644 research outputs found
Braiding fluxes in Pauli Hamiltonian
Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have
gapless zero modes. We study the adiabatic evolution of these modes under the
slow motion of fluxons with fluxes . The positions,
, of the fluxons are viewed as controls. We are
interested in the holonomies associated with closed paths in the space of
controls. The holonomies can sometimes be abelian, but in general are not. They
can sometimes be topological, but in general are not. We analyze some of the
special cases and some of the general ones. Our most interesting results
concern the cases where holonomy turns out to be topological which is the case
when all the fluxons are subcritical, , and the number of zero modes
is . If it is also non-abelian. In the special case that the
fluxons carry identical fluxes the resulting anyons satisfy the Burau
representations of the braid group
Time-Energy coherent states and adiabatic scattering
Coherent states in the time-energy plane provide a natural basis to study
adiabatic scattering. We relate the (diagonal) matrix elements of the
scattering matrix in this basis with the frozen on-shell scattering data. We
describe an exactly solvable model, and show that the error in the frozen data
cannot be estimated by the Wigner time delay alone. We introduce the notion of
energy shift, a conjugate of Wigner time delay, and show that for incoming
state the energy shift determines the outgoing state.Comment: 11 pages, 1 figur
Visualizing Two Qubits
The notions of entanglement witnesses, separable and entangled states for two
qubits system can be visualized in three dimensions using the SLOCC equivalence
classes. This visualization preserves the duality relations between the various
sets and allows us to give ``proof by inspection'' of a non-elementary result
of the Horodeckies that for two qubits, Peres separability test is iff. We then
show that the CHSH Bell inequalities can be visualized as circles and cylinders
in the same diagram. This allows us to give a geometric proof of yet another
result of the Horodeckies, which optimizes the violation of the CHSH Bell
inequality. Finally, we give numerical evidence that, remarkably, allowing
Alice and Bob to use three rather than two measurements each, does not help
them to distinguish any new entangled SLOCC equivalence class beyond the CHSH
class.Comment: 22 pages, 5 figures. Added several reference
- …