The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.Comment: 24 pages, 7 figures; v2: typos corrected, reference added, published in Eur. Phys. J.

Jet evolution from weak to strong coupling

Recent studies, using the AdS/CFT correspondence, of the radiation produced by a decaying system or by an accelerated charge in the N=4 supersymmetric Yang-Mills theory, led to a striking result: the 'supergravity backreaction', which is supposed to describe the energy density at infinitely strong coupling, yields exactly the same result as at zero coupling, that is, it shows no trace of quantum broadening. We argue that this is not a real property of the radiation at strong coupling, but an artifact of the backreaction calculation, which is unable to faithfully capture the space-time distribution of the radiation. This becomes obvious in the case of a decaying system ('virtual photon'), for which the backreaction is tantamount to computing a three-point function in the conformal gauge theory, which is independent of the coupling since protected by symmetries. Whereas this non-renormalization property is specific to the conformal N=4 SYM theory, we argue that the failure of the three-point function to provide a local measurement is in fact generic: it holds in any field theory with non-trivial interactions. To properly study a localized distribution, one should rather compute a four-point function, as standard in deep inelastic scattering. We substantiate these considerations with studies of the radiation produced by the decay of a time-like photon at both weak and strong coupling. We show that by computing four-point functions, in perturbation theory at weak coupling and, respectively, from Witten diagrams at strong coupling, one can follow the quantum evolution and thus demonstrate the broadening of the energy distribution. This broadening is slow when the coupling is weak but it proceeds as fast as possible in the limit of a strong coupling.Comment: 49 pages, 6 figure

Analytic pulse design for selective population transfer in many-level quantum systems: maximizing amplitude of population oscillations

State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum systems is presented.Comment: Published in Phys.Rev.A. This is the final published versio

Resumming large higher-order corrections in non-linear QCD evolution

Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by taking into account successive soft gluon emissions strongly ordered in lifetime. We further resum single logarithms generated by the first non-singular part of the splitting functions and by the one-loop running of the coupling. The resulting collinearly improved BK equation admits stable solutions, which are used to successfully fit the HERA data at small-x for physically acceptable initial conditions and reasonable values of the fit parameters.Comment: 4 pages, 4 figures, based on talk given at Hard Probes 2015, 29 June - 3 July 2015, Montreal, Canad

Resummation of Large Logarithms in the Rapidity Evolution of Color Dipoles

Perturbative corrections beyond leading-log accuracy to BFKL and BK equations, describing the rapidity evolution of QCD scattering amplitudes at high energy, exhibit strong convergence problems due to radiative corrections enhanced by large single and double transverse logs. We identify explicitly the physical origin of double transverse logs and resum them directly in coordinate space as appropriate for BK equation, in terms of an improved local-in-rapidity evolution kernel. Numerical results show the crucial role of double-logarithmic resummation for BK evolution, which is stabilized and slowed down by roughly a factor of two.Comment: 6 pages, 4 figures; Proceedings of the XXIII International Workshop on Deep-Inelastic Scattering (27 April-May 1 2015, Dallas (USA)

Comparison of quantum mechanical and classical trajectory calculations of cross sections for ion-atom impact ionization of negative - and positive -ions for heavy ion fusion applications

Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I$^{-}$ and Cs$^{+}$ ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential.Comment: submitted to Phys. Rev.