2007/08/31 by Stephen L. Adler, Stephen L Adler, Angelo Bassi · 1 citation
Computer Science · Physics and Astronomy · #Differential equation #Eigenvalues and eigenvectors #Formalism (music) #Gaussian #Perturbation (astronomy) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wave function collapse #White noise #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/40/50/012
published as J. Phys. A:Math. Theor.{\bf 40} (2007) 15083-15098 · Latex, 20 pages;references added and minor revisions; published as J. Phys. A: Math. Theor. {\bf 40} (2007) 15083-15098
openalex publication_date 2007/11/28 · arxiv created 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We set up a general formalism for models of spontaneous wavefunction collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the non-Schrödinger terms of the equation induce the collapse of the wavefunction to one of the common eigenstates of the collapsing operators, and that the collapse occurs with the correct quantum probabilities. We also develop a perturbation expansion of the solution of the equation with respect to the parameter which sets the strength of the collapse process; such an approximation allows one to compute the leading-order terms for the deviations of the predictions of collapse models with respect to those of standard quantum mechanics. This analysis shows that to leading order, the 'imaginary noise' trick can be used for non-white Gaussian noise.