2,580 research outputs found
On sl(2)-equivariant quantizations
By computing certain cohomology of Vect(M) of smooth vector fields we prove
that on 1-dimensional manifolds M there is no quantization map intertwining the
action of non-projective embeddings of the Lie algebra sl(2) into the Lie
algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant
quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear
Mathematical Physic
Natural and projectively equivariant quantizations by means of Cartan Connections
The existence of a natural and projectively equivariant quantization in the
sense of Lecomte [20] was proved recently by M. Bordemann [4], using the
framework of Thomas-Whitehead connections. We give a new proof of existence
using the notion of Cartan projective connections and we obtain an explicit
formula in terms of these connections. Our method yields the existence of a
projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant
quantization exists in the flat situation in the sense of [18], thus solving
one of the problems left open by M. Bordemann.Comment: 13 page
Fluctuations and skewness of the current in the partially asymmetric exclusion process
We use functional Bethe Ansatz equations to calculate the cumulants of the
total current in the partially asymmetric exclusion process. We recover known
formulas for the first two cumulants (mean value of the current and diffusion
constant) and obtain an explicit finite size formula for the third cumulant.
The expression for the third cumulant takes a simple integral form in the limit
where the asymmetry scales as the inverse of the square root of the size of the
system, which corresponds to a natural separation between weak and strong
asymmetry.Comment: 21 pages, 3 figure
Thermodynamic formalism for systems with Markov dynamics
The thermodynamic formalism allows one to access the chaotic properties of
equilibrium and out-of-equilibrium systems, by deriving those from a dynamical
partition function. The definition that has been given for this partition
function within the framework of discrete time Markov chains was not suitable
for continuous time Markov dynamics. Here we propose another interpretation of
the definition that allows us to apply the thermodynamic formalism to
continuous time.
We also generalize the formalism --a dynamical Gibbs ensemble construction--
to a whole family of observables and their associated large deviation
functions. This allows us to make the connection between the thermodynamic
formalism and the observable involved in the much-studied fluctuation theorem.
We illustrate our approach on various physical systems: random walks,
exclusion processes, an Ising model and the contact process. In the latter
cases, we identify a signature of the occurrence of dynamical phase
transitions. We show that this signature can already be unravelled using the
simplest dynamical ensemble one could define, based on the number of
configuration changes a system has undergone over an asymptotically large time
window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of
Statistical Physic
Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories.Comment: 30 pages, 9 figures, typeset for pdflatex; revised versio
Resonance trapping and saturation of decay widths
Resonance trapping appears in open many-particle quantum systems at high
level density when the coupling to the continuum of decay channels reaches a
critical strength. Here a reorganization of the system takes place and a
separation of different time scales appears. We investigate it under the
influence of additional weakly coupled channels as well as by taking into
account the real part of the coupling term between system and continuum. We
observe a saturation of the mean width of the trapped states. Also the decay
rates saturate as a function of the coupling strength. The mechanism of the
saturation is studied in detail. In any case, the critical region of
reorganization is enlarged. When the transmission coefficients for the
different channels are different, the width distribution is broadened as
compared to a chi_K^2 distribution where K is the number of channels. Resonance
trapping takes place before the broad state overlaps regions beyond the
extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.
Correlation between structural studies and third order NLO properties of selected new quinolinium semi-organic compounds
New quinolinium semi-organic compounds of formula ( C 9 H 8 N ) 2 + · SO 4 2 - , H 2 O (I) (bis-quinolinium sulphate monohydrate) and ( C 9 H 8 N ) + · NO 3 - (II) (quinolinium nitrate) have been synthesized and characterized by UV–Vis absorption spectroscopy, nonlinear optical (NLO) measurements and by single crystal X-ray diffraction. The third order nonlinear optical properties of (I) and (II) were investigated using two methods: the degenerate four wave mixing technique (DFWM) performed in solution at λ = 532 nm and the third-harmonic generation (THG) measurements carried out on thin films at λ = 1064 nm. The NLO measurements showed that compound (I) presents better nonlinear optical properties compared to compound (II). To understand further the optical behaviour of (I) and (II), the crystal structures of both compounds were determined from accurate single crystal X-ray diffraction measurements performed at 100 K. The crystallographic studies revealed the key role of the intermolecular interactions and the molecular arrangements in the enhancement of the NLO properties
Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths
A phenomenological schematic model of multipole giant resonances (GR) is
considered which treats the external interaction via common decay channels on
the same footing as the coherent part of the internal residual interaction. The
damping due to the coupling to the sea of complicated states is neglected. As a
result, the formation of GR is governed by the interplay and competition of two
kinds of collectivity, the internal and the external one. The mixing of the
doorway components of a GR due to the external interaction influences
significantly their multipole strengths, widths and positions in energy. In
particular, a narrow resonance state with an appreciable multipole strength is
formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997
Comments on the topological open membrane
Just as non-commutative gauge theories arise from quantising open strings in
a large magnetic field, non-Abelian two-form gauge theories may conceivably be
constructed by quantising open membranes in a large three-form magnetic
background. We make some observations that arise in following this strategy,
with an emphasis on the relation to the quantisation of volume-preserving
diffeomorphisms (vpd). In particular, we construct consistent non-Abelian
interactions of a two-form in 3+1 dimensions, based on gauge invariance under
vpd.Comment: 6 pages, latex2e, uses revtex
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