324 research outputs found
A Christoffel-Darboux formula for multiple orthogonal polynomials
Bleher and Kuijlaars recently showed that the eigenvalue correlations from
matrix ensembles with external source can be expressed by means of a kernel
built out of special multiple orthogonal polynomials. We derive a
Christoffel-Darboux formula for this kernel for general multiple orthogonal
polynomials. In addition, we show that the formula can be written in terms of
the solution of the Riemann-Hilbert problem for multiple orthogonal
polynomials, which will be useful for asymptotic analysis.Comment: 11 pages, no figure
Field-free two-direction alignment alternation of linear molecules by elliptic laser pulses
We show that a linear molecule subjected to a short specific elliptically
polarized laser field yields postpulse revivals exhibiting alignment
alternatively located along the orthogonal axis and the major axis of the
ellipse. The effect is experimentally demonstrated by measuring the optical
Kerr effect along two different axes. The conditions ensuring an optimal
field-free alternation of high alignments along both directions are derived.Comment: 5 pages, 4 color figure
Entanglement may enhance the channel capacity in arbitrary dimensions
We consider explicitly two examples of d-dimensional quantum channels with
correlated noise and show that, in agreement with previous results on Pauli
qubit channels, there are situations where maximally entangled input states
achieve higher values of the output mutual information than product states. We
obtain a strong dependence of this effect on the nature of the noise
correlations as well as on the parity of the space dimension, and conjecture
that when entanglement gives an advantage in terms of mutual information,
maximally entangled states achieve the channel capacity.Comment: 12 pages, 3 figure
Laser control for the optimal evolution of pure quantum states
Starting from an initial pure quantum state, we present a strategy for
reaching a target state corresponding to the extremum (maximum or minimum) of a
given observable. We show that a sequence of pulses of moderate intensity,
applied at times when the average of the observable reaches its local or global
extremum, constitutes a strategy transferable to different control issues.
Among them, post-pulse molecular alignment and orientation are presented as
examples. The robustness of such strategies with respect to experimentally
relevant parameters is also examined.Comment: 16 pages, 9 figure
Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
We study the capacity of d-dimensional quantum channels with memory modeled
by correlated noise. We show that, in agreement with previous results on Pauli
qubit channels, there are situations where maximally entangled input states
achieve higher values of mutual information than product states. Moreover, a
strong dependence of this effect on the nature of the noise correlations as
well as on the parity of the space dimension is found. We conjecture that when
entanglement gives an advantage in terms of mutual information, maximally
entangled states saturate the channel capacity.Comment: 10 pages, 5 figure
Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
We study a model of non-intersecting squared Bessel processes in the
confluent case: all paths start at time at the same positive value , remain positive, and are conditioned to end at time at . In
the limit , after appropriate rescaling, the paths fill out a
region in the -plane that we describe explicitly. In particular, the paths
initially stay away from the hard edge at , but at a certain critical
time the smallest paths hit the hard edge and from then on are stuck to
it. For we obtain the usual scaling limits from random matrix
theory, namely the sine, Airy, and Bessel kernels. A key fact is that the
positions of the paths at any time constitute a multiple orthogonal
polynomial ensemble, corresponding to a system of two modified Bessel-type
weights. As a consequence, there is a matrix valued
Riemann-Hilbert problem characterizing this model, that we analyze in the large
limit using the Deift-Zhou steepest descent method. There are some novel
ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure
Time-dependent unitary perturbation theory for intense laser driven molecular orientation
We apply a time-dependent perturbation theory based on unitary
transformations combined with averaging techniques, on molecular orientation
dynamics by ultrashort pulses. We test the validity and the accuracy of this
approach on LiCl described within a rigid-rotor model and find that it is more
accurate than other approximations. Furthermore, it is shown that a noticeable
orientation can be achieved for experimentally standard short laser pulses of
zero time average. In this case, we determine the dynamically relevant
parameters by using the perturbative propagator, that is derived from this
scheme, and we investigate the temperature effects on the molecular orientation
dynamics.Comment: 16 pages, 6 figure
Large n limit of Gaussian random matrices with external source, Part III: Double scaling limit
We consider the double scaling limit in the random matrix ensemble with an
external source \frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM defined on Hermitian matrices, where is a diagonal matrix with two eigenvalues of equal multiplicities. The value is critical since the eigenvalues
of accumulate as on two intervals for and on one
interval for . These two cases were treated in Parts I and II, where
we showed that the local eigenvalue correlations have the universal limiting
behavior known from unitary random matrix ensembles. For the critical case
new limiting behavior occurs which is described in terms of Pearcey
integrals, as shown by Br\'ezin and Hikami, and Tracy and Widom. We establish
this result by applying the Deift/Zhou steepest descent method to a -matrix valued Riemann-Hilbert problem which involves the construction of a
local parametrix out of Pearcey integrals. We resolve the main technical issue
of matching the local Pearcey parametrix with a global outside parametrix by
modifying an underlying Riemann surface.Comment: 36 pages, 9 figure
Allosteric modulation of the GTPase activity of a bacterial LRRK2 homolog by conformation-specific Nanobodies
Mutations in the Parkinson's disease (PD)-associated protein leucine-rich repeat kinase 2 (LRRK2) commonly lead to a reduction of GTPase activity and increase in kinase activity. Therefore, strategies for drug development have mainly been focusing on the design of LRRK2 kinase inhibitors. We recently showed that the central RocCOR domains (Roc: Ras of complex proteins; COR: C-terminal of Roc) of a bacterial LRRK2 homolog cycle between a dimeric and monomeric form concomitant with GTP binding and hydrolysis. PD-associated mutations can slow down GTP hydrolysis by stabilizing the protein in its dimeric form. Here, we report the identification of two Nanobodies (NbRoco1 and NbRoco2) that bind the bacterial Roco protein (CtRoco) in a conformation-specific way, with a preference for the GTP-bound state. NbRoco1 considerably increases the GTP turnover rate of CtRoco and reverts the decrease in GTPase activity caused by a PD-analogous mutation. We show that NbRoco1 exerts its effect by allosterically interfering with the CtRoco dimer–monomer cycle through the destabilization of the dimeric form. Hence, we provide the first proof of principle that allosteric modulation of the RocCOR dimer–monomer cycle can alter its GTPase activity, which might present a potential novel strategy to overcome the effect of LRRK2 PD mutations
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