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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Sensitivity to perturbations and quantum phase transitions.

D A Wisniacki1, A J Roncaglia

  • 1Departamento de Física, FCEyN, UBA and IFIBA, CONICET, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 18, 2013
PubMed
Summary
This summary is machine-generated.

The local density of states reveals the transition from quantum integrability to chaos in the Dicke model. However, it shows no sign of the quantum phase transition, unlike the fidelity amplitude decay.

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Area of Science:

  • Quantum mechanics
  • Many-body physics
  • Quantum chaos

Background:

  • Local density of states and fidelity amplitude measure quantum irreversibility.
  • The Dicke Hamiltonian models a single-mode bosonic field interacting with N two-level atoms.
  • This system transitions from quasi-integrability to quantum chaos for finite instances.

Purpose of the Study:

  • To investigate quantum irreversibility measures in the Dicke Hamiltonian.
  • To analyze the impact of integrability-chaos transitions and quantum phase transitions on these measures.

Main Methods:

  • Studying the local density of states and its Fourier transform (fidelity amplitude).
  • Analyzing the Dicke Hamiltonian, a paradigmatic many-body system.
  • Examining system behavior in finite instances versus the thermodynamic limit.

Main Results:

  • The width of the local density of states clearly indicates the transition from integrability to chaos.
  • No trace of the quantum phase transition is observed in the local density of states.
  • A connection between the local density of states and the decay of the fidelity amplitude is established.

Conclusions:

  • The local density of states is a sensitive indicator of the transition from integrability to chaos in quantum systems.
  • Quantum phase transitions in the Dicke model are not reflected in the local density of states.
  • Fidelity amplitude decay is linked to these quantum dynamics, providing further insights into irreversibility.