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Quantum localization measures in phase space.

D Villaseñor1, S Pilatowsky-Cameo1, M A Bastarrachea-Magnani2

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We introduce a general scheme using Rényi occupations to measure quantum state localization in phase space. This method clarifies differences between localization measures in chaotic systems, revealing context-dependent results in unbounded spaces.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Quantum chaos

Background:

  • Quantifying quantum state localization in phase space is crucial for understanding quantum system dynamics and equilibration.
  • Current methods for measuring localization are not unique and capture different facets of quantum states.
  • The interacting spin-boson Dicke model provides a relevant system for studying localization in complex quantum dynamics.

Purpose of the Study:

  • To develop a general scheme for defining quantum state localization in measure spaces.
  • To introduce Rényi occupations as a foundational concept for deriving various localization measures.
  • To analyze and compare different localization measures within the chaotic regime of the Dicke model.

Main Methods:

  • Development of a general framework for localization measures based on Rényi occupations.
  • Application of the scheme to the four-dimensional phase space of the interacting spin-boson Dicke model.
  • Comparative analysis of two Husimi function-based localization measures in the chaotic regime.

Main Results:

  • A general scheme for defining quantum state localization using Rényi occupations is presented.
  • The study elucidates the origin of differences between two specific localization measures based on the Husimi function.
  • It is shown that defining maximal delocalization in unbounded spaces necessitates a bounded reference subspace, leading to contextual outcomes.

Conclusions:

  • The Rényi occupation scheme offers a unified approach to quantifying quantum state localization.
  • Understanding the contextuality of localization measures is vital, especially in unbounded phase spaces.
  • This work provides a new perspective on characterizing quantum states in complex models like the Dicke model.