The Resource Quantum fractals : from Heisenberg's uncertainty to Barnsley's fractality, Arkadiusz Jadczyk

Quantum fractals : from Heisenberg's uncertainty to Barnsley's fractality, Arkadiusz Jadczyk

Label
Quantum fractals : from Heisenberg's uncertainty to Barnsley's fractality
Title
Quantum fractals
Title remainder
from Heisenberg's uncertainty to Barnsley's fractality
Statement of responsibility
Arkadiusz Jadczyk
Creator
Author
Subject
Genre
Language
  • eng
  • eng
Summary
Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions: -->: What are fractals?; How do fractal patterns emerge from quantum observations and relativistic light aberration effects?; What are the open problems with iterated function systems based on Mobius transformations?; Can quantum fractals be experimentally detected?; What are quantum jumps?; Is quantum theory complete and/or universal?; Is the sta
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Jadczyk, Arkadiusz
Dewey number
530.1201514742
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QC20.7.F73
LC item number
.J33 2014
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Fractals
  • Mathematical physics
  • Quantum theory
Label
Quantum fractals : from Heisenberg's uncertainty to Barnsley's fractality, Arkadiusz Jadczyk
Instantiates
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Preface; Contents; 1. Introduction; 2. What are Quantum Fractals?; 2.1 Cantor set; 2.1.1 Cantor set through "Chaos Game"; 2.2 Iterated function systems; 2.2.1 Definition of IFS; 2.2.2 Frobenius-Perron operator; 2.3 Cantor set throughmatrix eigenvector; 2.4 Quantum iterated function systems; 2.5 Example: The "impossible" quantum fractal; 2.5.1 24 symmetries - the octahedral group; 2.5.2 Construction of the 24-elements SQIFS; 2.5.3 Open problems; 2.6 Action on the plane; 2.7 Lorentz group, SL(2,C), and relativistic aberration; 2.7.1 The Lorentz group
  • 3.1 Hyperbolic quantum fractals3.1.1 The circle; 3.1.1.1 Contracting and expanding regions; 3.1.1.2 Place dependent probabilities; 3.1.1.3 Images; 3.1.1.4 Frobenius-Perron operator; 3.1.1.5 Details of the calculations; 3.1.2 Platonic quantum fractals for a qubit; 3.1.2.1 Platonic solids; 3.1.2.2 Approximations to the invariant measure; 3.1.2.3 Geometric interpretation of transformations and probabilities; 3.1.2.4 Quantum Tetrahedron; 3.1.2.5 Quantum Octahedron; 3.1.2.6 Quantum Cube; 3.1.2.7 Quantum Icosahedron; 3.1.2.8 Quantum Dodecahedron
  • 3.2 Controlling chaotic behavior and fractal dimension3.3 Quantum fractals on n-spheres; 3.3.1 Clifford algebras; 3.3.1.1 Notation; 3.3.1.2 Examples of Clifford algebras; 3.3.1.3 Even and odd parts, principal automorphism and anti-automorphism, conjugation; 3.3.1.4 Examples; 3.3.1.5 The norm function; 3.3.1.6 Spin group; 3.3.1.7 Vector space isomorphism between the Clifford and the Grassmann algebra; 3.3.1.8 Paravectors; 3.3.1.9 Example; 3.3.1.10 The trace; 3.3.1.11 Algebra isomorphism between C+(V 1,Q1) and R(2, C(V,Q)); 3.3.1.12 Mobius transformations
  • 3.3.1.13 Conformal spin geometry of n-spheres
Dimensions
unknown
Extent
1 online resource (358 p.)
Form of item
online
Isbn
9789814569873
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)3710000000214656
  • (EBL)1766809
  • (SSID)ssj0001287815
  • (PQKBManifestationID)12443314
  • (PQKBTitleCode)TC0001287815
  • (PQKBWorkID)11291580
  • (PQKB)10583307
  • (MiAaPQ)EBC1766809
  • (WSP)00008992
  • (EXLCZ)993710000000214656
Label
Quantum fractals : from Heisenberg's uncertainty to Barnsley's fractality, Arkadiusz Jadczyk
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Preface; Contents; 1. Introduction; 2. What are Quantum Fractals?; 2.1 Cantor set; 2.1.1 Cantor set through "Chaos Game"; 2.2 Iterated function systems; 2.2.1 Definition of IFS; 2.2.2 Frobenius-Perron operator; 2.3 Cantor set throughmatrix eigenvector; 2.4 Quantum iterated function systems; 2.5 Example: The "impossible" quantum fractal; 2.5.1 24 symmetries - the octahedral group; 2.5.2 Construction of the 24-elements SQIFS; 2.5.3 Open problems; 2.6 Action on the plane; 2.7 Lorentz group, SL(2,C), and relativistic aberration; 2.7.1 The Lorentz group
  • 3.1 Hyperbolic quantum fractals3.1.1 The circle; 3.1.1.1 Contracting and expanding regions; 3.1.1.2 Place dependent probabilities; 3.1.1.3 Images; 3.1.1.4 Frobenius-Perron operator; 3.1.1.5 Details of the calculations; 3.1.2 Platonic quantum fractals for a qubit; 3.1.2.1 Platonic solids; 3.1.2.2 Approximations to the invariant measure; 3.1.2.3 Geometric interpretation of transformations and probabilities; 3.1.2.4 Quantum Tetrahedron; 3.1.2.5 Quantum Octahedron; 3.1.2.6 Quantum Cube; 3.1.2.7 Quantum Icosahedron; 3.1.2.8 Quantum Dodecahedron
  • 3.2 Controlling chaotic behavior and fractal dimension3.3 Quantum fractals on n-spheres; 3.3.1 Clifford algebras; 3.3.1.1 Notation; 3.3.1.2 Examples of Clifford algebras; 3.3.1.3 Even and odd parts, principal automorphism and anti-automorphism, conjugation; 3.3.1.4 Examples; 3.3.1.5 The norm function; 3.3.1.6 Spin group; 3.3.1.7 Vector space isomorphism between the Clifford and the Grassmann algebra; 3.3.1.8 Paravectors; 3.3.1.9 Example; 3.3.1.10 The trace; 3.3.1.11 Algebra isomorphism between C+(V 1,Q1) and R(2, C(V,Q)); 3.3.1.12 Mobius transformations
  • 3.3.1.13 Conformal spin geometry of n-spheres
Dimensions
unknown
Extent
1 online resource (358 p.)
Form of item
online
Isbn
9789814569873
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)3710000000214656
  • (EBL)1766809
  • (SSID)ssj0001287815
  • (PQKBManifestationID)12443314
  • (PQKBTitleCode)TC0001287815
  • (PQKBWorkID)11291580
  • (PQKB)10583307
  • (MiAaPQ)EBC1766809
  • (WSP)00008992
  • (EXLCZ)993710000000214656

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