Regensburg 2025 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 56: Quantum Dynamics, Decoherence, and Quantum Information (joint session DY/TT)

TT 56.7: Talk

Friday, March 21, 2025, 11:00–11:15, H37

Linear differential equation approach to the Loschmidt amplitude — •Michael Vogl — King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

The Loschmidt amplitude is a popular quantity that allows making predictions about the stability of quantum states under time evolution. We present an approach that allows us to find a linear differential equation that can be used to compute the Loschmidt amplitude. This approach, while in essence perturbative, has the advantage that it converges at finite order. We demonstrate that the approach for generically chosen matrix Hamiltonians often offers advantages over Taylor and cumulant expansions even when we truncate at finite order. Even in low dimensional systems such as two band Hamiltonians (multi-Weyl semimetals and AB bilayer graphene) it can be used to obtain general formulas for the Loschmidt amplitude after a quench. Results readily generalize to find transmission amplitudes and specific contributions of the partition function, too. Our method can also be applied to many body spin and fermionic Hamiltonians. Here, while the approach still offers advantages, more care has to be taken than in a generic case. We also provide an estimate for a breakdown time of the approximation.

Keywords: Loschmidt amplitude; Time evolution; State stability