
number states]; Luís PRA(07)
[exponential, using Rényi entropy
as uncertainty measure]; > s.a. entanglement
examples [cluster states].
Semiclassical States > s.a. coherent
states; quantum field theory states; semiclassial
quantum mechanics.
* 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 {|![]()
}
of
states labelled by points
in
in
phase space, together with a set {(Fi,
i,
i)}
of observables and tolerances, such that |![]()
|Fi|![]()
– Fi(
)|
i and
(
Fi)omega2
i,
for all
and i.
@ 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; > s.a. coherent, Squeezed
States.
@ With classical behavior: Davidovic & Lalovic JPA(98);
Kus
& Bengtsson PRA(09)-a0905 [most-classical
states]; > s.a. semiclassical
quantum mechanics.
@ Constrained systems: Shvedov ht/01 [first-class], mp/05-in
[linear C, quadratic H]; Ashtekar et al PRD(05)gq [kinematical
and physical states].
@ Special systems: Arsenovic et al PRA(99)
[for spin-1/2]; Blanchard & Olkiewicz
PLA(00)
[open systems]; Yang & Kellman
PRA(02)
[EBK wave function near resonance]; Dell'Antonio & Tenuta
JPA(04)mp/03 [with
constraining potential]; Schulman PRL(04)
[particles, evolution of spreads]; Giraud et al PRA(08) [spin states]; > s.a. photon, semiclassical
quantum gravity [including
non-classical].
@ Related topics: de Gosson mp/02 [symplectic
area]; Solovej & Spitzer CMP(03)
[semiclassical
calculus]; Genoni et al PRA(07)-a0704 [departure
from Gaussianity]; Hajícek FP-a0901 [maximum
entropy states]; Ishikawa & Tobita a0906 [wave-packet
coherent length]; Budiyono a0907 ["most
probable wave function", and finite-size
progressing solution]; Badziag et al PRL(09)
[there are no "classical"
states]; > s.a. entanglement, wigner
functions; zeno effect [semiclassical evolution].
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send feedback and suggestions to bombelli at olemiss.edu – modified 10
nov 2009