7,136 research outputs found
Mock Modular Mathieu Moonshine Modules
We construct super vertex operator algebras which lead to modules for
moonshine relations connecting the four smaller sporadic simple Mathieu groups
with distinguished mock modular forms. Starting with an orbifold of a free
fermion theory, any subgroup of Co_0 that fixes a 3-dimensional subspace of its
unique non-trivial 24-dimensional representation commutes with a certain N=4
superconformal algebra. Similarly, any subgroup of Co_0 that fixes a
2-dimensional subspace of the 24-dimensional representation commutes with a
certain N=2 superconformal algebra. Through the decomposition of the
corresponding twined partition functions into characters of the N=4 (resp. N=2)
superconformal algebra, we arrive at mock modular forms which coincide with the
graded characters of an infinite-dimensional Z-graded module for the
corresponding group. The Mathieu groups are singled out amongst various other
possibilities by the moonshine property: requiring the corresponding weak
Jacobi forms to have certain asymptotic behaviour near cusps. Our constructions
constitute the first examples of explicitly realized modules underlying
moonshine phenomena relating mock modular forms to sporadic simple groups.
Modules for other groups, including the sporadic groups of McLaughlin and
Higman--Sims, are also discussed.Comment: 94 pages, including 56 pages of tables; v2: updated references and
minor revisions to abstract, introduction and sections 8 and
Dynamical Properties of Multi-Armed Global Spirals in Rayleigh-Benard Convection
Explicit formulas for the rotation frequency and the long-wavenumber
diffusion coefficients of global spirals with arms in Rayleigh-Benard
convection are obtained. Global spirals and parallel rolls share exactly the
same Eckhaus, zigzag and skewed-varicose instability boundaries. Global spirals
seem not to have a characteristic frequency or a typical size ,
but their product is a constant under given experimental
conditions. The ratio of the radii of any two dislocations (,
) inside a multi-armed spiral is also predicted to be constant. Some of
these results have been tested by our numerical work.Comment: To appear in Phys. Rev. E as Rapid Communication
Probing tiny motions of nanomechanical resonators: classical or quantum mechanical?
We propose a spectroscopic approach to probe tiny vibrations of a
nanomechanical resonator (NAMR), which may reveal classical or quantum behavior
depending on the decoherence-inducing environment. Our proposal is based on the
detection of the voltage-fluctuation spectrum in a superconducting transmission
line resonator (TLR), which is {\it indirectly} coupled to the NAMR via a
controllable Josephson qubit acting as a quantum transducer. The classical
(quantum mechanical) vibrations of the NAMR induce symmetric (asymmetric) Stark
shifts of the qubit levels, which can be measured by the voltage fluctuations
in the TLR. Thus, the motion of the NAMR, including if it is quantum mechanical
or not, could be probed by detecting the voltage-fluctuation spectrum of the
TLR.Comment: 4 pages, 3 figures. to appear in Physical Review Letter
Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits
Going beyond the entanglement of microscopic objects (such as photons, spins,
and ions), here we propose an efficient approach to produce and control the
quantum entanglement of three macroscopic coupled superconducting qubits. By
conditionally rotating, one by one, selected Josephson charge qubits, we show
that their Greenberger-Horne-Zeilinger (GHZ) entangled states can be
deterministically generated. The existence of GHZ correlations between these
qubits could be experimentally demonstrated by effective single-qubit
operations followed by high-fidelity single-shot readouts. The possibility of
using the prepared GHZ correlations to test the macroscopic conflict between
the noncommutativity of quantum mechanics and the commutativity of classical
physics is also discussed.Comment: 4 Pages with 1 figure. to appear in Physical Review Letter
Mathieu Moonshine and N=2 String Compactifications
There is a `Mathieu moonshine' relating the elliptic genus of K3 to the
sporadic group M_{24}. Here, we give evidence that this moonshine extends to
part of the web of dualities connecting heterotic strings compactified on K3
\times T^2 to type IIA strings compactified on Calabi-Yau threefolds. We
demonstrate that dimensions of M_{24} representations govern the new
supersymmetric index of the heterotic compactifications, and appear in the
Gromov--Witten invariants of the dual Calabi-Yau threefolds, which are elliptic
fibrations over the Hirzebruch surfaces F_n.Comment: 28 pages; v2: minor changes, published versio
Long-Term Variations of the Electron Slot Region and Global Radiation Belt Structure
We report the observations of changes of the nominal position of the quiet-time radiation belt slot over the solar cycles. It has been found that the slot region, believed to be a result of enhanced precipitation losses of energetic electrons due to their interactions with VLF waves in the magnetosphere, tends to shift to higher L (approximately 3) during a solar maximum compared to its canonical L value of approximately 2.5, which is more typical of a solar minimum. The solar-cycle migration of the slot can be understood in terms of the solar-cycle changes in ionospheric densities, which may cause the optimal wave-particle interaction region during higher solar activity periods to move to higher altitudes and higher latitudes, thus higher L. Our analysis also suggests that the primary wave-particle interaction processes that result in the slot formation are located off of the magnetic equator
Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit
We analyze the optical selection rules of the microwave-assisted transitions
in a flux qubit superconducting quantum circuit (SQC). We show that the
parities of the states relevant to the superconducting phase in the SQC are
well-defined when the external magnetic flux , then the
selection rules are same as the ones for the electric-dipole transitions in
usual atoms. When , the symmetry of the potential of
the artificial "atom'' is broken, a so-called -type "cyclic"
three-level atom is formed, where one- and two-photon processes can coexist. We
study how the population of these three states can be selectively transferred
by adiabatically controlling the electromagnetic field pulses. Different from
-type atoms, the adiabatic population transfer in our three-level
-atom can be controlled not only by the amplitudes but also by the
phases of the pulses
Shortcuts to adiabaticity in superconducting circuits for fast multi-partite state generation
Shortcuts to adiabaticity provides a flexible method to accelerate and
improve a quantum control task beyond adiabatic criteria. Here we propose the
reverse-engineering approach to design the longitudinal coupling between a set
of qubits coupled to several field modes, for achieving a fast generation of
multi-partite quantum gates in photonic or qubit-based architecture. We show
that the enhancing generation time is at the nanosecond scale that does not
scale with the number of system components. In addition, our protocol does not
suffer noticeable detrimental effects due to the dissipative dynamics. Finally,
the possible implementation is discussed with the state-of-the-art circuit
quantum electrodynamics architecture.Comment: 11 pages, 8 figure
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