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Localization in space and time in disordered-lattice open quantum dynamics.

Sam Genway1, Igor Lesanovsky1, Juan P Garrahan1

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We discovered a dynamical phase transition in exciton behavior on a disordered lattice. This transition, driven by a thermal environment, reveals a novel localization in system dynamics, impacting exploration of the lattice.

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Area of Science:

  • Condensed matter physics
  • Quantum dynamics
  • Disordered systems

Background:

  • Excitons in two-dimensional lattices are crucial for optoelectronic devices.
  • On-site disorder and thermal environments significantly influence exciton behavior.
  • Understanding exciton dynamics is key to controlling energy transport.

Purpose of the Study:

  • To investigate the dynamics of excitons on a disordered lattice coupled to a thermal bath.
  • To identify and characterize any phase transitions in the system's temporal trajectories.
  • To explore spatial features of exciton dynamics and determine an ergodic timescale.

Main Methods:

  • Utilizing a two-dimensional tight-binding lattice model for excitons.
  • Introducing on-site disorder to the lattice.
  • Coupling the system to a thermal environment at infinite temperature.
  • Analyzing temporal trajectories and employing a generalized inverse participation ratio.

Main Results:

  • Observed rich exciton dynamics despite a uniform steady state.
  • Uncovered a dynamical phase transition in the space of temporal trajectories.
  • Identified this transition as a localization in bath-generated dynamics.
  • Deduced an ergodic timescale for the lattice based on spatial dynamics.

Conclusions:

  • A dynamical phase transition, characterized by localization, occurs in the exciton dynamics.
  • The interplay between disorder and thermal environment leads to complex, non-trivial behavior.
  • The generalized inverse participation ratio provides a method to quantify ergodic properties in such systems.