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Non-equilibrium almost-stationary states for interacting electrons on a lattice | | Stefan Teufel
; | | Date: |
11 Aug 2017 | | Abstract: | Consider a family of Hamiltonians $H_0^Lambda$ for systems of interacting
fermions on finite subsets $Lambdasubsetmathbb{Z}^d$ of the lattice
$mathbb{Z}^d$ that has a spectral gap above the ground state uniformly in the
system size $|Lambda|$. We show that for a large class of perturbations $V$
there exist non-equilibrium almost-stationary states (NEASS) for the perturbed
Hamiltonian $H=H_0+V_varepsilon$, even if the perturbation closes the spectral
gap. Almost-stationarity refers to the property that expectations of intensive
quantities in these states are constant over long (super-polynomial in
$frac{1}{varepsilon}$) times up to small (super-polynomial in $varepsilon$)
errors, uniformly in the size $|Lambda|$ of the system. These NEASS are
connected to the ground state of the unperturbed Hamiltonian by quasi-local
unitary transformations. The class of allowed perturbations $V_varepsilon$
includes slowly varying potentials and small quasi-local perturbations. Both
types of perturbations need not be small in norm. Slowly varying potentials
typically close the gap of $H_0$, but leave a local gap structure intact.
We also prove an adiabatic-type theorem for time-dependent NEASS associated
with time-dependent perturbations. Based on this theorem, we show that when
starting from the ground state of the unperturbed gapped system and then
adiabatically turning on the perturbation (which might close the gap), then the
final state of the corresponding Schr"odinger evolution is given by a NEASS up
to errors that are asymptotically smaller than any power of the adiabatic
parameter. The NEASS that is finally reached is independent of the precise form
of the switching function. | | Source: | arXiv, 1708.3581 | | Services: | Forum | Review | PDF | Favorites | |
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