dorsal/arxiv
View SchemaGeneralized stochastic Schroedinger equations for state vector collapse
| Authors | Stephen L. Adler, Todd A. Brun |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103037 |
| URL | https://arxiv.org/abs/quant-ph/0103037 |
| DOI | 10.1088/0305-4470/34/23/302 |
| Journal | J. Phys. A 34, 4797-4809 (2001). |
Abstract
A number of authors have proposed stochastic versions of the Schr\"odinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. We discuss here two directions for generalization of these equations. First, we study a general class of norm preserving stochastic evolution equations, and show that even after making several specializations, there is an infinity of possible stochastic Schr\"odinger equations for which state vector collapse is provable. Second, we explore the problem of formulating a relativistic stochastic Schr\"odinger equation, using a manifestly covariant equation for a quantum field system based on the interaction picture of Tomonaga and Schwinger. The stochastic noise term in this equation can couple to any local scalar density that commutes with the interaction energy density, and leads to collapse onto spatially localized eigenstates. However, as found in a similar model by Pearle, the equation predicts an infinite rate of energy nonconservation proportional to $\delta^3(\vec 0)$, arising from the local double commutator in the drift term.
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"abstract": "A number of authors have proposed stochastic versions of the Schr\\\"odinger\nequation, either as effective evolution equations for open quantum systems or\nas alternative theories with an intrinsic collapse mechanism. We discuss here\ntwo directions for generalization of these equations. First, we study a general\nclass of norm preserving stochastic evolution equations, and show that even\nafter making several specializations, there is an infinity of possible\nstochastic Schr\\\"odinger equations for which state vector collapse is provable.\nSecond, we explore the problem of formulating a relativistic stochastic\nSchr\\\"odinger equation, using a manifestly covariant equation for a quantum\nfield system based on the interaction picture of Tomonaga and Schwinger. The\nstochastic noise term in this equation can couple to any local scalar density\nthat commutes with the interaction energy density, and leads to collapse onto\nspatially localized eigenstates. However, as found in a similar model by\nPearle, the equation predicts an infinite rate of energy nonconservation\nproportional to $\\delta^3(\\vec 0)$, arising from the local double commutator in\nthe drift term.",
"arxiv_id": "quant-ph/0103037",
"authors": [
"Stephen L. Adler",
"Todd A. Brun"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/34/23/302",
"journal_ref": "J. Phys. A 34, 4797-4809 (2001).",
"title": "Generalized stochastic Schroedinger equations for state vector collapse",
"url": "https://arxiv.org/abs/quant-ph/0103037"
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