437 research outputs found
Quantum Fields on Star Graphs with Bound States at the Vertex
We investigate the propagation of a massless scalar field on a star graph,
modeling the junction of quantum wires. The vertex of the graph is
represented by a point-like impurity (defect), characterized by a one-body
scattering matrix. The general case of off-critical scattering matrix with
bound and/or antibound states is considered. We demonstrate that the
contribution of these states to the scalar field is fixed by causality (local
commutativity), which is the key point of our investigation. Two different
regimes of the theory emerge at this stage. If bound sates are absent, the
energy is conserved and the theory admits unitary time evolution. The behavior
changes if bound states are present, because each such state generates a kind
of damped harmonic oscillator in the spectrum of the field. These oscillators
lead to the breakdown of time translation invariance. We study in both regimes
the electromagnetic conductance of the Luttinger liquid on the quantum wire
junction. We derive an explicit expression for the conductance in terms of the
scattering matrix and show that antibound and bound states have a different
impact, giving raise to oscillations with exponentially damped and growing
amplitudes respectively.Comment: LaTex 1+29 pages, 2 figures: Expanded version with new title and
abstract; clarifying comments, fig.2 and references added; final version to
appear in J. Math. Phy
From quantum to elliptic algebras
It is shown that the elliptic algebra at the
critical level c=-2 has a multidimensional center containing some trace-like
operators t(z). A family of Poisson structures indexed by a non-negative
integer and containing the q-deformed Virasoro algebra is constructed on this
center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m
integer, they commute when in addition p=q^{2k} for k integer non-zero, and
they belong to the center of when k is odd. The
Poisson structures obtained for t(z) in these classical limits contain the
q-deformed Virasoro algebra, characterizing the structures at generic values of
p, q and m as new algebras.Comment: LaTeX2e Document - packages subeqn,amsfont
Central extensions of classical and quantum q-Viraroso algebras
We investigate the central extensions of the q-deformed (classical and
quantum) Virasoro algebras constructed from the elliptic quantum algebra
A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions,
we solve them, both in the classical and in the quantum case (for sl(2)). We
find that the consistent central extensions are much more general that those
found previously in the literature.Comment: Latex2e, needs amsfonts and amssymb package
Deformed W_N algebras from elliptic sl(N) algebras
We extend to the sl(N) case the results that we previously obtained on the
construction of W_{q,p} algebras from the elliptic algebra
A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the
critical level c=-N has an extended center containing trace-like operators
t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining
q-deformations of the W_N algebra, are constructed. The operators t(z) also
close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes
Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson
structures obtained in these classical limits contain different q-deformed W_N
algebras depending on the parity of h, characterizing the exchange structures
at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page
Universal construction of W_{p,q} algebras
We present a direct construction of abstract generators for q-deformed W_N
algebras. This procedure hinges upon a twisted trace formula for the elliptic
algebra A_{q,p}(sl(N)_c) generalizing the previously known formulae for quantum
groups.Comment: packages amsfonts, amssym
Persistent oscillations after quantum quenches in d dimensions
We obtain analytical results for the time evolution of local observables in systems undergoing quantum quenches in d spatial dimensions. For homogeneous systems we show that oscillations undamped in time occur when the state produced by the quench includes single-quasiparticle modes and the observable couples to those modes. In particular, a quench of the transverse field within the ferromagnetic phase of the Ising model produces undamped oscillations of the order parameter when d>1. For the more general case in which the quench is performed only in a subregion of the whole d-dimensional space occupied by the system, the time evolution occurs inside a light cone spreading away from the boundary of the quenched region as time increases. The additional condition for undamped oscillations is that the volume of the quenched region is extensive in all dimensions
How Future Space-Based Weak Lensing Surveys Might Obtain Photometric Redshifts Independently
We study how the addition of on-board optical photometric bands to future
space-based weak lensing instruments could affect the photometric redshift
estimation of galaxies, and hence improve estimations of the dark energy
parameters through weak lensing. Basing our study on the current proposed
Euclid configuration and using a mock catalog of galaxy observations, various
on-board options are tested and compared with the use of ground-based
observations from the Large Synoptic Survey Telescope (LSST) and Pan-STARRS.
Comparisons are made through the use of the dark energy Figure of Merit, which
provides a quantifiable measure of the change in the quality of the scientific
results that can be obtained in each scenario. Effects of systematic offsets
between LSST and Euclid photometric calibration are also studied. We find that
adding two (U and G) or even one (U) on-board optical band-passes to the
space-based infrared instrument greatly improves its photometric redshift
performance, bringing it close to the level that would be achieved by combining
observations from both space-based and ground-based surveys while freeing the
space mission from reliance on external datasets.Comment: Accepted for publication in PASP. A high-quality version of Fig 1 can
be found on http://www.ap.smu.ca/~sawicki/DEphoto
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