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Shape of the quantum diffusion front.

J Zhong1, R B Diener, D A Steck

  • 1Department of Physics, University of Texas, Austin 78712, USA.

Physical Review Letters
|April 6, 2001
PubMed
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Quantum diffusion exhibits a well-defined wave packet front, described by a stretched exponential function. This finding, supported by numerical and analytical methods, reveals a universal relationship between diffusion exponents.

Area of Science:

  • Quantum dynamics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Quantum diffusion describes the spreading of wave packets in quantum systems.
  • Understanding the dynamics of quantum wave packets is crucial for various physical phenomena.

Purpose of the Study:

  • To characterize the front shape of quantum diffusion.
  • To establish a universal relation between exponents governing wave packet spreading.

Main Methods:

  • Numerical simulations on quasiperiodic systems and the Anderson model.
  • Analytical derivation using the memory function formalism.
  • Application to experimental data from the quantum kicked rotor.

Main Results:

Related Experiment Videos

  • The wave packet front follows a stretched exponential form: P(x,t) = A(t)exp(-|x/w|^gamma).
  • The spreading width scales as w(t) ~ t^beta.
  • A universal relation gamma = 1/(1-beta) was found between the exponents.

    • Conclusions:

    • Quantum diffusion fronts have a well-defined shape characterized by universal exponents.
    • The memory function formalism provides an analytical basis for these observations.
    • The findings have implications for understanding quantum transport and experimental systems like the quantum kicked rotor.