11,821 research outputs found
Search for exact local Hamiltonians for general fractional quantum Hall states
We report on our systematic attempts at finding local interactions for which
the lowest-Landau-level projected composite-fermion wave functions are the
unique zero energy ground states. For this purpose, we study in detail the
simplest non-trivial system beyond the Laughlin states, namely bosons at
filling and identify local constraints among clusters of
particles in the ground state. By explicit calculation, we show that no
Hamiltonian up to (and including) four particle interactions produces this
state as the exact ground state, and speculate that this remains true even when
interaction terms involving greater number of particles are included.
Surprisingly, we can identify an interaction, which imposes an energetic
penalty for a specific entangled configuration of four particles with relative
angular momentum of , that produces a unique zero energy solution (as
we have confirmed for up to 12 particles). This state, referred to as the
-state, is not identical to the projected composite-fermion state, but
the following facts suggest that the two might be topologically equivalent: the
two sates have a high overlap; they have the same root partition; the quantum
numbers for their neutral excitations are identical; and the quantum numbers
for the quasiparticle excitations also match. On the quasihole side, we find
that even though the quantum numbers of the lowest energy states agree with the
prediction from the composite-fermion theory, these states are not separated
from the others by a clearly identifiable gap. This prevents us from making a
conclusive claim regarding the topological equivalence of the state
and the composite-fermion state. Our study illustrates how new candidate states
can be identified from constraining selected many particle configurations and
it would be interesting to pursue their topological classification.Comment: 21 pages, 11 figure
Hydrogen-like Atoms from Ultrarelativistic Nuclear Collisions
The number of hydrogen-like atoms produced when heavy nuclei collide is
estimated for central collisions at the Relativistic Heavy Ion Collider using
the sudden approximation of Baym et al. As first suggested by Schwartz, a
simultaneous measurement of the hydrogen and hadron spectra will allow an
inference of the electron or muon spectra at low momentum where a direct
experimental measurement is not feasible.Comment: 6 pages, 4 figure
The Exchange Gate in Solid State Spin Quantum Computation: The Applicability of the Heisenberg Model
Solid state quantum computing proposals rely on adiabatic operations of the
exchange gate among localized spins in nanostructures. We study corrections to
the Heisenberg interaction between lateral semiconductor quantum dots in an
external magnetic field. Using exact diagonalization we obtain the regime of
validity of the adiabatic approximation. We also find qualitative corrections
to the Heisenberg model at high magnetic fields and in looped arrays of spins.
Looped geometries of localized spins generate flux dependent, multi-spin terms
which go beyond the basic Heisenberg model.Comment: 13 pages, 8 figure
Vibration control of large linear quadratic symmetric systems
Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples
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