Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Open Quantum Systems Decoherence Quantum Simulation Quantum Chemistry

Fractals, coherent states and self-similarity induced noncommutative geometry

arXiv

Authors: Giuseppe Vitiello

Year

2012

Paper ID

8700

Status

Preprint

Abstract Read

~2 min

Abstract Words

Citations

N/A

Abstract

The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the q-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative geometry in the plane. The examples of the Koch curve and logarithmic spiral are considered in detail. It is suggested that the dynamical formation of fractals originates from the coherent boson condensation induced by the generators of the squeezed coherent states, whose (fractal) geometrical properties thus become manifest. The macroscopic nature of fractals appears to emerge from microscopic coherent local deformation processes.

Why This Paper Matters

This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
It adds a 2012 reference point for readers tracking recent quantum research.
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the q-deformed algebra of coherent states.

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in

Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:1206.1854 [2] arXiv https://arxiv.org/abs/1206.1854 [3] Publisher https://arxiv.org/abs/1206.1854

Local Citation Graph (Related-Paper Links)

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0

Likes: 0 Dislikes: 0

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.