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We analyze the time decay of the Loschmidt echo for similar Hamiltonians. This quantum effect reveals how imperfect time reversal impacts initial states in deformed Wigner matrices.

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Area of Science:

  • Quantum mechanics
  • Statistical physics

Background:

  • The Loschmidt echo quantifies the fidelity of time-reversed quantum states.
  • Deformed Wigner matrices are used to model complex quantum systems.

Purpose of the Study:

  • To analyze the time decay of the Loschmidt echo for two closely related Hamiltonians.
  • To investigate the impact of imperfect time reversal on quantum states.

Main Methods:

  • Utilizing deformed Wigner matrices as model Hamiltonians.
  • Developing and applying new two-resolvent laws for analyzing quantum systems.

Main Results:

  • Characterizing the time decay of the Loschmidt echo.
  • Demonstrating the utility of two-resolvent laws for non-orthogonal eigenbasis Hamiltonians.

Conclusions:

  • The study provides insights into quantum state stability under time reversal.
  • New mathematical tools are introduced for analyzing quantum dynamics with non-commuting Hamiltonians.