659 research outputs found

### Field Quantization in 5D Space-Time with Z$_2$-parity and Position/Momentum Propagator

Field quantization in 5D flat and warped space-times with Z$_2$-parity is
comparatively examined. We carefully and closely derive 5D
position/momentum(P/M) propagators. Their characteristic behaviours depend on
the 4D (real world) momentum in relation to the boundary parameter ($l$) and
the bulk curvature (\om). They also depend on whether the 4D momentum is
space-like or time-like. Their behaviours are graphically presented and the
Z$_2$ symmetry, the "brane" formation and the singularities are examined. It is
shown that the use of absolute functions is important for properly treating the
singular behaviour. The extra coordinate appears as a {\it directed} one like
the temperature. The $\delta(0)$ problem, which is an important consistency
check of the bulk-boundary system, is solved {\it without} the use of
KK-expansion. The relation between P/M propagator (a closed expression which
takes into account {\it all} KK-modes) and the KK-expansion-series propagator
is clarified. In this process of comparison, two views on the extra space
naturally come up: orbifold picture and interval (boundary) picture.
Sturm-Liouville expansion (a generalized Fourier expansion) is essential there.
Both 5D flat and warped quantum systems are formulated by the Dirac's bra and
ket vector formalism, which shows the warped model can be regarded as a {\it
deformation} of the flat one with the {\it deformation parameter} \om. We
examine the meaning of the position-dependent cut-off proposed by
Randall-Schwartz.Comment: 44 figures, 22(fig.)+41 pages, to be published in Phys.Rev.D, Fig.4
is improve

### Deep-inelastic scattering and the operator product expansion in lattice QCD

We discuss the determination of deep-inelastic hadron structure in lattice
QCD. By using a fictitious heavy quark, direct calculations of the Compton
scattering tensor can be performed in Euclidean space that allow the extraction
of the moments of structure functions. This overcomes issues of operator mixing
and renormalisation that have so far prohibited lattice computations of higher
moments. This approach is especially suitable for the study of the twist-two
contributions to isovector quark distributions, which is practical with current
computing resources. While we focus on the isovector unpolarised distribution,
our method is equally applicable to other quark distributions and to
generalised parton distributions. By looking at matrix elements such as
$$ (where $V^\mu$ and $A^\nu$ are vector
and axial-vector heavy-light currents) within the same formalism, moments of
meson distribution amplitudes can also be extracted.Comment: 10 pages, 5 figures, version accepted for publicatio

### On $L^2$ -functions with bounded spectrum

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$,
whose Fourier transform has bounded support. We obtain a description of
continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that
$f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$.
Only injective affine maps $\varphi$ have this property

### Some Applications of the Lee-Yang Theorem

For lattice systems of statistical mechanics satisfying a Lee-Yang property
(i.e., for which the Lee-Yang circle theorem holds), we present a simple proof
of analyticity of (connected) correlations as functions of an external magnetic
field h, for Re h > 0 or Re h < 0. A survey of models known to have the
Lee-Yang property is given. We conclude by describing various applications of
the aforementioned analyticity in h.Comment: 16 page

### OPE Convergence in Conformal Field Theory

We clarify questions related to the convergence of the OPE and conformal
block decomposition in unitary Conformal Field Theories (for any number of
spacetime dimensions). In particular, we explain why these expansions are
convergent in a finite region. We also show that the convergence is
exponentially fast, in the sense that the operators of dimension above Delta
contribute to correlation functions at most exp(-a Delta). Here the constant
a>0 depends on the positions of operator insertions and we compute it
explicitly.Comment: 26 pages, 6 figures; v2: a clarifying note and two refs added; v3:
note added concerning an extra constant factor in the main error estimate,
misprint correcte

### On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators

The spectra of the Schr\"odinger operators with periodic potentials are
studied. When the potential is real and periodic, the spectrum consists of at
most countably many line segments (energy bands) on the real line, while when
the potential is complex and periodic, the spectrum consists of at most
countably many analytic arcs in the complex plane.
In some recent papers, such operators with complex $\mathcal{PT}$-symmetric
periodic potentials are studied. In particular, the authors argued that some
energy bands would appear and disappear under perturbations. Here, we show that
appearance and disappearance of such energy bands imply existence of nonreal
spectra. This is a consequence of a more general result, describing the local
shape of the spectrum.Comment: 5 pages, 2 figure

### The H=xp model revisited and the Riemann zeros

Berry and Keating conjectured that the classical Hamiltonian H = xp is
related to the Riemann zeros. A regularization of this model yields
semiclassical energies that behave, in average, as the non trivial zeros of the
Riemann zeta function. However, the classical trajectories are not closed,
rendering the model incomplete. In this paper, we show that the Hamiltonian H =
x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum
coincides with the average Riemann zeros. This result is generalized to
Dirichlet L-functions using different self-adjoint extensions of H. We discuss
the relation of our work to Polya's fake zeta function and suggest an
experimental realization in terms of the Landau model.Comment: 5 pages, 3 figure

### Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential
eigenvalue problem lies at the heart of the R-matrix methods for both the
Schr\"odinger and Dirac particles. A central issue that should be carefully
analyzed when functional series are applied is their convergence. In the
present paper, we study the properties of the eigenfunction expansions
appearing in nonrelativistic and relativistic $R$-matrix theories. In
particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13,
491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761
(1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular
formulation of the R-matrix theory for Dirac particles, the functional series
fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical
Physics, 21 pages, 1 figur

### Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

We argue that the freezing transition scenario, previously explored in the
statistical mechanics of 1/f-noise random energy models, also determines the
value distribution of the maximum of the modulus of the characteristic
polynomials of large N x N random unitary (CUE) matrices. We postulate that our
results extend to the extreme values taken by the Riemann zeta-function zeta(s)
over sections of the critical line s=1/2+it of constant length and present the
results of numerical computations in support. Our main purpose is to draw
attention to possible connections between the statistical mechanics of random
energy landscapes, random matrix theory, and the theory of the Riemann zeta
function.Comment: published version with a few misprints corrected and references adde

### Bose-Einstein-condensed systems in random potentials

The properties of systems with Bose-Einstein condensate in external
time-independent random potentials are investigated in the frame of a
self-consistent stochastic mean-field approximation. General considerations are
presented, which are valid for finite temperatures, arbitrary strengths of the
interaction potential, and for arbitrarily strong disorder potentials. The
special case of a spatially uncorrelated random field is then treated in more
detail. It is shown that the system consists of three components, condensed
particles, uncondensed particles and a glassy density fraction, but that the
pure Bose glass phase with only a glassy density does not appear. The theory
predicts a first-order phase transition for increasing disorder parameter,
where the condensate fraction and the superfluid fraction simultaneously jump
to zero. The influence of disorder on the ground-state energy, the stability
conditions, the compressibility, the structure factor, and the sound velocity
are analyzed. The uniform ideal condensed gas is shown to be always
stochastically unstable, in the sense that an infinitesimally weak disorder
destroys the Bose-Einstein condensate, returning the system to the normal
state. But the uniform Bose-condensed system with finite repulsive interactions
becomes stochastically stable and exists in a finite interval of the disorder
parameter.Comment: Latex file, final published varian

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