Transverse beam tails due to inelastic scattering

Non-Gaussian beam tails producing low beam lifetimes and background to the experimental detectors can be a serious performance limitation in colliding beam facilities. We describe simulations and measurement of non-Gaussian beam tails, performed on the e+ e- collider LEP, that revealed the importance of inelastic particule scattering as launching processes of particules to large amplitude

Observations and simulations of beam tails in LEP

Transverse beam tails have been measured in LEP using scraping collimators and loss monitors. Very significant non-Gaussian tails are present for colliding beams and high beam-beam tune shift. On a lower but still significant level, non-Gaussian tails are also present in the horizontal plane for a single beam. Comparison of measurements with detailed simulations allowed us to identify off-momentum particles produced by scattering processes as a source of significant transverse tails

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law

This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact results in systems with sizes well beyond the reach of exact diagonalisation techniques. We describe an algorithm to approximate the ground state of a local Hamiltonian on a L times L lattice with the topology of a torus. Accurate results are obtained for L={4,6,8}, whereas approximate results are obtained for larger lattices. As an application of the approach, we analyse the scaling of the ground state entanglement entropy at the quantum critical point of the model. We confirm the presence of a positive additive constant to the area law for half a torus. We also find a logarithmic additive correction to the entropic area law for a square block. The single copy entanglement for half a torus reveals similar corrections to the area law with a further term proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly improved numerical results for the scaling of the entropies and several new sections. The manuscript has now 19 pages and 30 Figure

Beam Tails in LEP

Beam tails have been measured in LEP using scraping collimators and loss monistors for separated and colliding beams. Significant non-Gaussian beam tails have been observed with colliding beams for high beam-beam tune shift parameters and bunch currents

Larkin-Ovchinnikov state in resonant Fermi gas

We construct the phase diagram of a homogeneous two component Fermi gas with population imbalance under a Feshbach resonance. In particular, we study the physics and stability of the Larkin-Ovchinnikov phase. We show that this phase is stable over a much larger parameter range than what has been previously reported by other authors.Comment: Typos correcte

Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance

Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field theoretical methods, we investigate the Casimir interaction between two spherical particles and between a single particle and a planar boundary of the fluid. We exploit the conformal symmetry at the critical point to map both cases onto a highly symmetric geometry where the fluid is bounded by two concentric spheres with radii R_- and R_+. In this geometry the singular part of the free energy F only depends upon the ratio R_-/R_+, and the stress tensor, which we use to calculate F, has a particularly simple form. Different boundary conditions (surface universality classes) are considered, which either break or preserve the order-parameter symmetry. We also consider profiles of thermodynamic densities in the presence of two spheres. Explicit results are presented for an ordinary critical point to leading order in epsilon=4-d and, in the case of preserved symmetry, for the Gaussian model in arbitrary spatial dimension d. Fundamental short-distance properties, such as profile behavior near a surface or the behavior if a sphere has a `small' radius, are discussed and verified. The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B 51, 13717 (1995

Theory of 2D superconductor with broken inversion symmetry

A detailed theory of a phase diagram of a 2D surface superconductor in a parallel magnetic field is presented. A spin-orbital interaction of the Rashba type is known to produce at a high magnetic field $h$ (and in the absence of impurities) an inhomogeneous superconductive phase similar to the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state with an order parameter $\Delta(r) \propto \cos(Qr)$. We consider the case of a strong Rashba interaction with the spin-orbital splitting much larger than the superconductive gap $\Delta$, and show that at low temperatures $T\leq 0.4 T_{c0}$ the LOFF-type state is separated from the usual homogeneous state by a first-order phase transition line. At higher temperatures another inhomogeneous state with $\Delta(r) \propto \exp(i Qr)$ intervenes between the uniform BCS state and the LOFF-like state at $g\mu_B h \approx 1.5 T_{c0}$. The modulation vector $Q$ in both phases is of the order of $g\mu_B h/v_F$. The superfluid density $n_s^{yy}$ vanishes in the region around the second-order transition line between the BCS state and the new ``helical'' state. Non-magnetic impurities suppress both inhomogeneous states, and eliminate them completely at $T_{c0}\tau \leq 0.11$. However, once an account is made of the next-order term over the small parameter $\alpha/v_F \ll 1$, a relatively long-wave helical modulation with $Q \sim g\mu_B h\alpha/v_F^2$ is found to develop from the BCS state. This long-wave modulation is stable with respect to disorder. In addition, we predict that unusual vortex defects with a continuous core exist near the phase boundary between the helical and the LOFF-like states. In particular, in the LOFF-like state these defects may carry a half-integer flux.Comment: 23 pages, 14 figure

Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

Theory of quasi-one dimensional imbalanced Fermi gases

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D `tubes') with spin imbalance, where strong intratube quantum fluctuations invalidate mean field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against inter-tube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.Comment: new expanded version, 8 pages, updated reference

Halo Estimates and Simulations for Linear Colliders

Halo simulations and estimates are important for the design of future linear accelerators. We describe the main processes with analytic estimates and present our generic simulations in application to the ILC