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Loschmidt echo for deformed Wigner matrices
László Erdős1, Joscha Henheik1, Oleksii Kolupaiev1
1Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
Letters in Mathematical Physics
|February 3, 2025
Summary
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.
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.
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