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Non-adiabatic Fast Control of Mixed States based on Lewis-Riesenfeld Invariant
We apply the inversely-engineered control method based on Lewis-Riesenfeld
invariants to control mixed states of a two-level quantum system. We show that
the inversely-engineered control passages of mixed states - and pure states as
special cases - can be made significantly faster than the conventional
adiabatic control passages, which renders the method applicable to quantum
computation. We devise a new type of inversely-engineered control passages, to
be coined the antedated control passages, which further speed up the control
significantly. We also demonstrate that by carefully tuning the control
parameters, the inversely-engineered control passages can be optimized in terms
of speed and energy cost.Comment: 9 pages, 9 figures, version to appear in J. Phys. Soc. Jp
Non-universal size dependence of the free energy of confined systems near criticality
The singular part of the finite-size free energy density of the O(n)
symmetric field theory in the large-n limit is calculated at finite
cutoff for confined geometries of linear size L with periodic boundary
conditions in 2 < d < 4 dimensions. We find that a sharp cutoff
causes a non-universal leading size dependence
near which dominates the universal scaling term . This
implies a non-universal critical Casimir effect at and a leading
non-scaling term of the finite-size specific heat above .Comment: RevTex, 4 page
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