Non-Linear Quantum Mechanics| Non-Linear Quantum Mechanics |
In General
> s.a. brownian motion; Newton-Schrödinger
Equation; schrödinger equation [including WKB].
* Motivation: Include as part of the
dynamical evolution the transformation associated with the wave-function collapse.
* Feature: Superluminal propagation,
a generic phenomenon in a large class on non-dissipative quantum theories.
@ Intros, reviews: Goss Levi PT(89)oct;
news Nat(90)jul;
Svetlichny qp/04 [arXiv bibliography];
Habib et al qp/05-conf [intro].
@ General references:
Białynicki-Birula & Mycielski AP(76);
Giusto et al PhyD(84);
Białynicki-Birula in(86);
Weinberg AP(89),
PRL(89)
+ comment Peres PRL(89);
Castro JMP(90)
[and geometric quantum mechanics];
Jordan PLA(90);
Nattermann qp/97;
Puszkarz qp/97,
qp/97,
qp/99,
qp/99,
qp/99;
Davidson NCB-qp/01;
Strauch PRE(07)-a0707 [propagation scheme];
Rego-Monteiro & Nobre JMP(13) [classical field theory];
Helou & Chen JPCS(17)-a1709 [and interpretations];
Rówiński a1901 [foundations].
@ Derivations, motivation: Parwani qp/06-proc,
TMP(07) [information theory-motivated];
Adami et al JSP(07) [from many-body dynamics];
Lochan & Singh Pra-a0912 [and quantum measurement, superpositions, and time];
Wu et al IJTP(10)-a1104 [and Gross-Pitaevskii equation];
Molladavoudi et al PLA(12).
@ Non-polynomial: Parwani BJP(05)qp/04-proc,
AP(05) [information-theoretic argument];
Parwani & Tan PLA(07)qp/06 [solutions].
@ Modified versions: Kibble CMP(78),
Elze JPCS(07)-a0704 [relativistic];
Andrianov & Ioffe JPA(12) [supersymmetric, rev].
@ Difficulties:
Caticha PLA(98)qp,
PRA(98)qp;
Doebner qp/98-proc;
Puszkarz qp/98 [energy non-uniqueness];
Lücke qp/99 [non-locality];
Burq & Zworski CMP(05) [semiclassical, instability];
Cavalcanti et al a1206 [the preparation problem];
Ho & Hsu IJMPA(15)-a1401 [non-locality].
@ Related topics: Minelli & Pascolini NCB(85) [conservation laws];
Valentini PRA(90) [and complementarity];
Lücke qp/95 [observables];
Bona qp/99-proc [for density matrices],
qp/99-proc [symmetries].
Applications and Phenomenology > s.a. Ehrenfest Theorem.
@ General refarences: Czachor & Doebner PLA(02)qp/01 [multi-particle correlations];
Rapedius & Korsch JPA(08) [barrier penetration];
> s.a. cosmic rays.
@ And causality: Gisin PLA(90);
Polchinski PRL(91)
[and EPR, comment Mielnik qp/00];
Cassidy PRD(95) [and closed timelike curves];
Mielnik PLA(01);
Kent PRA(05)qp/02 [consistent];
> s.a. causality violations.
@ Tests: Bollinger et al PRL(89);
Majumder et al PRL(90)
[optically pumped 201Hg];
Jordan PRA(10)-a1002 [tests of linearity, conceptual].
@ Special systems:
Gattobigio et al JMP(99) [on half-line];
Gardiner et al PRA(00)qp/99 [with chaotic potential];
Shu & Zhang JMP(06) [harmonic potential];
Doikou et al NPB(08)-a0706 [on an interval];
Carles & Sparber JPA(12)-a1110 [coherent states in periodic potentials].
@ And gravity: Soni Pra(02)gq/00;
Singh gq/03;
Svetlichny IJTP(05),
JGSP(06)qp-conf [at the Planck scale];
Wick a2008 [spacetime wavefunctions, curved spacetime];
> s.a. quantum-gravity phenomenology.
@ And cosmology:
Georg & Rosenzweig JCAP(20)-a1804 [power spectrum].
@ Numerical simulations: Luo a0912;
Mocz & Succi a1503/PRE.
@ Solutions: Minelli & Pascolini LNC(80),
in(80) [solitons];
Bon et al NCA(87) [thermodynamic description];
Teismann RPMP(05) [L2 solutions].
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send feedback and suggestions to bombelli at olemiss.edu – modified 21 aug 2020