Finite-Size Effects in the ϕ4\phi^{4} Field Theory Above the Upper Critical Dimension

We demonstrate that the standard O(n) symmetric $\phi^{4}$ field theory does not correctly describe the leading finite-size effects near the critical point of spin systems on a $d$-dimensional lattice with $d > 4$. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For $n \to \infty$ and $n=1$ explicit results are given for the susceptibility and for the Binder cumulant. They imply that recent analyses of Monte-Carlo results for the five-dimensional Ising model are not conclusive.Comment: 4 pages, latex, 1 figur

High Energy Photon-Photon Collisions at a Linear Collider

High intensity back-scattered laser beams will allow the efficient conversion of a substantial fraction of the incident lepton energy into high energy photons, thus significantly extending the physics capabilities of an electron-electron or electron-positron linear collider. The annihilation of two photons produces C=+ final states in virtually all angular momentum states. The annihilation of polarized photons into the Higgs boson determines its fundamental two-photon coupling as well as determining its parity. Other novel two-photon processes include the two-photon production of charged lepton pairs, vector boson pairs, as well as supersymmetric squark and slepton pairs and Higgstrahlung. The one-loop box diagram leads to the production of pairs of neutral particles. High energy photon-photon collisions can also provide a remarkably background-free laboratory for studying possibly anomalous $W W$ collisions and annihilation. In the case of QCD, each photon can materialize as a quark anti-quark pair which interact via multiple gluon exchange. The diffractive channels in photon-photon collisions allow a novel look at the QCD pomeron and odderon. Odderon exchange can be identified by looking at the heavy quark asymmetry. In the case of electron-photon collisions, one can measure the photon structure functions and its various components. Exclusive hadron production processes in photon-photon collisions test QCD at the amplitude level and measure the hadron distribution amplitudes which control exclusive semi-leptonic and two-body hadronic B-decays.Comment: Invited talk, presented at the 5th International Workshop On Electron-Electron Interactions At TeV Energies, Santa Cruz, California, 12-14 December 200

Beam energy measurement at linear colliders using spin precession

Linear collider designs foresee some bends of about 5-10 mrad. The spin precession angle of one TeV electrons on 10 mrad bend is 23.2 rad and it changes proportional to the energy. Measurement of the spin direction using Compton scattering of laser light on electrons before and after the bend allows determining the beam energy with an accuracy about of 10^{-5}. In this paper the principle of the method, the procedure of the measurement and possible errors are discussed. Some remarks about importance of plasma focusing effects in the method of beam energy measurement using Moller scattering are given.Comment: 7 pages, Latex, 4 figures(.eps). In v.3 corresponds to journal publication. Talk at 26-th Advanced ICFA Beam Dynamic Workshop on Nanometre-Size Colliding Beams (Nanobeam2002), Lausanne, Switzerland, Sept 2-6, 200

On the origin of cosmic rays

Uniform and metagalactic cosmic ray models - halo, disk, and nonstationary galactic model

Detecting photon-photon scattering in vacuum at exawatt lasers

In a recent paper, we have shown that the QED nonlinear corrections imply a phase correction to the linear evolution of crossing electromagnetic waves in vacuum. Here, we provide a more complete analysis, including a full numerical solution of the QED nonlinear wave equations for short-distance propagation in a symmetric configuration. The excellent agreement of such a solution with the result that we obtain using our perturbatively-motivated Variational Approach is then used to justify an analytical approximation that can be applied in a more general case. This allows us to find the most promising configuration for the search of photon-photon scattering in optics experiments. In particular, we show that our previous requirement of phase coherence between the two crossing beams can be released. We then propose a very simple experiment that can be performed at future exawatt laser facilities, such as ELI, by bombarding a low power laser beam with the exawatt bump.Comment: 8 pages, 6 figure

Two-dimensional nonstationary model of the propagation of an electron beam in a vacuum

A two dimensional nonstationary model of the propagation of a relativistic electron beam injected into a vacuum is considered. Collision effects are ignored and there are no external fields. Two types of the electron current propagation are shown from the computer simulation of the Maxwell-Vlasov equations

Adiabatic Faraday effect in a two-level Hamiltonian formalism

The helicity of a photon traversing a magnetized plasma can flip when the B-field along the trajectory slowly reverses. Broderick and Blandford have recently shown that this intriguing effect can profoundly change the usual Faraday effect for radio waves. We study this phenomenon in a formalism analogous to neutrino flavor oscillations: the evolution is governed by a Schroedinger equation for a two-level system consisting of the two photon helicities. Our treatment allows for a transparent physical understanding of this system and its dynamics. In particular, it allows us to investigate the nature of transitions at intermediate adiabaticities.Comment: 8 pages, 2 eps figures, and a note added. Title changed. Matches published versio

Soliton states in mesoscopic two-band-superconducting cylinders

In the framework of the Ginzburg-Landau approach, we present a self-consistent theory of specific soliton states in mesoscopic (thin-walled) two-band-superconducting cylinders in external parallel magnetic fields. Such states arise in the presence of "Josephson-type" interband coupling, when phase winding numbers are different for each component of the superconducting order parameter. We evaluate the Gibbs free energy of the sysyem up to second-order terms in a certain dimensionless parameter $\epsilon\approx\frac{\mathcal{L}_{m}}{\mathcal{L}_{k}}\ll1$, where $\mathcal{L}_{m}$ and $\mathcal{L}_{k}$ are the magnetic and kinetic inductance, respectively. We derive the complete set of exact soliton solutions. These solutions are thoroughly analyzed from the viewpoint of both local and global (thermodynamic) stability. In particular, we show that rotational-symmetry-breaking caused by the formation of solitons gives rise to a zero-frequency rotational mode. Although soliton states prove to be thermodynamically metastable, the minimal energy gap between the lowest-lying single-soliton states and thermodynamically stable zero-soliton states can be much smaller than the magnetic Gibbs free energy of the latter states, provided that intraband "penetration depths" differ substantially and interband coupling is weak. The results of our investigation may apply to a wide class of mesoscopic doubly-connected structures exhibiting two-band superconductivity.Comment: 15 pages, 3 figure