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Quantum hyperdiffusion in one-dimensional tight-binding lattices.

Zhenjun Zhang1, Peiqing Tong, Jiangbin Gong

  • 1Department of Physics, Nanjing Normal University, Nanjing, Jiangsu, People's Republic of China.

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Transient quantum hyperdiffusion, a faster-than-ballistic wave packet spreading, occurs in specific tight-binding lattices. This phenomenon depends on sublattice potential strength and energy band alignment, with quasiperiodic cases showing exceptional exponents.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Solid-state physics

Background:

  • Wave packet spreading dynamics are crucial for understanding transport in quantum systems.
  • Tight-binding lattices offer a simplified yet powerful model for studying electronic properties.
  • Quantum hyperdiffusion, faster-than-ballistic spreading, has been observed in specific lattice configurations.

Purpose of the Study:

  • To investigate the occurrence and characteristics of transient quantum hyperdiffusion.
  • To identify the key parameters influencing quantum hyperdiffusion in tight-binding lattices.
  • To explain the underlying physical mechanisms and explore potential for enhanced exponents.

Main Methods:

  • Numerical simulations of wave packet evolution in modified tight-binding lattices.
  • Analysis of energy band structures and eigenstate properties.
  • Systematic variation of sublattice potential strength and type (periodic, disordered, quasiperiodic).

Main Results:

  • Transient quantum hyperdiffusion is a typical feature in tight-binding lattices with embedded sublattices.
  • The phenomenon is contingent on the sublattice on-site potential strength being below critical thresholds.
  • Energy band mismatch and eigenstate structure are identified as key explanatory factors.
  • Quasiperiodic sublattices can lead to hyperdiffusion exponents exceeding three.

Conclusions:

  • Embedded sublattices with controlled on-site potentials can induce transient quantum hyperdiffusion.
  • The observed phenomenon is linked to specific band structure and eigenstate properties.
  • Quantum hyperdiffusion offers a pathway to achieve significantly faster-than-ballistic transport in engineered lattices.