371 research outputs found
On the Consistency of the Solutions of the Space Fractional Schr\"odinger Equation
Recently it was pointed out that the solutions found in literature for the
space fractional Schr\"odinger equation in a piecewise manner are wrong, except
the case with the delta potential. We reanalyze this problem and show that an
exact and a proper treatment of the relevant integral proves otherwise. We also
discuss effective potential approach and present a free particle solution for
the space and time fractional Schr\"odinger equation in general coordinates in
terms of Fox's H-functions
The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index
We study fundamental properties of the fractional, one-dimensional Weyl
operator densely defined on the Hilbert space
and determine the asymptotic behaviour of
both the free Green's function and its variation with respect to energy for
bound states. In the sequel we specify the Birman-Schwinger representation for
the Schr\"{o}dinger operator
and extract the finite-rank portion which is essential for the asymptotic
expansion of the ground state. Finally, we determine necessary and sufficient
conditions for there to be a bound state for small coupling constant .Comment: 16 pages, 1 figur
Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles
We apply some methods of homology and K-theory to special classes of branes
wrapping homologically nontrivial cycles. We treat the classification of
four-geometries in terms of compact stabilizers (by analogy with Thurston's
classification of three-geometries) and derive the K-amenability of Lie groups
associated with locally symmetric spaces listed in this case. More complicated
examples of T-duality and topology change from fluxes are also considered. We
analyse D-branes and fluxes in type II string theory on with torsion flux and demonstrate in details
the conjectured T-duality to with no flux. In the
simple case of , T-dualizing the circles reduces to
duality between with
flux and with no flux.Comment: 27 pages, tex file, no figure
T-duality for principal torus bundles
In this paper we study T-duality for principal torus bundles with H-flux. We
identify a subset of fluxes which are T-dualizable, and compute both the dual
torus bundle as well as the dual H-flux. We briefly discuss the generalized
Gysin sequence behind this construction and provide examples both of non
T-dualizable and of T-dualizable H-fluxes.Comment: 9 pages, typos removed and minor corrections mad
Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions
We study the long-time behavior of decoupled continuous-time random walks
characterized by superheavy-tailed distributions of waiting times and symmetric
heavy-tailed distributions of jump lengths. Our main quantity of interest is
the limiting probability density of the position of the walker multiplied by a
scaling function of time. We show that the probability density of the scaled
walker position converges in the long-time limit to a non-degenerate one only
if the scaling function behaves in a certain way. This function as well as the
limiting probability density are determined in explicit form. Also, we express
the limiting probability density which has heavy tails in terms of the Fox
-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur
"Chain scenario" for Josephson tunneling with pi-shift in YBa2Cu3O7
We point out that all current Josephson-junction experiments probing directly
the symmetry of the superconducting state in YBa2Cu3O7, can be interpreted in
terms of the bilayer antiferromagnetic spin fluctuation model, which renders
the superconducting state with the order parameters of extended symmetry,
but with the opposite signs in the bonding and antibonding Cu-O plane bands.
The essential part of our interpretation includes the Cu-O chain band which
would have the order parameter of the same sign as antibonding plane band. We
show that in this case net Josephson currents along and perpendicular to the
chains have the phase shift equal to pi.Comment: 4 pages, revtex, 1 figure uuencoded (POSTSCRIPT figure replaced - the
previous file did not print Greek letters correctly
On transversally elliptic operators and the quantization of manifolds with -structure
An -structure on a manifold is an endomorphism field
\phi\in\Gamma(M,\End(TM)) such that . Any -structure
determines an almost CR structure E_{1,0}\subset T_\C M given by the
-eigenbundle of . Using a compatible metric and connection
on , we construct an odd first-order differential operator ,
acting on sections of , whose principal symbol is of the
type considered in arXiv:0810.0338. In the special case of a CR-integrable
almost -structure, we show that when is the generalized
Tanaka-Webster connection of Lotta and Pastore, the operator is given by D
= \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann
operator.
We then describe two "quantizations" of manifolds with -structure that
reduce to familiar methods in symplectic geometry in the case that is a
compatible almost complex structure, and to the contact quantization defined in
\cite{F4} when comes from a contact metric structure. The first is an
index-theoretic approach involving the operator ; for certain group actions
will be transversally elliptic, and using the results in arXiv:0810.0338,
we can give a Riemann-Roch type formula for its index. The second approach uses
an analogue of the polarized sections of a prequantum line bundle, with a CR
structure playing the role of a complex polarization.Comment: 31 page
D-branes, KK-theory and duality on noncommutative spaces
We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology, a refinement of open string T-duality, and a general criterion for cancellation of global worldsheet anomalies
On the Bloch Theorem Concerning Spontaneous Electric Current
We study the Bloch theorem which states absence of the spontaneous current in
interacting electron systems. This theorem is shown to be still applicable to
the system with the magnetic field induced by the electric current. Application
to the spontaneous surface current is also examined in detail. Our result
excludes the possibility of the recently proposed -wave superconductivity
having the surface flow and finite total current.Comment: 12 pages, LaTeX, 3 Postscript figure
Solution of generalized fractional reaction-diffusion equations
This paper deals with the investigation of a closed form solution of a
generalized fractional reaction-diffusion equation. The solution of the
proposed problem is developed in a compact form in terms of the H-function by
the application of direct and inverse Laplace and Fourier transforms.
Fractional order moments and the asymptotic expansion of the solution are also
obtained.Comment: LaTeX, 18 pages, corrected typo
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