Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Quantum Physics

arXiv:2204.07734 (quant-ph)
[Submitted on 16 Apr 2022]

Title:The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems

Authors:Alexander A. Andrianov, Mikhail V. Ioffe, Ekaterina A. Izotova, Oleg O. Novikov
View PDF
Abstract:Open quantum systems are, in general, described by a density matrix that is evolving under transformations belonging to a dynamical semigroup. They can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space of dimension $2$. First, we find final fixed states (called pointers) of an evolution of an open system, and we then obtain a general solution to the FGKLS equation and confirm that it converges to a pointer. After this, we check that the solution has physical meaning, i.e., it is Hermitian, positive and has trace equal to $1$, and find a moment of time starting from which the FGKLS equation can be used - the range of applicability of the semigroup symmetry. Next, we study the behavior of a solution for a weak interaction with an environment and make a distinction between interacting and non-interacting cases. Finally, we prove that there cannot exist oscillating solutions to the FGKLS equation, which would resemble the behavior of a closed quantum system.
Comments: 27 p.p
Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:2204.07734 [quant-ph]
  (or arXiv:2204.07734v1 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.2204.07734
Journal reference: Symmetry, 14 (2022) 754
Related DOI: https://doi.org/10.3390/sym14010754

Submission history

From: Mikhail V. Ioffe [view email]
[v1] Sat, 16 Apr 2022 07:03:54 UTC (25 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
quant-ph
< prev   |   next >
new | recent | 2022-04
Change to browse by:
hep-th
math
math-ph
math.MP

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)