Analyzing flow anisotropies with excursion sets in relativistic heavy-ion collisions

We show that flow anisotropies in relativistic heavy-ion collisions can be analyzed using a certain technique of shape analysis of excursion sets recently proposed by us for CMBR fluctuations to investigate anisotropic expansion history of the universe. The technique analyzes shapes (sizes) of patches above (below) certain threshold value for transverse energy/particle number (the excursion sets) as a function of the azimuthal angle and rapidity. Modeling flow by imparting extra anisotropic momentum to the momentum distribution of particles from HIJING, we compare the resulting distributions for excursion sets at two different azimuthal angles. Angles with maximum difference in the two distributions identify the event plane, and the magnitude of difference in the two distributions relates to the magnitude of momentum anisotropy, i.e. elliptic flow.Comment: 5 pages, 4 figure

Signal Recovery in Perturbed Fourier Compressed Sensing

In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of measurements. However due to system calibration errors, the system may measure the Fourier transform at frequencies $\{u_i + \delta_i\}_{i=1}^M$ that are different from the base frequencies and where $\{\delta_i\}_{i=1}^M$ are unknown. Ignoring perturbations of this nature can lead to major errors in signal recovery. In this paper, we present a simple but effective alternating minimization algorithm to recover the perturbations in the frequencies \emph{in situ} with the signal, which we assume is sparse or compressible in some known basis. In many cases, the perturbations $\{\delta_i\}_{i=1}^M$ can be expressed in terms of a small number of unique parameters $P \ll M$. We demonstrate that in such cases, the method leads to excellent quality results that are several times better than baseline algorithms (which are based on existing off-grid methods in the recent literature on direction of arrival (DOA) estimation, modified to suit the computational problem in this paper). Our results are also robust to noise in the measurement values. We also provide theoretical results for (1) the convergence of our algorithm, and (2) the uniqueness of its solution under some restrictions.Comment: New theortical results about uniqueness and convergence now included. More challenging experiments now include

Strings with a confining core in a Quark-Gluon Plasma

We consider the intersection of N different interfaces interpolating between different $Z_N$ vacua of an SU(N) gauge theory using the Polyakov loop order parameter. Topological arguments show that at such a string-like junction, the order parameter should vanish, implying that the core of this string (i.e. the junction region of all the interfaces) is in the confining phase. Using the effective potential for the Polyakov loop proposed by Pisarski for QCD, we use numerical minimization technique and estimate the energy per unit length of the core of this string to be about 2.7 GeV/fm at a temperature about twice the critical temperature. For the parameters used, the interface tension is obtained to be about 7 GeV/fm$^2$. Lattice simulation of pure gauge theories should be able to investigate properties of these strings. For QCD with quarks, it has been discussed in the literature that this $Z_N$ symmetry may still be meaningful, with quark contributions leading to explicit breaking of this $Z_N$ symmetry. With this interpretation, such {\it QGP} strings may play important role in the evolution of the quark-gluon plasma phase and in the dynamics of quark-hadron transition.Comment: 18 pages, 6 figures, RevTe

Current-induced gap opening in interacting topological insulator surfaces

Two-dimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized two-terminal conductance. Quantization is protected by time-reversal symmetry, which forbids elastic backscattering. Paradoxically, the current-carrying state itself breaks the time-reversal symmetry that protects it. Here we show that the combination of electron-electron interactions and momentum-dependent spin polarization in helical edge states gives rise to feedback through which an applied current opens a gap in the edge state dispersion, thereby breaking the protection against elastic backscattering. Current-induced gap opening is manifested via a nonlinear contribution to the system's $I-V$ characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous current-induced gap opening mechanism for the surface states of three-dimensional TIs.Comment: 6 pages, 2 figures, published versio