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) [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]; > s.a. quantum-gravity phenomenology.
@ And cosmology: Georg & Rosenzweig 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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