CoChat
Sign Up
Cited by 87Quantum Mechanics and ApplicationsQuantum chaos and dynamical systemsAdvanced Thermodynamics and Statistical Mechanics

Stochastic path integrals and open quantum systems

Strunz, Walter T.·1996·Physical Review A
DOI 10.1103/physreva.54.2664
Open this paper in CoChat — free account

Abstract

The general theory of path integral propagators for the solution of linear quantum state diffusion (LQSD) stochastic Schr\"odinger equations describing open quantum systems is developed. Both Hamiltonian and, where possible, Lagrangian path integrals are derived and their connection established. The Hamiltonian version turns out to be more suitable. The results also show how the stochastic terms in the LQSD equation introduce a weight functional under the path integral, thus restricting the set of contributing paths. The center of this weight functional is determined by the stochastic processes governing the LQSD equation. In general, this picture holds in a semiclassical limit only. Some peculiarities of stochastic path integrals are pointed out. We evaluate the stochastic path integral in closed form for soluble models, gaining further insight into the behavior of the solutions of the LQSD equation. \textcopyright{} 1996 The American Physical Society.

Integrity signals

Registry

Crossref · 10.1103/physreva.54.2664

Cites

32 of 32 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The representations assigned to triangles are simple representations of SO(4) of the form (j,j), i.e. class-1 representations with respect to SO(3), characterized by vanishing of the second Casimir.

    “the representations of the triangles are 'simple representations' of SO(4) of the form (j, j ), i.e. representations of class 1 with respect to the subgroup SO(3) [66], characterized by the vanishing of the second Casimir of the group”

    From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [66]

  • Simple representations of the Lorentz group can be realized on square integrable functions on hyperboloids in Minkowski space: Q1, Q0, and Q-1.

    “In fact [66], the simple representations of the Lorentz group can be realized in the space of square integrable functions on hyperboloids in Minkowski space.These are Q 1 , or Lobachevskian space, characterized by x µ x µ = 1 and x 0 > 0, the positive null cone Q 0 , with x µ x µ = 0 and x 0 > 0, and the imaginary Lobachevskian space Q -1 , with x µ x µ = -1.”

    From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [66]

  • The Hilbert space used to define the operators is built from gauge invariant cylindrical functions on the space of connections A.

    “The Hilbert space in which we will define the operators is constructed from the gauge invariant cylindrical functions on A [6,7,12,19,20].”

    From Volume and quantizations (1997) · cites this paper as [19]

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
Strunz, W. T.
Affiliations
University of London (GB)
Corresponding author
Strunz, Walter T.
ORCID
Strunz, Walter T.
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
1996-10-01
Volume
54
Issue
4
Pages
2664-2674
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.54.2664
OpenAlex
W1992243061
Cited by
87
References
32
Citations by year
2025: 1 · 2024: 1 · 2023: 4 · 2021: 2 · 2019: 1 · 2018: 1 · 2017: 1 · 2014: 1 · 2013: 1 · 2012: 2
FWCI
8.16
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
stochastic path integral, open quantum systems, stochastic Schrödinger equation, Hamiltonian path integral, semiclassical limit

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review