首页/论文/quant-ph/9710033

arXiv quant-ph/97100331997-10quant-ph

Gisin Nonlocality of the Doebner-Goldin 2-Particle Equation

W. Luecke

备注：: 7 pages, LaTeX, minor corrections and additions

英文摘要：

Gisin's argument against deterministic nonlinear Schroedinger equations is shown to be valid for every (formally) nonlinearizable case of the general Doebner-Goldin 2-particle equation in the following form: The time-dependence of the position probability distribution of a particle `behind the moon' may be instantaneously changed by an arbitrarily small instantaneous change of the potential `inside the laboratory'.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Nonlinear Gauge Transformations and Exact Solutions of the Doebner-Goldin Equation

Invariants of nonlinear gauge transformations of a family of nonlinear Schrödinger equations proposed by Doebner and Goldin are used to characterize the behaviour of exact solutions of these equations.

1995-06-21hep-thnlin.SIquant-ph

On Integrable Doebner-Goldin Equations

We suggest a method for integrating sub-families of a family of nonlinear {\sc Schrödinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie} symmetries. Since the method of integration involves non-local transformations of dependent and independent variables, general solutions obtained include implicitly determined functions. By properly specifying one of the arbitrary functions contained in these solutions, we obtain broad classes of explicit square integrable solutions. The physical significance and some analytical p…

1995-10-10hep-thnlin.SIquant-ph

Symmetry, Local Linearization, and Gauge Classification of the Doebner-Goldin Equation

For the family of nonlinear Schrödinger equations derived by H.-D.~Doebner and G.A.~Goldin (J.Phys.A 27, 1771) we calculate the complete set of Lie symmetries. For various subfamilies we find different finite and infinite dimensional Lie symmetry algebras. Two of the latter lead to a local transformation linearizing the particular subfamily. One type of these transformations leaves the whole family of equations invariant, giving rise to a gauge classification of the family. The Lie symmetry algebras and their corresponding subalgebras are finally characterized by gauge invariant parameters.

1995-06-23hep-thnlin.SIquant-ph

Nonlinear Quantum Mechanics and Locality

It is shown that, in order to avoid unacceptable nonlocal effects, the free parameters of the general Doebner-Goldin equation have to be chosen such that this nonlinear Schrödinger equation becomes Galilean covariant.

1997-07-30quant-ph

Nonlinear Schroedinger Dynamics and Nonlinear Observables

It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are described in full detail for a special case of the nonlinear Doebner-Goldin equation.

1995-05-30quant-ph

Remarks on a Nonlinear Quantum Theory

Motivated by recent proposals (Bialynicki-Birula, Mycielski; Haag, Bannier; Weinberg; Doebner, Goldin) for nonlinear quantum mechanical evolution equations for pure states some principal difficulties in the framework of usual quantum theory, which is based on its inherent linear structure, are discussed. A generic construction of nonlinear evolution equations through nonlinear gauge transformations is indicated.

1998-03-04quant-ph

更多相关论文收起更多论文

Non-linear Schroedinger Equations, Separation and Symmetry

We investigate the symmetry properties of hierarchies of non-linear Schroedinger equations (introduced by Doebner and Goldin, and Goldin and Svetlichny), which describe non-interacting systems in which tensor product wave-functions evolve by independent evolution of the factors (the separation property). We show that there are obstructions to lifting symmetries existing at a certain number of particles to higher numbers. Such obstructions vanish for particles without internal degrees of freedom and the usual space-time symmetries. For particles with internal degrees of freedom, such as spin, t…

1999-06-29quant-ph

Generalized Quantum Mechanics and Nonlinear Gauge Transformations

Motivated by the problems of interpretation of a nonlinear evolution equation in quantum mechanics we discuss in this contribution the concept of nonlinear gauge transformations, that has recently been introduced in joint work with Doebner and Goldin, in the framework of Mielnik's Generalized Quantum Mechanics. Using these gauge transformations we construct linear quantum systems in a ``nonlinear disguise'', and a gauge generalization of these (in analogy to the minimal coupling of orthodox quantum mechanics) leads to a unification of Bialynicki-Birula--Mycielski and Doebner--Goldin evolution …

1997-03-12hep-thphysics.gen-phquant-ph

On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics

Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schroedinger equations, e.g. as proposed by Doebner and Goldin, yields a Galilean quantum electrodynamics.

2000-06-18quant-ph

Borel quantization and nonlinear quantum mechanics. A review of developments in the series "Symmetries in Science" I - XIII

The results, different aspects and applications of our method of quantisation on configuration manifolds - called Borel Quantisation - were presented at meetings of the series `Symmetries in Science' and can be found in the published proceedings. The developments with numerous coauthors, on Borel quantisation and the related family of nonlinear Schrödinger equations called Doebner-Goldin equations, are reviewed and commented here.

2006-01-26quant-ph

On gauge transformations of Bäcklund type and higher order nonlinear Schrödinger equations

We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class of Bäcklund transformations. These transformations satisfy certain reasonable, previously proposed requirements for gauge transformations. Their application to the Schrödinger equation results in higher order partial differential equations. As an example, we derive a general family of 6th-order nonlinear Schrödinger equations, closed under our nonlinear gauge group. We also introduce a new gauge invariant current ${…

2002-01-02quant-ph

Quantum Mechanics without spacetime V - Why a quantum theory of gravity should be non-linear-

If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be necessarily non-linear. This is true independent of the mathematical structure used for describing such a formulation of quantum mechanics. A specific model which exhibits this non-linearity is constructed, using the language of noncommutative geometry. We derive a non-linear Schrodinger equation for the quantum dynamics of a particle; this equation reduces …

2005-04-18gr-qchep-thquant-ph

Higher Order Modification of the Schroedinger Equation

We modify the Schrödinger equation in a way that preserves its main properties but makes use of higher order derivative terms. Although the modification represents an analogy to the Doebner-Goldin modification, it can differ from it quite distinctively. A particular model of this modification including derivatives up to the fourth order is examined in greater detail. We observe that a special variant of this model partially retains the linear superposition principle for the wave packets of standard quantum mechanics remain solutions to it. It is a peculiarity of this variant that a periodic st…

1999-05-17quant-ph

Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schrödinger Equations

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically-motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously for a family of nonlinear Schrödinger equations. The gene…

1997-09-17quant-ph

Nonlinear gauge transformation for a class of Schroedinger equations containing complex nonlinearities

We consider a wide class of nonlinear canonical quantum systems described by a one-particle Schroedinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the continuity equation. In this way we are able to obtain a new quantum system obeying to a nonlinear Schroedinger equation with a real nonlinearity. As an application of this theory we consider a few already studied Schroedinger equations as that containing the nonlinearity introduced by the exclusion-inclusion principle, the Doebner-Goldin equation and others. PACS nu…

2002-09-11cond-matmath-phmath.MP

Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schroedinger Equation

We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like {\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS) are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to {\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<π/(2g), being identically equa…

1998-11-06nlin.PSpatt-solquant-ph

Nonlinear Phase Modification of the Schroedinger Equation

A nonlinear modification of the Schrödinger equation is proposed in which the Lagrangian density for the Schrödinger equation is extended by terms polynomial in $Δ^{m}\ln (Ψ^{*}/Ψ)$ multiplied by $Ψ^{*}Ψ$. This introduces a homogeneous nonlinearity in a Galilean invariant manner through the phase $S$ rather than the amplitude $R$ of the wave function $Ψ=R\exp (iS)$. From this general scheme we choose the simplest minimal model defined in some reasonable way. The model in question offers the simplest way to modify the Bohm formulation of quantum mechanics so as to allow a leading phase contribu…

1999-05-17quant-ph

The inevitable nonlinearity of quantum gravity falsifies the many-worlds interpretation of quantum mechanics

There are fundamental reasons as to why there should exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. It follows as a consequence that quantum mechanics as we know it is a limiting case of a more general nonlinear quantum theory, with the nonlinearity becoming significant at the Planck mass/energy scale. This nonlinearity is responsible for a dynamically induced collapse of the wave-function, during a quantum measurement, and it hence falsifies the many-worlds interpretation of quantum mechanics. We illustrate this conclusion using a mathematic…

2007-05-16gr-qchep-thquant-ph