Resonance Broadening and Heating of Charged Particles in Magnetohydrodynamic Turbulence

The heating, acceleration, and pitch-angle scattering of charged particles by MHD turbulence are important in a wide range of astrophysical environments, including the solar wind, accreting black holes, and galaxy clusters. We simulate the interaction of high-gyrofrequency test particles with fully dynamical simulations of subsonic MHD turbulence, focusing on the parameter regime with beta ~ 1, where beta is the ratio of gas to magnetic pressure. We use the simulation results to calibrate analytical expressions for test particle velocity-space diffusion coefficients and provide simple fits that can be used in other work. The test particle velocity diffusion in our simulations is due to a combination of two processes: interactions between particles and magnetic compressions in the turbulence (as in linear transit-time damping; TTD) and what we refer to as Fermi Type-B (FTB) interactions, in which charged particles moving on field lines may be thought of as beads spiralling around moving wires. We show that test particle heating rates are consistent with a TTD resonance which is broadened according to a decorrelation prescription that is Gaussian in time. TTD dominates the heating for v_s >> v_A (e.g. electrons), where v_s is the thermal speed of species s and v_A is the Alfven speed, while FTB dominates for v_s << v_A (e.g. minor ions). Proton heating rates for beta ~ 1 are comparable to the turbulent cascade rate. Finally, we show that velocity diffusion of collisionless, large gyrofrequency particles due to large-scale MHD turbulence does not produce a power-law distribution function.Comment: 20 pages, 15 figures; accepted by The Astrophysical Journal; added clarifying appendices, but no major changes to result

Precision Spectroscopy of AdS/CFT

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weights of the corresponding non-near-BPS operators in planar N=4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the `t Hooft coupling lambda. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in lambda. This one-loop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly non-trivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.Comment: 26 pages, 1 figure, v2: typos correcte

Generalization of the model of Hawking radiation with modified high frequency dispersion relation

The Hawking radiation is one of the most interesting phenomena predicted by the theory of quantum field in curved space. The origin of Hawking radiation is closely related to the fact that a particle which marginally escapes from collapsing into a black hole is observed at the future infinity with infinitely large redshift. In other words, such a particle had a very high frequency when it was near the event horizon. Motivated by the possibility that the property of Hawking radiation may be altered by some unknowned physics which may exist beyond some critical scale, Unruh proposed a model which has higher order spatial derivative terms. In his model, the effects of unknown physics are modeled so as to be suppressed for the waves with a wavelength much longer than the critical scale, $k_0^{-1}$. Surprisingly, it was shown that the thermal spectrum is recovered for such modified models. To introduce such higher order spatial derivative terms, the Lorentz invariance must be violated because one special spatial direction needs to be chosen. In previous works, the rest frame of freely-falling observers was employed as this special reference frame. Here we give an extension by allowing a more general choice of the reference frame. Developing the method taken by Corley, % and especially focusing on subluminal case, we show that the resulting spectrum of created particles again becomes the thermal one at the Hawking temperature even if the choice of the reference frame is generalized. Using the technique of the matched asymptotic expansion, we also show that the correction to the thermal radiation stays of order $k_0^{-2}$ or smaller when the spectrum of radiated particle around its peak is concerned.Comment: 23 pages, 5 postscript figures, submitted to Physical Review

Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime

Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein-Podolsky-Rosen-states (EPR-states). FC gives rise to technologies enabling efficient atom-photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered.Comment: 26 pages, 4 figure

Real-time gauge/gravity duality: Prescription, Renormalization and Examples

We present a comprehensive analysis of the prescription we recently put forward for the computation of real-time correlation functions using gauge/gravity duality. The prescription is valid for any holographic supergravity background and it naturally maps initial and final data in the bulk to initial and final states or density matrices in the field theory. We show in detail how the technique of holographic renormalization can be applied in this setting and we provide numerous illustrative examples, including the computation of time-ordered, Wightman and retarded 2-point functions in Poincare and global coordinates, thermal correlators and higher-point functions.Comment: 85 pages, 13 figures; v2: added comments and reference

Valley Views: Instantons, Large Order Behaviors, and Supersymmetry

The elucidation of the properties of the instantons in the topologically trivial sector has been a long-standing puzzle. Here we claim that the properties can be summarized in terms of the geometrical structure in the configuration space, the valley. The evidence for this claim is presented in various ways. The conventional perturbation theory and the non-perturbative calculation are unified, and the ambiguity of the Borel transform of the perturbation series is removed. A `proof' of Bogomolny's ``trick'' is presented, which enables us to go beyond the dilute-gas approximation. The prediction of the large order behavior of the perturbation theory is confirmed by explicit calculations, in some cases to the 478-th order. A new type of supersymmetry is found as a by-product, and our result is shown to be consistent with the non-renormalization theorem. The prediction of the energy levels is confirmed with numerical solutions of the Schr\"{o}dinger equation.Comment: 78 pages, Latex, 22 eps figure

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.Comment: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal versio

Scaling and superscaling solutions from the functional renormalization group

We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed points of the renormalization group flow of these models, which emerge as scaling solutions. In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory, while in three dimension they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart. We also study the analytically continued flow in fractal dimensions between 2 and 4 and determine the critical dimensions for which irrelevant operators become relevant and change the universality class of the scaling solution. We also include novel analytic and numerical investigations of the properties that determine the occurrence of the scaling solutions within the method. For each solution we offer new techniques to compute the spectrum of the deformations and obtain the corresponding critical exponents.Comment: 23 pages, 14 figures; v2: several improvements, new references, version to appear in PR