127 research outputs found

### Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional
Brownian motion. The functional law of the iterated logarithm, functional
L\'{e}vy's modulus of continuity and many other results are its particular
cases. Applications to approximation theory are discussed.Comment: AMS-LaTeX, 23 page

### An optimal series expansion of the multiparameter fractional Brownian motion

We derive a series expansion for the multiparameter fractional Brownian
motion. The derived expansion is proven to be rate optimal.Comment: 21 pages, no figures, final version, to appear in Journal of
Theoretical Probabilit

### Gluon condensate and c-quark mass in pseudoscalar sum rules at 3-loop order

Charmonium sum rules for pseudoscalar 0^{-+} state eta_c(1S) are analyzed
within perturbative QCD and Operator Product Expansion. The perturbative part
of the pseudoscalar correlator is considered at alpha_s^2 order and the
contribution of the gluon condensate is taken into account with alpha_s
correction. The OPE series includes the operators of dimension D=6,8 computed
both in the instanton and factorization model. The method of moments in MS-bar
scheme allows to establish acceptable values of the charm quark mass and gluon
condensate, using the experimental mass of eta_c. In result of the analisys the
charm quark mass is found to be m_c(m_c)=1.26+-0.02 GeV independently of the
condensate value. The sensitivity of the results to various approximations for
the massive 3-loop pseudoscalar correlator is discussed.Comment: 19 pages, 1 latex + 5 eps files. v2: Operators of dimension D=8
included; the condensate restriction relaxed; c-quark mass is found
m_c(m_c)=1.26+-0.02 GeV independently of other sum rules and condensate
value. To appear in JHE

### The Effective Potential of the N=0* Yang-Mills Theory

We study the \N=4 SYM theory with SU(N) gauge group in the large N limit,
deformed by giving equal mass to the four adjoint fermions. With this
modification, a potential is dynamically generated for the six scalars in the
theory, \phi^i. We show that the resulting theory is stable (perturbatively in
the 't Hooft coupling), and that there are some indications that =0 is
the vacuum of the theory. Using the AdS/CFT correspondence, we compare the
results to the corresponding supergravity computation, i.e. brane probing a
deformed AdS_5 x S^5 background, and we find qualitative agreement.Comment: 12 pages, 2 figures, version to appear in JHE

### Effective Actions near Singularities

We study the heterotic string compactified on K3 x T^2 near the line T=U,
where the effective action becomes singular due to an SU(2) gauge symmetry
enhancement. By `integrating in' the light W^\pm vector multiplets we derive a
quantum corrected effective action which is manifestly SU(2) invariant and
non-singular. This effective action is found to be consistent with a residual
SL(2,Z) quantum symmetry on the line T=U. In an appropriate decompactification
limit, we recover the known SU(2) invariant action in five dimensions.Comment: 33 pages, LaTeX. v2: cosmetic correction on titlepage. v3: references
and note adde

### Systematic study of tunable laser cooling for trapped-ion experiments

We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ionâ€™s motional ground state. The simulations were experimentally benchmarked with a single 172Yb+ ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks

### Rotating strings and D2-branes in type IIA reduction of M-theory on G2 manifold and their semiclassical limits

We consider rotating strings and D2-branes on type IIA background, which
arises as dimensional reduction of M-theory on manifold of G2 holonomy, dual to
N=1 gauge theory in four dimensions. We obtain exact solutions and explicit
expressions for the conserved charges. By taking the semiclassical limit, we
show that the rotating strings can reproduce only one type of semiclassical
behavior, exhibited by rotating M2-branes on G2 manifolds. Our further
investigation leads to the conclusion that the rotating D2-branes reproduce two
types of the semiclassical energy-charge relations known for membranes in
eleven dimensions.Comment: LaTeX, 29 pages, no figures; V2:comments added; V3:no changes, to
appear in JHE

### The beat of a fuzzy drum: fuzzy Bessel functions for the disc

The fuzzy disc is a matrix approximation of the functions on a disc which
preserves rotational symmetry. In this paper we introduce a basis for the
algebra of functions on the fuzzy disc in terms of the eigenfunctions of a
properly defined fuzzy Laplacian. In the commutative limit they tend to the
eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of
the first kind, thus deserving the name of fuzzy Bessel functions.Comment: 30 pages, 8 figure

### Wightman function and vacuum densities for a Z_2-symmetric thick brane in AdS spacetime

Positive frequency Wightman function, vacuum expectation values of the field
square and the energy-momentum tensor induced by a Z_{2}-symmetric brane with
finite thickness located on (D+1)- dimensional AdS background are evaluated for
a massive scalar field with general curvature coupling parameter. For the
general case of static plane symmetric interior structure the expectation
values in the region outside the brane are presented as the sum of free AdS and
brane induced parts. For a conformally coupled massless scalar the brane
induced part in the vacuum energy-momentum tensor vanishes. In the limit of
strong gravitational fields the brane induced parts are exponentially
suppressed for points not too close to the brane boundary. As an application of
general results a special model is considered in which the geometry inside the
brane is a slice of the Minkowski spacetime orbifolded along the direction
perpendicular to the brane. For this model the Wightman function, vacuum
expectation values of the field square and the energy-momentum tensor inside
the brane are evaluated as well and their behavior is discussed in various
asymptotic regions of the parameters. It is shown that for both minimally and
conformally coupled scalar fields the interior vacuum forces acting on the
brane boundaries tend to decrease the brane thickness.Comment: 25 pages, 6 figures, discussion adde

### Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green
Function in cylindrical coordinates, which is equivalent to obtaining the
solution of the Helmholtz equation for a general ring source. The Fourier
coefficients of the Helmholtz Green function are split into their half
advanced+half retarded and half advanced-half retarded components. Closed form
solutions are given for these components in terms of a Horn function and a
Kampe de Feriet function, respectively. The systems of partial differential
equations associated with these two-dimensional hypergeometric functions are
used to construct a fourth-order ordinary differential equation which both
components satisfy. A second fourth-order ordinary differential equation for
the general Fourier coefficent is derived from an integral representation of
the coefficient, and both differential equations are shown to be equivalent.
Series solutions for the various Fourier coefficients are also given, mostly in
terms of Legendre functions and Bessel/Hankel functions. These are derived from
the closed form hypergeometric solutions or an integral representation, or
both. Numerical calculations comparing different methods of calculating the
Fourier coefficients are presented

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