Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Time evolution of quantum fractals

Wojcik1, Bialynicki-Birula, Zyczkowski

  • 1Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/46, 02-668 Warszawa, Poland and College of Science (Szkola Nauk Scislych), Al. Lotnikow 32/46, 02-668 Warszawa, Poland.

Physical Review Letters
|December 2, 2000
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Hints for a cure in a muscular dystrophy variant

Trends in cell biology·2000
Same author

Dynamical entropy for systems with stochastic perturbation

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000
Same author

Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

Physical review letters·2000
Same author

Microchemical identification of gamma-hydroxybutyrate (GHB)

Journal of forensic sciences·2000
Same author

Inhibition of the proteasome as a therapeutic approach.

Drug discovery today·1999
Same author

Nonspreading Wave Packets for Rydberg Electrons in Rotating Molecules with Electric Dipole Moments.

Physical review letters·1996
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

We present a method to construct quantum wave functions with specific fractal dimensions for various quantum systems. The fractal dimension of the probability density remains constant over time, revealing a universal relationship in quantum carpets.

Area of Science:

  • Quantum mechanics
  • Mathematical physics
  • Fractal geometry

Background:

  • Quantum wave functions describe the probability distribution of particles.
  • Fractal dimensions offer a way to quantify the complexity of geometric shapes.
  • Understanding the dimensional properties of quantum systems is crucial for theoretical advancements.

Purpose of the Study:

  • To develop a general method for constructing quantum wave functions with prescribed fractal dimensions.
  • To investigate the time evolution of the fractal dimension of probability densities.
  • To establish a universal relationship between spatial and temporal fractal dimensions in quantum systems.

Main Methods:

  • Construction of wave functions for systems like the infinite potential well, harmonic oscillator, linear potential, and free particle.

Related Experiment Videos

  • Application of the box-counting dimension to analyze the probability density |Psi(x,t)|(2).
  • Derivation of a universal relation connecting fractal dimensions of space and time cross sections.

    • Main Results:

    • A general construction for wave functions with arbitrary fractal dimensions is proposed.
    • The box-counting dimension of the probability density is invariant under time evolution.
    • A universal relation D(t) = 1+Dx/2 is proven for fractal quantum carpets.

    Conclusions:

    • The study provides a novel approach to generating fractal quantum states.
    • Time evolution preserves the fractal nature of quantum probability densities.
    • The established universal relation offers new insights into the geometry of quantum dynamics.