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Unitary evolution for a two-level quantum system in fractional-time scenario.

D Cius1, L Menon2, M A F Dos Santos2

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Summary

Researchers mapped nonunitary time-evolution operators from fractional-time Schrödinger equations to unitary ones. This was achieved using a dynamical Hilbert space and a time-dependent metric operator, enabling standard quantum mechanics interpretations.

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Area of Science:

  • Quantum Mechanics
  • Theoretical Physics

Background:

  • Fractional-time Schrödinger equation (FTSE) leads to nonunitary time-evolution operators.
  • Nonunitary evolution does not preserve the norm of quantum states, complicating interpretation.

Purpose of the Study:

  • To demonstrate the possibility of mapping nonunitary operators to unitary ones.
  • To enable standard quantum mechanics interpretations for systems described by FTSE.

Main Methods:

  • Utilized a time-dependent non-Hermitian quantum formalism.
  • Introduced a dynamical Hilbert space with a time-dependent metric operator.
  • Constructed a Hermitian time-dependent Dyson map.

Main Results:

  • Successfully mapped nonunitary time-evolution operators to unitary ones.
  • Showcased that the system evolves unitarily with respect to the time-dependent metric.
  • Provided three examples of Hamiltonians and their corresponding unitary dynamics and Dyson maps.

Conclusions:

  • The proposed method allows for a unitary description of quantum systems governed by FTSE.
  • This approach facilitates proper interpretation of quantum mechanics for non-Hermitian systems.