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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
Summary
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.
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.
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