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Scattering and Perturbation Theory for Discrete-Time Dynamics.

Alessandro Bisio1, Nicola Mosco1, Paolo Perinotti1

  • 1Dipartimento di Fisica, Università di Pavia, via Bassi 6, 27100 Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, 27100, Pavia, Italy.

Physical Review Letters
|July 9, 2021
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Summary
This summary is machine-generated.

We developed a scattering theory for discrete-time quantum systems, defining a scattering operator and its quasienergy conservation. This framework aids in analyzing quantum simulators and comparing continuous-time and discretized models.

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Area of Science:

  • Quantum mechanics
  • Theoretical physics
  • Computational physics

Background:

  • Scattering processes are fundamental in quantum mechanics.
  • Understanding discrete-time quantum evolution is crucial for quantum simulations.
  • Existing scattering theories primarily focus on continuous-time systems.

Purpose of the Study:

  • To systematically develop a scattering theory for discrete-time quantum systems.
  • To define and analyze properties of the scattering operator in discrete time.
  • To compare scattering amplitudes between continuous and discrete time models.

Main Methods:

  • Definition and general properties of the discrete-time scattering operator.
  • Development of two perturbative techniques for scattering operator expansion (Lippmann-Schwinger and Dyson series analogies).
  • Rigorous assessment of scattering amplitude comparison for bounded Hamiltonians.

Main Results:

  • Established a framework for scattering in discrete-time quantum systems.
  • Demonstrated quasienergy conservation modulo 2π.
  • Provided a method to compare scattering in continuous versus discretized models.

Conclusions:

  • The developed formalism is applicable to various quantum simulators, including quantum walks and cellular automata.
  • The study offers a rigorous method for analyzing scattering in discrete quantum dynamics.
  • Case study on a 1D fermion cellular automaton validates the framework.