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Sushruth Muralidharan1, Kinjalk Lochan2, S Shankaranarayanan3

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We studied quantum harmonic chains after a local quantum quench, finding they reach a generalized thermal state. Delocalized states equilibrate faster, with criteria identified for this relaxation.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Investigating quantum systems after a sudden change (quench) is crucial for understanding thermalization.
  • The quantum harmonic chain is a fundamental model for studying such dynamics.
  • Generalized Gibbs Ensemble (GGE) is a theoretical framework for describing non-equilibrium quantum systems.

Purpose of the Study:

  • To examine the equilibration and generalized thermalization of a quantum harmonic chain under a local quantum quench.
  • To verify the applicability of the Generalized Gibbs Ensemble (GGE) to this system.
  • To identify factors influencing the speed of equilibration and states not described by GGE.

Main Methods:

  • Applying a local quantum quench by connecting two disjoint harmonic chains of different sizes.
  • Utilizing Bogoliubov transformations to analyze the evolution of system eigenstates.
  • Analyzing phase space properties and stimulated emission to determine equilibration criteria.

Main Results:

  • The quantum harmonic chain equilibrates to a GGE description, even in an infinite-dimensional Hilbert space.
  • Equilibration between subsystems was observed, mirroring classical system behavior.
  • More delocalized initial eigenstates (quantified by inverse participation ratio) equilibrate more rapidly.
  • Criteria for late-time relaxation and identification of states potentially not described by GGE were established.

Conclusions:

  • The GGE provides a valid description for the thermalization of quantum harmonic chains after a local quantum quench.
  • Initial state delocalization is a key factor in the rate of equilibration.
  • Understanding these criteria is essential for predicting the long-term behavior of quantum many-body systems.