10,156 research outputs found
Magnetic dipole-dipole interaction induced by the electromagnetic field
We give a derivation for the indirect interaction between two magnetic
dipoles induced by the quantized electromagnetic field. It turns out that the
interaction between permanent dipoles directly returns to the classical form;
the interaction between transition dipoles does not directly return to the
classical result, yet returns in the short-distance limit. In a finite volume,
the field modes are highly discrete, and both the permanent and transition
dipole-dipole interactions are changed. For transition dipoles, the changing
mechanism is similar with the Purcell effect, since only a few number of nearly
resonant modes take effect in the interaction mediation; for permanent dipoles,
the correction comes from the boundary effect: if the dipoles are placed close
to the boundary, the influence is strong, otherwise, their interaction does not
change too much from the free space case.Comment: 8 pages, 2 figure
Tensor effects on gap evolution of N=40 from non-relativistic and relativistic mean-field theory
Tensor effects on the N=40 gap evolution of N=40 isotones are studied by
employing the Skyrme-Hartree-Fock-Bogoliubov (SHFB) and relativistic
Hartree-Fock-Bogoliubov (RHFB) theories. The results with and without the
inclusion of the tensor component are compared with the experimental data. When
the tensor force is included, both of the two different approaches are found to
give the same trend and agree with the experimental one, which indicates the
necessity of introducing the tensor force in the evolution of N=40 subshell and
on the other hand the reliability of the methods. Furthermore, it is shown that
the gap evolution is primarily determined by the corresponding tensor
contributions from and -tensor coupling in the relativistic
framework.Comment: 4 pages, 3 figure
Quantum Cohomology under Birational Maps and Transitions
This is an expanded version of the third author's lecture in String-Math 2015
at Sanya. It summarizes some of our works in quantum cohomology.
After reviewing the quantum Lefschetz and quantum Leray--Hirsch, we discuss
their applications to the functoriality properties under special smooth flops,
flips and blow-ups. Finally, for conifold transitions of Calabi--Yau 3-folds,
formulations for small resolutions (blow-ups along Weil divisors) are sketched.Comment: 20 pages. A contribution to "Proceedings of the String-Math 2015
Conference" to be published in AMS Proceedings of Symposia in Pure
Mathematic
Invariance of Quantum Rings under Ordinary Flops I: Quantum corrections and reduction to local models
This is the first of a sequence of papers proving the quantum invariance
under ordinary flops over an arbitrary smooth base.
In this first part, we determine the defect of the cup product under the
canonical correspondence and show that it is corrected by the small quantum
product attached to the extremal ray. We then perform various reductions to
reduce the problem to the local models.
In Part II, we develop a quantum Leray--Hirsch theorem and use it to show
that the big quantum cohomology ring is invariant under analytic continuations
in the K\"ahler moduli space for ordinary flops of splitting type. In Part III,
together with F. Qu, we remove the splitting condition by developing a quantum
splitting principle, and hence solve the problem completely.Comment: 38 pages, the final version to appear in Algebraic Geometr
Shadows of Kerr-like black holes in a modified gravity theory
In this paper, the shadows cast by non-rotating and rotating modified gravity
black holes are investigated. In addition to the black hole spin parameter
and the inclination angle of observer, another parameter
measuring the deviation of gravitational constant from the Newton one is also
found to affect the shape of the black hole shadow. The result shows that, for
fixed values of and , the size and perimeter of the shadows cast
by the non-rotating and rotating black holes significantly increase with the
parameter , while the distortions decrease with . Moreover, the
energy emission rate of the black hole in high energy case is also
investigated, and the result shows that the peak of the emission rate decreases
with the parameter .Comment: 14 pages, 8 figure
Flops, motives and invariance of quantum rings
For ordinary flops, the correspondence defined by the graph closure is shown
to give equivalence of Chow motives and to preserve the Poincar\'e pairing. In
the case of simple ordinary flops, this correspondence preserves the big
quantum cohomology ring after an analytic continuation over the extended
K\"ahler moduli space.
For Mukai flops, it is shown that the birational map for the local models is
deformation equivalent to isomorphisms. This implies that the birational map
induces isomorphisms on the full quantum rings and all the quantum corrections
attached to the extremal ray vanish.Comment: 51 pages, 2 figures, final version to appear in Annals of Mathematic
Base Station Cooperation in Millimeter Wave Cellular Networks: Performance Enhancement of Cell-Edge Users
Millimeter wave (mmWave) signals are much more sensitive to blockage, which
results in a significant increase of the outage probability, especially for the
users at the edge of the cells. In this paper, we exploit the technique of base
station (BS) cooperation to improve the performance of the cell-edge users in
the downlink transmission of mmWave cellular networks. We design two
cooperative schemes, which are referred to as fixed-number BS cooperation (FNC)
scheme and fixed-region BS cooperation (FRC) scheme, respectively. In FNC
scheme, the cooperative BSs consist of the M nearest BSs around the served
cell-edge users, and in FRC scheme, the cooperative BSs include all the BSs
located within a given region. We derive the expressions for the average rate
and outage probability of a typical cell-edge user located at the origin based
on the stochastic geometry framework. To reduce the computational complexity of
our analytical results for the outage probability, we further propose a Gamma
approximation based method to provide approximations with satisfying accuracy.
Our analytical results incorporate the critical characteristics of mmWave
channels, i.e., the blockage effects, the different path loss of LOS and NLOS
links and the highly directional antenna arrays. Simulation results show that
the performance of the cell-edge users is greatly improved when mmWave networks
are combined with the technique of BS cooperation.Comment: To be published in IEEE Transactions on Communication
Towards theory in conifold transitions for Calabi-Yau threefolds
For projective conifold transitions between Calabi-Yau threefolds and
, with close to in the moduli, we show that the combined information
provided by the model (Gromov--Witten theory in all genera) and model
(variation of Hodge structures) on , linked along the vanishing cycles,
determines the corresponding combined information on . Similar result holds
in the reverse direction when linked with the exceptional curves.Comment: 47 pages, references updated. To appear in J. Diff. Geometr
Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem
This is the second of a sequence of papers proving the quantum invariance for
ordinary flops over an arbitrary smooth base. In this paper, we complete the
proof of the invariance of the big quantum rings under ordinary flops of
splitting type.
To achieve that, several new ingredients are introduced. One is a quantum
Leray--Hirsch theorem for the local model (a certain toric bundle) which
extends the quantum D module of Dubrovin connection on the base by a
Picard--Fuchs system of the toric fibers.
Nonsplit flops as well as further applications of the quantum Leray--Hirsch
theorem will be discussed in subsequent papers. In particular, a quantum
splitting principle is developed in Part III which reduces the general ordinary
flops to the split case solved here.Comment: 39 pages, the final version to appear in Algebraic Geometr
Vortex states and spin textures of rotating spin-orbit-coupled Bose-Einstein condensates in a toroidal trap
We consider the ground-state properties of Rashba spin-orbit-coupled
pseudo-spin-1/2 Bose-Einstein condensates (BECs) in a rotating two-dimensional
(2D) toroidal trap. In the absence of spin-orbit coupling (SOC), the increasing
rotation frequency enhances the creation of giant vortices for the initially
miscible BECs, while it can lead to the formation of semiring density patterns
with irregular hidden vortex structures for the initially immiscible BECs.
Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for
the initially immiscible BECs. Combined effects of rotation, SOC, and
interatomic interactions on the vortex structures and typical spin textures of
the ground state of the system are discussed systematically. In particular, for
fixed rotation frequency above the critical value, the increasing isotropic SOC
favors a visible vortex ring in each component which is accompanied by a hidden
giant vortex plus a (several) hidden vortex ring(s) in the central region. In
the case of 1D anisotropic SOC, large SOC strength results in the generation of
hidden linear vortex string and the transition from initial phase separation
(phase mixing) to phase mixing (phase separation). Furthermore, the peculiar
spin textures including skyrmion lattice, skyrmion pair and skyrmion string are
revealed in this system.Comment: 11pages,8figure
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