324,801 research outputs found
Emergence of Topological and Strongly Correlated Ground States in trapped Rashba Spin-Orbit Coupled Bose Gases
We theoretically study an interacting few-body system of Rashba spin-orbit
coupled two-component Bose gases confined in a harmonic trapping potential. We
solve the interacting Hamiltonian at large Rashba coupling strengths using
Exact Diagonalization scheme, and obtain the ground state phase diagram for a
range of interatomic interactions and particle numbers. At small particle
numbers, we observe that the bosons condense to an array of topological states
with n+1/2 quantum angular momentum vortex configurations, where n = 0, 1, 2,
3... At large particle numbers, we observe two distinct regimes: at weaker
interaction strengths, we obtain ground states with topological and symmetry
properties that are consistent with mean-field theory computations; at stronger
interaction strengths, we report the emergence of strongly correlated ground
states.Comment: 14 pages, 9 figure
Dirichlet forms in simulation
Equipping the probability space with a local Dirichlet form with square field
operator and generator allows to improve Monte Carlo computations
of expectations, densities, and conditional expectations, as soon as we are
able to simulate a random variable together with and . We
give examples on the Wiener space, on the Poisson space and on the Monte Carlo
space. When is real-valued we give an explicit formula yielding the density
at the speed of the law of large numbers
Precision Spectroscopy of AdS/CFT
We extend recent remarkable progress in the comparison of the dynamical
energy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weights
of the corresponding non-near-BPS operators in planar N=4 supersymmetric gauge
theory. On the string side the computations are feasible, using semiclassical
methods, if angular momentum quantum numbers are large. This results in a
prediction of gauge theory anomalous dimensions to all orders in the `t Hooft
coupling lambda. On the gauge side the direct computation of these dimensions
is feasible, using a recently discovered relation to integrable (super) spin
chains, provided one considers the lowest order in lambda. This one-loop
computation then predicts the small-tension limit of the string spectrum for
all (i.e. small or large) quantum numbers. In the overlapping window of large
quantum numbers and small effective string tension, the string theory and gauge
theory results are found to match in a mathematically highly non-trivial
fashion. In particular, we compare energies of states with (i) two large
angular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5
each, and show that the solutions are related by an analytic continuation.
Finally, numerical evidence is presented on the gauge side that the agreement
persists also at higher (two) loop order.Comment: 26 pages, 1 figure, v2: typos correcte
Ergodicity and spectral cascades in point vortex flows on the sphere
A.C.P. was supported under DOD (MURI) Grant No. N000141110087 ONR. The computations were supported by the CUNY HPCC under NSF Grants No. CNS-0855217 and No. CNS-0958379.We present results for the equilibrium statistics and dynamic evolution of moderately large [n = O (102 - 103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensemble-averaged wave-number spectra of the nonsingular velocity field induced by the vortices exhibit the expected k-1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.Publisher PDFPeer reviewe
Atomic Mass Dependence of Hadron Production in Deep Inelastic Scattering on Nuclei
Hadron production in lepton-nucleus deep inelastic scattering is studied in
an absorption model. In the proposed model, the early stage of hadronization in
the nuclear medium is dominated by prehadron formation and absorption,
controlled by flavor-dependent formation lengths and absorption cross sections.
Computations for hadron multiplicity ratios are presented and compared with the
HERMES experimental data for pions, kaons, protons and antiprotons. The
mass-number dependence of hadron attenuation is shown to be sensitive to the
underlying hadronization dynamics. Contrary to common expectations for
absorption models, a leading term proportional to A^{2/3} is found. Deviations
from the leading behavior arise at large mass-numbers and large hadron
fractional momenta.Comment: 30 pages, 10 figures, v2: minor changes (legend in figs 5 & 6 is
added), v3: additional explanations are added, v4: Version combines v3 and
the erratum hep-ph/050803
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