Entanglement in the quantum Ising model

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based on a property of the latter model termed ratio weak-mixing. Our proof applies equally to a large class of disordered interactions

Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves

We study the nonlinear energy transfer around the peak of the spectrum of surface gravity waves by taking into account nonhomogeneous effects. In the narrow-banded approximation the kinetic equation resulting from a nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at the same time the random version of the Benjamin-Feir instability and the Landau damping phenomenon. We analytically derive the values of the Phillips' constant $\alpha$ and the enhancement factor $\gamma$ for which the narrow-banded approximation of the JONSWAP spectrum is unstable. By performing numerical simulations of the nonlinear Schr\"{o}dinger equation we check the validity of the prediction of the related kinetic equation. We find that the effect of Landau damping is to suppress the formation of coherent structures. The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure

Energy Loss versus Shadowing in the Drell-Yan Reaction on Nuclei

We present a new analysis of the E772 and E866 experiments on the nuclear dependence of Drell-Yan (DY) lepton pair production resulting from the bombardment of $^2H$, Be, C, Ca, Fe, and W targets by 800 GeV/c protons at Fermilab. We employ a light-cone formulation of the DY reaction in the rest frame of the nucleus, where the dimuons detected at small values of Bjorken x_2 << 1 may be considered to originate from the decay of a heavy photon radiated from an incident quark in a bremsstrahlung process. We infer the energy loss of the quark by examining the suppression of the nuclear-dependent DY ratios seen as a function of projectile momentum fraction x_1 and dimuon mass M. Shadowing, which also leads to nuclear suppression of dimuons, is calculated within the same approach employing the results of phenomenological fits to deep inelastic scattering data from HERA. The analysis yields -dE/dz =2.73 +/- 0.37 +/- 0.5 GeV/fm for the rate of quark energy loss per unit path length, a value consistent with theoretical expectations including the effects of the inelastic interaction of the incident proton at the surface of the nucleus. This is the first observation of a nonzero energy loss effect in such experiments.Comment: 43 pages including 17 figure

Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj

Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.

Many body physics from a quantum information perspective

The quantum information approach to many body physics has been very successful in giving new insight and novel numerical methods. In these lecture notes we take a vertical view of the subject, starting from general concepts and at each step delving into applications or consequences of a particular topic. We first review some general quantum information concepts like entanglement and entanglement measures, which leads us to entanglement area laws. We then continue with one of the most famous examples of area-law abiding states: matrix product states, and tensor product states in general. Of these, we choose one example (classical superposition states) to introduce recent developments on a novel quantum many body approach: quantum kinetic Ising models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of correlated electron systems". Improved version new references adde