Effective Heisenberg equations for quadratic Hamiltonians
A. E. Teretenkov
TL;DR
This paper derives effective Heisenberg equations for quadratic fermionic and bosonic Hamiltonians using averaging techniques and perturbative expansions, providing a simplified description of quantum dynamics.
Contribution
It introduces a method to obtain effective time-local Heisenberg equations for quadratic Hamiltonians via averaging and perturbation, applicable to both fermionic and bosonic systems.
Findings
Derived effective Heisenberg equations for quadratic fermionic Hamiltonians.
Extended the approach to bosonic quadratic Hamiltonians.
Provided a perturbative framework for time-local quantum dynamics.
Abstract
We discuss effective quantum dynamics obtained by averaging projector with respect to free dynamics. For unitary dynamics generated by quadratic fermionic Hamiltonians we obtain effective Heisenberg dynamics. By perturbative expansions we obtain the correspondent effective time-local Heisenberg equations. We also discuss a similar problem for bosonic case.
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum chaos and dynamical systems · Quantum many-body systems