The adiabatic theorem and linear response theory for extended quantum systems

Understand

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$.

• Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint.
• In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom.
• Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap.