198 research outputs found
Bergman kernels and symplectic reduction
We generalize several recent results concerning the asymptotic expansions of
Bergman kernels to the framework of geometric quantization and establish an
asymptotic symplectic identification property. More precisely, we study the
asymptotic expansion of the -invariant Bergman kernel of the spin^c Dirac
operator associated with high tensor powers of a positive line bundle on a
symplectic manifold. We also develop a way to compute the coefficients of the
expansion, and compute the first few of them, especially, we obtain the scalar
curvature of the reduction space from the -invariant Bergman kernel on the
total space. These results generalize the corresponding results in the
non-equivariant setting, which has played a crucial role in the recent work of
Donaldson on stability of projective manifolds, to the geometric quantization
setting. As another kind of application, we generalize some Toeplitz operator
type properties in semi-classical analysis to the framework of geometric
quantization. The method we use is inspired by Local Index Theory, especially
by the analytic localization techniques developed by Bismut and Lebeau.Comment: 132 page
Playing with Derivation Modes and Halting Conditions
In the area of P systems, besides the standard maximally parallel derivation
mode, many other derivation modes have been investigated, too. In this paper, many
variants of hierarchical P systems and tissue P systems using different derivation modes
are considered and the effects of using di erent derivation modes, especially the maximally
parallel derivation modes and the maximally parallel set derivation modes, on the
generative and accepting power are illustrated. Moreover, an overview on some control
mechanisms used for (tissue) P systems is given.
Furthermore, besides the standard total halting mode, we also consider different halting
conditions such as unconditional halting and partial halting and explain how the use
of different halting modes may considerably change the computing power of P systems
and tissue P systems
Excitation spectra of a 3He impurity on 4He clusters
The diffusion Monte Carlo technique is used to calculate and analyze the
excitation spectrum of a single 3He atom bound to a cluster with N 4He atoms,
with the aim of establishing the most adequate filling ordering of
single-fermion orbits to the mixed clusters with a large number of 3He atoms.
The resulting ordering looks like the rotational spectrum of a diatomic
molecule, being classified only by the angular momentum of the level, although
vibrational-like excitations appear at higher energies for sufficiently large
N
Rate-Distortion-Based Physical Layer Secrecy with Applications to Multimode Fiber
Optical networks are vulnerable to physical layer attacks; wiretappers can
improperly receive messages intended for legitimate recipients. Our work
considers an aspect of this security problem within the domain of multimode
fiber (MMF) transmission. MMF transmission can be modeled via a broadcast
channel in which both the legitimate receiver's and wiretapper's channels are
multiple-input-multiple-output complex Gaussian channels. Source-channel coding
analyses based on the use of distortion as the metric for secrecy are
developed. Alice has a source sequence to be encoded and transmitted over this
broadcast channel so that the legitimate user Bob can reliably decode while
forcing the distortion of wiretapper, or eavesdropper, Eve's estimate as high
as possible. Tradeoffs between transmission rate and distortion under two
extreme scenarios are examined: the best case where Eve has only her channel
output and the worst case where she also knows the past realization of the
source. It is shown that under the best case, an operationally separate
source-channel coding scheme guarantees maximum distortion at the same rate as
needed for reliable transmission. Theoretical bounds are given, and
particularized for MMF. Numerical results showing the rate distortion tradeoff
are presented and compared with corresponding results for the perfect secrecy
case.Comment: 30 pages, 5 figures, accepted to IEEE Transactions on Communication
A Characterization of ET0L and EDT0L Languages
There exists a PT0L language such that the following holds. A language is an ET0L language if and only if there exists a mapping induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that . There exists an infinite collection of EPDT0L languages () such that the family EDT0L is characterized in the following way. A language is an EDT0L language if and only if there exists , a homomorphism and a regular language such that .\u
The Casimir effect with quantized charged spinor matter in background magnetic field
We study the influence of a background uniform magnetic field and boundary
conditions on the vacuum of a quantized charged spinor matter field confined
between two parallel neutral plates; the magnetic field is directed
orthogonally to the plates. The admissible set of boundary conditions at the
plates is determined by the requirement that the Dirac Hamiltonian operator be
self-adjoint. It is shown that, in the case of a sufficiently strong magnetic
field and a sufficiently large separation of the plates, the generalized
Casimir force is repulsive, being independent of the choice of a boundary
condition, as well as of the distance between the plates. The detection of this
effect seems to be feasible in the foreseeable future.Comment: 33 pages, 1 figure, formulas (98) and (102) corrected. arXiv admin
note: text overlap with arXiv:1401.695
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