Trace identities and their semiclassical implications

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically {\it integrable} maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The same technique is not applicable for {\it chaotic} maps, and the compatibility of the semiclassical theory in this case remains unsettled. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions.Comment: LaTeX - IOP styl

A comparison of extremal optimization with flat-histogram dynamics for finding spin-glass ground states

We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations. Keywords: extremal optimization. flat-histogram algorithm, equal-hit algorithm, spin-glass model, ground state.Comment: 10 LaTeX pages, 2 figure

Deeply Virtual Compton Scattering

We study in QCD the physics of deeply-virtual Compton scattering (DVCS)---the virtual Compton process in the large s and small t kinematic region. We show that DVCS can probe a new type of off-forward parton distributions. We derive an Altarelli-Parisi type of evolution equations for these distributions. We also derive their sum rules in terms of nucleon form-factors of the twist-two quark and gluon operators. In particular, we find that the second sum rule is related to fractions of the nucleon spin carried separately by quarks and gluons. We estimate the cross section for DVCS and compare it with the accompanying Bethe-Heitler process at CEBAF and HERMES kinematics.Comment: 20 pages, 2 figures, replaced with the version to appear in Phys. Rev.

Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.

Optimization by thermal cycling

Thermal cycling is an heuristic optimization algorithm which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively, where the amplitude slowly decreases. In recent years, it has been successfully applied to two combinatorial optimization tasks, the traveling salesman problem and the search for low-energy states of the Coulomb glass. In these cases, the algorithm is far more efficient than usual simulated annealing. In its original form the algorithm was designed only for the case of discrete variables. Its basic ideas are applicable also to a problem with continuous variables, the search for low-energy states of Lennard-Jones clusters.Comment: Submitted to Proceedings of the Workshop "Complexity, Metastability and Nonextensivity", held in Erice 20-26 July 2004. Latex, 7 pages, 3 figure

Off-forward parton distributions and Shuvaev's transformations

We review Shuvaev's transformations, that relate off-forward parton distributions (OFPDs) to so-called effective forward parton distributions (EFPDs). The latter evolve like conventional forward partons. We express nonforward amplitudes, depending on OFPDs, directly in terms of EFPDs and construct a model for the EFPDs, which allows to consistently express them in terms of the conventional forward parton distributions and nucleon form factors. Our model is self-consistent for arbitrary x, xi, mu, and t.Comment: 13 pages, 7 eps-figures, LaTeX2e, added references, corrected typo

DVCS amplitude at tree level: Transversality, twist-3, and factorization

We study the virtual Compton amplitude in the generalized Bjorken region (q^2 -> Infinity, t small) in QCD by means of a light-cone expansion of the product of e.m. currents in string operators in coordinate space. Electromagnetic gauge invariance (transversality) is maintained by including in addition to the twist-2 operators 'kinematical' twist-3 operators which appear as total derivatives of twist-2 operators. The non-forward matrix elements of the elementary twist-2 operators are parametrized in terms of two-variable spectral functions (double distributions), from which twist-2 and 3 skewed distributions are obtained through reduction formulas. Our approach is equivalent to a Wandzura-Wilczek type approximation for the twist-3 skewed distributions. The resulting Compton amplitude is manifestly transverse up to terms of order t/q^2. We find that in this approximation the tensor amplitude for longitudinal polarization of the virtual photon is finite, while the one for transverse polarization contains a divergence already at tree level. However, this divergence has zero projection on the polarization vector of the final photon, so that the physical helicity amplitudes are finite.Comment: 34 pages, revtex, 1 eps figure included using epsf. Misprints corrected, one reference adde

Light Cone Sum Rules for gamma* N -> Delta Transition Form Factors

A theoretical framework is suggested for the calculation of gamma* N -> Delta transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ``soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ``minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentumComment: 38 pages, 10 figures; some typos fixed and references added, to appear in Phys. Rev.

Hard Leptoproduction of Charged Vector Mesons

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of charged vector mesons. These processes are determined by nonforward parton distribution functions which are nondiagonal in quark flavor. We derive relations between flavor diagonal and nondiagonal distribution functions based on isospin symmetry. Furthermore, we discuss general features of rho^+ and rho^- production cross sections, and present estimates based on a simple model for nonforward distribution functions.Comment: 8 pages, Late

Hard exclusive processes and higher-order QCD corrections

The short review of the higher order corrections to the hard exclusive processes is given. Different approaches are discussed and the importance of higher-order calculations is stressed.Comment: 17 pages; talk given at the 9th Adriatic Meeting, Dubrovnik 200