4,936 research outputs found

### The Segal-Bargmann Transform on Classical Matrix Lie Groups

We study the complex-time Segal-Bargmann transform
$\mathbf{B}_{s,\tau}^{K_N}$ on a compact type Lie group $K_N$, where $K_N$ is
one of the following classical matrix Lie groups: the special orthogonal group
$\mathrm{SO}(N,\mathbb{R})$, the special unitary group $\mathrm{SU}(N)$, or the
compact symplectic group $\mathrm{Sp}(N)$. Our work complements and extends the
results of Driver, Hall, and Kemp on the Segal-Bargman transform for the
unitary group $\mathrm{U}(N)$. We provide an effective method of computing the
action of the Segal-Bargmann transform on \emph{trace polynomials}, which
comprise a subspace of smooth functions on $K_N$ extending the polynomial
functional calculus. Using these results, we show that as $N\to\infty$, the
finite-dimensional transform $\mathbf{B}_{s,\tau}^{K_N}$ has a meaningful limit
$\mathscr{G}_{s,\tau}^{(\beta)}$ (where $\beta$ is a parameter associated with
$\mathrm{SO}(N,\mathbb{R})$, $\mathrm{SU}(N)$, or $\mathrm{Sp}(N)$), which can
be identified as an operator on the space of complex Laurent polynomials

### Holographic Butterfly Effect and Diffusion in Quantum Critical Region

We investigate the butterfly effect and charge diffusion near the quantum
phase transition in holographic approach. We argue that their criticality is
controlled by the holographic scaling geometry with deformations induced by a
relevant operator at finite temperature. Specifically, in the quantum critical
region controlled by a single fixed point, the butterfly velocity decreases
when deviating from the critical point. While, in the non-critical region, the
behavior of the butterfly velocity depends on the specific phase at low
temperature. Moreover, in the holographic Berezinskii-Kosterlitz-Thouless
transition, the universal behavior of the butterfly velocity is absent.
Finally, the tendency of our holographic results matches with the numerical
results of Bose-Hubbard model. A comparison between our result and that in the
$O(N)$ nonlinear sigma model is also given.Comment: 41 pages, 7 figures, minor revisions, refs adde

### Holographic Shear Viscosity in Hyperscaling Violating Theories without Translational Invariance

In this paper we investigate the ratio of shear viscosity to entropy density,
$\eta/s$, in hyperscaling violating geometry with lattice structure. We show
that the scaling relation with hyperscaling violation gives a strong constraint
to the mass of graviton and usually leads to a power law of temperature,
$\eta/s\sim T^\kappa$. We find the exponent $\kappa$ can be greater than two
such that the new bound for viscosity raised in arXiv:1601.02757 is violated.
Our above observation is testified by constructing specific solutions with UV
completion in various holographic models. Finally, we compare the boundedness
of $\kappa$ with the behavior of entanglement entropy and conjecture a relation
between them.Comment: 38 pages, 8 figures: 1 appendix added, 2 figures added, 1 references
adde

### High-Energy Gamma-Rays from GRB X-ray Flares

The recent detection of X-ray flares during the afterglow phase of gamma-ray
bursts (GRBs) suggests an inner-engine origin, at radii inside the forward
shock. There must be inverse Compton (IC) emission arising from such flare
photons scattered by forward shock afterglow electrons when they are passing
through the forward shock. We find that this IC emission produces high energy
gamma-ray flares, which may be detected by AGILE, GLAST and ground-based TeV
telescopes. The anisotropic IC scattering between flare photons and forward
shock electrons does not affect the total IC component intensity, but cause a
time delay of the IC component peak relative to the flare peak. The anisotropic
scattering effect may also weaken, to some extent, the suppression effect of
the afterglow intensity induced by the enhanced electron cooling due to flare
photons. We speculate that this IC component may already have been detected by
EGRET from a very strong burst--GRB940217. Future observations by GLAST may
help to distinguish whether X-ray flares originate from late central engine
activity or from external shocks.Comment: 4 pages, Contributed talk presented at "The First GLAST Symposium",
Feb.5-8 2007, Stanford Universit

### On the magnetization of gamma-ray burst blast waves

The origin of magnetic fields that permeate the blast waves of gamma-ray
bursts (GRBs) is a long-standing problem. The present paper argues that in four
GRBs revealing extended emission at >100 MeV, with follow-up in the radio,
optical and X-ray domains at later times, this magnetization can be described
as the partial decay of the micro-turbulence that is generated in the shock
precursor. Assuming that the bulk of the extended emission >100 MeV can be
interpreted as synchrotron emission of shock accelerated electrons, we model
the multi-wavelength light curves of GRB 090902B, GRB 090323, GRB 090328 and
GRB 110731A, using a simplified then a full synchrotron calculation with
power-law-decaying microturbulence \epsilon_B \propto t^{\alpha_t} (t denotes
the time since injection through the shock, in the comoving blast frame). We
find that these models point to a consistent value of the decay exponent -0.5 <
\alpha_t < -0.4.Comment: 8 pages, 4 figures - discussion added, conclusions unchanged -
version to appear in MNRA

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