  Strong magnetic fields impact quantum-chromodynamics (QCD) properties in
several situations; examples include the early universe, magnetars, and
heavy-ion collisions. These examples share a common trait: time evolution. A
prominent QCD property impacted by a strong magnetic field is the quark
condensate, an approximate order parameter of the QCD transition between a
high-temperature quark-gluon phase and a low-temperature hadronic phase. We use
the linear sigma model with quarks to address the quark condensate time
evolution under a strong magnetic field. We use the closed time path formalism
of nonequilibrium quantum field theory to integrate out the quarks and obtain a
mean-field Langevin equation for the condensate. The Langevin equation features
dissipation and noise kernels controlled by a damping coefficient. We compute
the damping coefficient for magnetic field and temperature values achieved in
peripheral relativistic heavy-ion collisions and solve the Langevin equation
for a temperature quench scenario. The magnetic field changes the dissipation
and noise pattern by increasing the damping coefficient compared to the
zero-field case. An increased damping coefficient increases fluctuations and
time scales controlling condensate's short-time evolution, a feature that can
impact hadron formation at the QCD transition. The formalism developed here can
be extended to include other order parameters, hydrodynamic modes, and system's
expansion to address magnetic field effects in complex settings as heavy-ion
collisions, the early universe, and magnetars.
