21,105 research outputs found
The Unhiggs
We examine a scenario where the Higgs is part of an approximate conformal
field theory, and has a scaling dimension greater than one. Such an unparticle
Higgs (or Unhiggs) can still break electroweak symmetry and unitarize WW
scattering, but its gauge couplings are suppressed. An Unhiggs model has a
reduced sensitivity of the weak scale to the cutoff, and can thus provide a
solution to the little hierarchy problem.Comment: 21 pages, 9 figures; v2: further discussion, references added,
version published in JHE
Sagnac Effect of Goedel's Universe
We present exact expressions for the Sagnac effect of Goedel's Universe. For
this purpose we first derive a formula for the Sagnac time delay along a
circular path in the presence of an arbitrary stationary metric in cylindrical
coordinates. We then apply this result to Goedel's metric for two different
experimental situations: First, the light source and the detector are at rest
relative to the matter generating the gravitational field. In this case we find
an expression that is formally equivalent to the familiar nonrelativistic
Sagnac time delay. Second, the light source and the detector are rotating
relative to the matter. Here we show that for a special rotation rate of the
detector the Sagnac time delay vanishes. Finally we propose a formulation of
the Sagnac time delay in terms of invariant physical quantities. We show that
this result is very close to the analogous formula of the Sagnac time delay of
a rotating coordinate system in Minkowski spacetime.Comment: 26 pages, including 4 figures, corrected typos, changed reference
Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
By applying the standard adiabatic approximation and using the accurate
analytical expression for the corresponding local chemical potential obtained
in our previous work [Phys. Rev. A \textbf{75}, 063610 (2007)] we derive an
effective 1D equation that governs the axial dynamics of mean-field
cigar-shaped condensates with repulsive interatomic interactions, accounting
accurately for the contribution from the transverse degrees of freedom. This
equation, which is more simple than previous proposals, is also more accurate.
Moreover, it allows treating condensates containing an axisymmetric vortex with
no additional cost. Our effective equation also has the correct limit in both
the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to
derive fully analytical expressions for ground-state properties such as the
chemical potential, axial length, axial density profile, and local sound
velocity. These analytical expressions remain valid and accurate in between the
above two extreme regimes. Following the same procedure we also derive an
effective 2D equation that governs the transverse dynamics of mean-field
disk-shaped condensates. This equation, which also has the correct limit in
both the quasi-2D and the Thomas-Fermi regime, is again more simple and
accurate than previous proposals. We have checked the validity of our equations
by numerically solving the full 3D Gross-Pitaevskii equation.Comment: 11 pages, 7 figures; Final version published in Phys. Rev. A;
Manuscript put in the archive and submitted to Phys. Rev. A on 17 July 200
Gap solitons in elongated geometries: the one-dimensional Gross-Pitaevskii equation and beyond
We report results of a systematic analysis of matter-wave gap solitons (GSs)
in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded
into a combination of a cigar-shaped trap and axial optical-lattice (OL)
potential. Basic cases of the strong, intermediate, and weak radial
(transverse) confinement are considered, as well as settings with shallow and
deep OL potentials. Only in the case of the shallow lattice combined with tight
radial confinement, which actually has little relevance to realistic
experimental conditions, does the usual one-dimensional (1D) cubic
Gross-Pitaevskii equation (GPE) furnish a sufficiently accurate description of
GSs. However, the effective 1D equation with the nonpolynomial nonlinearity,
derived in Ref. [Phys. Rev. A \textbf{77}, 013617 (2008)], provides for quite
an accurate approximation for the GSs in all cases, including the situation
with weak transverse confinement, when the soliton's shape includes a
considerable contribution from higher-order transverse modes, in addition to
the usual ground-state wave function of the respective harmonic oscillator.
Both fundamental GSs and their multipeak bound states are considered. The
stability is analyzed by means of systematic simulations. It is concluded that
almost all the fundamental GSs are stable, while their bound states may be
stable if the underlying OL potential is deep enough.Comment: 14 pages, 12 figures; v2: matches published versio
On the generalized Feng-Rao numbers of numerical semigroups generated by intervals
We give some general results concerning the computation of the generalized
Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup
generated by an interval, a formula for the Feng-Rao number is
obtained.Comment: 23 pages, 6 figure
Staircase to Higher-Order Topological Phase Transitions
We find a series of topological phase transitions of increasing order, beyond
the more standard second-order phase transition in a one-dimensional
topological superconductor. The jumps in the order of the transitions depend on
the range of the pairing interaction, which is parametrized by an algebraic
decay with exponent . Remarkably, in the limit the order
of the topological transition becomes infinite. We compute the critical
exponents for the series of higher-order transitions in exact form and find
that they fulfill the hyperscaling relation. We also study the critical
behaviour at the boundary of the system and discuss potential experimental
platforms of magnetic atoms in superconductors.Comment: 5+5pages, 7 figures. Accepted as a Rapid Communicatio
Raman-scattering study of the phonon dispersion in twisted bi-layer graphene
Bi-layer graphene with a twist angle \theta\ between the layers generates a
superlattice structure known as Moir\'{e} pattern. This superlattice provides a
\theta-dependent q wavevector that activates phonons in the interior of the
Brillouin zone. Here we show that this superlattice-induced Raman scattering
can be used to probe the phonon dispersion in twisted bi-layer graphene (tBLG).
The effect reported here is different from the broadly studied double-resonance
in graphene-related materials in many aspects, and despite the absence of
stacking order in tBLG, layer breathing vibrations (namely ZO' phonons) are
observed.Comment: 18 pages, 4 figures, research articl
Theory of spin, electronic and transport properties of the lateral triple quantum dot molecule in a magnetic field
We present a theory of spin, electronic and transport properties of a
few-electron lateral triangular triple quantum dot molecule in a magnetic
field. Our theory is based on a generalization of a Hubbard model and the
Linear Combination of Harmonic Orbitals combined with Configuration Interaction
method (LCHO-CI) for arbitrary magnetic fields. The few-particle spectra
obtained as a function of the magnetic field exhibit Aharonov-Bohm
oscillations. As a result, by changing the magnetic field it is possible to
engineer the degeneracies of single-particle levels, and thus control the total
spin of the many-electron system. For the triple dot with two and four
electrons we find oscillations of total spin due to the singlet-triplet
transitions occurring periodically in the magnetic field. In the three-electron
system we find a transition from a magnetically frustrated to the
spin-polarized state. We discuss the impact of these phase transitions on the
addition spectrum and the spin blockade of the lateral triple quantum dot
molecule.Comment: 30 pages (one column), 9 figure
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