Interacting quantum walkers: Two-body bosonic and fermionic bound states

We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles has a hard bound, and the richer situation where the particles are bound by a smooth confining potential. The main emphasis is on the velocity characterizing the ballistic spreading of these bound states, and on the structure of the asymptotic distribution profile of their center-of-mass coordinate. The latter profile generically exhibits many internal fronts.Comment: 31 pages, 14 figure

Survival of classical and quantum particles in the presence of traps

We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative differences in the temporal behavior of the survival probabilities of both kinds of particles. As a general rule, static traps are far less efficient to absorb quantum particles than classical ones. Several lattice geometries are successively considered: an infinite chain with a single trap, a finite ring with a single trap, a finite ring with several traps, and an infinite chain and a higher-dimensional lattice with a random distribution of traps with a given density. For the latter disordered systems, the classical and the quantum survival probabilities obey a stretched exponential asymptotic decay, albeit with different exponents. These results confirm earlier predictions, and the corresponding amplitudes are evaluated. In the one-dimensional geometry of the infinite chain, we obtain a full analytical prediction for the amplitude of the quantum problem, including its dependence on the trap density and strength.Comment: 35 pages, 10 figures, 2 tables. Minor update

Return probability of NN fermions released from a 1D confining potential

We consider $N$ non-interacting fermions prepared in the ground state of a 1D confining potential and submitted to an instantaneous quench consisting in releasing the trapping potential. We show that the quantum return probability of finding the fermions in their initial state at a later time falls off as a power law in the long-time regime, with a universal exponent depending only on $N$ and on whether the free fermions expand over the full line or over a half-line. In both geometries the amplitudes of this power-law decay are expressed in terms of finite determinants of moments of the one-body bound-state wavefunctions in the potential. These amplitudes are worked out explicitly for the harmonic and square-well potentials. At large fermion numbers they obey scaling laws involving the Fermi energy of the initial state. The use of the Selberg-Mehta integrals stemming from random matrix theory has been instrumental in the derivation of these results.Comment: 24 pages, 1 tabl

Accretion disc-corona and jet emission from the radio-loud narrow-line Seyfert 1 galaxy RX J1633.3+4719

We perform X-ray/ultraviolet (UV) spectral and X-ray variability studies of the radio-loud narrow-line Seyfert 1 (NLS1) galaxy RX J1633.3+4719 using XMM-Newton and Suzaku observations from 2011 and 2012. The 0.3-10 keV spectra consist of an ultrasoft component described by an accretion disc blackbody (kT_in = 39.6^{+11.2}_{-5.5} eV) and a power law due to the thermal Comptonization ({\Gamma} = 1.96^{+0.24}_{-0.31}) of the disc emission. The disc temperature inferred from the soft excess is at least a factor of 2 lower than that found for the canonical soft excess emission from radio-quiet NLS1s. The UV spectrum is described by a power law with photon index 3.05^{+0.56}_{-0.33}. The observed UV emission is too strong to arise from the accretion disc or the host galaxy, but can be attributed to a jet. The X-ray emission from RX J1633.3+4719 is variable with fractional variability amplitude $F_{\rm var}$=13.5$\pm1.0$ per cent. In contrast to radio-quiet active galactic nuclei (AGN), X-ray emission from the source becomes harder with increasing flux. The fractional rms variability increases with energy and the rms spectrum is well described by a constant disc component and a variable power-law continuum with the normalization and photon index being anticorrelated. Such spectral variability cannot be caused by variations in the absorption and must be intrinsic to the hot corona. Our finding of possible evidence for emission from the inner accretion disc, jet and hot corona from RX J1633.3+4719 in the optical to X-ray bands makes this object an ideal target to probe the disc-jet connection in AGN.Comment: 12 pages, 11 figures, 3 tables, Published in MNRA

A multi-wavelength study of star formation activity in the S235 complex

We have carried out an extensive multi-wavelength study to investigate the star formation process in the S235 complex. The S235 complex has a sphere-like shell appearance at wavelengths longer than 2 $\mu$m and harbors an O9.5V type star approximately at its center. Near-infrared extinction map traces eight subregions (having A$_{V}$ $>$ 8 mag), and five of them appear to be distributed in an almost regularly spaced manner along the sphere-like shell surrounding the ionized emission. This picture is also supported by the integrated $^{12}$CO and $^{13}$CO intensity maps and by Bolocam 1.1 mm continuum emission. The position-velocity analysis of CO reveals an almost semi-ring like structure, suggesting an expanding H\,{\sc ii} region. We find that the Bolocam clump masses increase as we move away from the location of the ionizing star. This correlation is seen only for those clumps which are distributed near the edges of the shell. Photometric analysis reveals 435 young stellar objects (YSOs), 59\% of which are found in clusters. Six subregions (including five located near the edges of the shell) are very well correlated with the dust clumps, CO gas, and YSOs. The average values of Mach numbers derived using NH$_{3}$ data for three (East~1, East~2, and Central~E) out of these six subregions are 2.9, 2.3, and 2.9, indicating these subregions are supersonic. The molecular outflows are detected in these three subregions, further confirming the on-going star formation activity. Together, all these results are interpreted as observational evidence of positive feedback of a massive star.Comment: 28 pages, 15 figures, 3 tables, Accepted for publication in The Astrophysical Journa

Partially Asymmetric Simple Exclusion Model in the Presence of an Impurity on a Ring

We study a generalized two-species model on a ring. The original model [1] describes ordinary particles hopping exclusively in one direction in the presence of an impurity. The impurity hops with a rate different from that of ordinary particles and can be overtaken by them. Here we let the ordinary particles hop also backward with the rate q. Using Matrix Product Ansatz (MPA), we obtain the relevant quadratic algebra. A finite dimensional representation of this algebra enables us to compute the stationary bulk density of the ordinary particles, as well as the speed of impurity on a set of special surfaces of the parameter space. We will obtain the phase structure of this model in the accessible region and show how the phase structure of the original model is modified. In the infinite-volume limit this model presents a shock in one of its phases.Comment: Adding more references and doing minor corrections, 16 pages and 3 Eps figure

Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field

We consider a spin half particle in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction. We find that the energy eigenvalues for this system are real even though the interaction is not PT invariant.Comment: Latex, no figs, 8 pages. (To appear in Mod. Phys. Lett. A