New approach to describe two coupled spins in a variable magnetic field
- URL: http://arxiv.org/abs/2011.11569v1
- Date: Mon, 23 Nov 2020 17:29:31 GMT
- Title: New approach to describe two coupled spins in a variable magnetic field
- Authors: Yuri Belousov, Roberto Grimaudo, Antonino Messina, Agostino Migliore,
and Alessandro Sergi
- Abstract summary: We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field.
We modify the time-dependent Schr"odinger equation through a change of representation.
The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
- Score: 55.41644538483948
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a method to describe the evolution of two spins coupled by
hyperfine interaction in an external time-dependent magnetic field. We apply
the approach to the case of hyperfine interaction with axial symmetry, which
can be solved exactly in a constant, appropriately oriented magnetic field. In
order to treat the nonstationary dynamical problem, we modify the
time-dependent Schr\"odinger equation through a change of representation that,
by exploiting an instantaneous (adiabatic) basis makes the time-dependent
Hamiltonian diagonal at any time instant. The solution of the transformed
time-dependent Schr\"odinger in the form of chronologically ordered exponents
with transparent pre-exponential coefficients is reported. This solution is
highly simplified when an adiabatically varying magnetic field perturbs the
system. The approach here proposed may be used for the perturbative treatment
of other dynamical problems with no exact solution.
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