8,828 research outputs found
Deformation of LeBrun's ALE metrics with negative mass
In this article we investigate deformations of a scalar-flat K\"ahler metric
on the total space of complex line bundles over CP^1 constructed by C. LeBrun.
In particular, we find that the metric is included in a one-dimensional family
of such metrics on the four-manifold, where the complex structure in the
deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the
proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family
of a Hirzebruch surface stated in the last paragraph in the proof of Theorem
1.2, and fixed a relevant error in the proof. Also added a reference [24]
about Kuranishi family of Hirzebruch surface
Multiscale expansion of the lattice potential KdV equation on functions of infinite slow-varyness order
We present a discrete multiscale expansion of the lattice potential
Korteweg-de Vries (lpKdV) equation on functions of infinite order of
slow-varyness. To do so we introduce a formal expansion of the shift operator
on many lattices holding at all orders. The lowest secularity condition from
the expansion of the lpKdV equation gives a nonlinear lattice equation,
depending on shifts of all orders, of the form of the nonlinear Schr\"odinger
(NLS) equationComment: 9 pages, submitted to Journ. Phys.
Double solid twistor spaces: the case of arbitrary signature
In a recent paper (math.DG/0701278) we constructed a series of new Moishezon
twistor spaces which is a kind of variant of the famous LeBrun twistor spaces.
In this paper we explicitly give projective models of another series of
Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a
generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied
by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of
'double solid type' on 3CP^2, projective models of present twistor spaces have
a natural structure of double covering of a CP^2-bundle over CP^1. We
explicitly give a defining polynomial of the branch divisor of the double
covering whose restriction to fibers are degree four. If n>3 these are new
twistor spaces, to the best of the author's knowledge. We also compute the
dimension of the moduli space of these twistor spaces. Differently from
math.DG/0701278, the present investigation is based on analysis of
pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was
"Explicit construction of new Moishezon twistor spaces, II".
Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator
A Lindblad master equation for a harmonic oscillator, which describes the
dynamics of an open system, is formally solved. The solution yields the
spectral resolution of the Liouvillian, that is, all eigenvalues and
eigenprojections are obtained. This spectral resolution is discussed in depth
in the context of the biorthogonal system and the rigged Hilbert space, and the
contribution of each eigenprojection to expectation values of physical
quantities is revealed. We also construct the ladder operators of the
Liouvillian, which clarify the structure of the spectral resolution.Comment: 22pages, no figure; title changed, minor corrections, references
added; minor correction
Quasi-elastic neutron scattering in the high-field phase of a Haldane antiferromagnet
Inelastic neutron scattering experiments on the Haldane-gap quantum
antiferromagnet NDMAP are performed in magnetic fields below and above the
critical field Hc at which the gap closes. Quasi-elastic neutron scattering is
found for H>Hc indicating topological excitations in the high field phase.Comment: Added to discussion section. v2: Updated figure
- …