12,533 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
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
Radiative and Collisional Jet Energy Loss in a Quark-Gluon Plasma
We calculate radiative and collisional energy loss of hard partons traversing
the quark-gluon plasma created at RHIC and compare the respective size of these
contributions. We employ the AMY formalism for radiative energy loss and
include additionally energy loss by elastic collisions. Our treatment of both
processes is complete at leading order in the coupling, and accounts for the
probabilistic nature of jet energy loss. We find that a solution of the
Fokker-Planck equation for the probability density distributions of partons is
necessary for a complete calculation of the nuclear modification factor
for pion production in heavy ion collisions. It is found that the
magnitude of is sensitive to the inclusion of both collisional and
radiative energy loss, while the average energy is less affected by the
addition of collisional contributions. We present a calculation of for
at RHIC, combining our energy loss formalism with a relativistic
(3+1)-dimensional hydrodynamic description of the thermalized medium.Comment: 4 pages, 4 figures, contributed to Quark Matter 2008, Jaipur, Indi
Particle yield fluctuations and chemical non-equilibrium at RHIC
We study charge fluctuations within the statistical hadronization model.
Considering both the particle yield ratios and the charge fluctuations we show
that it is possible to differentiate between chemical equilibrium and
non-equilibrium freeze-out conditions. As an example of the procedure we show
quantitatively how the relative yield ratio together with the
normalized net charge fluctuation v(Q)=\ave{\Delta Q^2}/\ave{\Nch} constrain
the chemical conditions at freeze-out. We also discuss the influence of the
limited detector acceptance on fluctuation measurements, and show how this can
be accounted for within a quantitative analysis.Comment: Accepted for publication by Physical Review
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