1,039 research outputs found
Surface-induced near-field scaling in the Knudsen layer of a rarefied gas
We report on experiments performed within the Knudsen boundary layer of a
low-pressure gas. The non-invasive probe we use is a suspended
nano-electro-mechanical string (NEMS), which interacts with He gas at
cryogenic temperatures. When the pressure is decreased, a reduction of the
damping force below molecular friction had been first reported in
Phys. Rev. Lett. Vol 113, 136101 (2014) and never reproduced since. We
demonstrate that this effect is independent of geometry, but dependent on
temperature. Within the framework of kinetic theory, this reduction is
interpreted as a rarefaction phenomenon, carried through the boundary layer by
a deviation from the usual Maxwell-Boltzmann equilibrium distribution induced
by surface scattering. Adsorbed atoms are shown to play a key role in the
process, which explains why room temperature data fail to reproduce it.Comment: Article plus supplementary materia
Monte carlo within simulated annealing for integral constrained optimizations
For years, Value-at-Risk and Expected Shortfall have been well established measures of market risk and the Basel Committee on Banking Supervision recommends their use when controlling risk. But their computations might be intractable if we do not rely on simplifying assumptions, in particular on distributions of returns. One of the difficulties is linked to the need for Integral Constrained Optimizations. In this article, two new stochastic optimization-based Simulated Annealing algorithms are proposed for addressing problems associated with the use of statistical methods that rely on extremizing a non-necessarily differentiable criterion function, therefore facing the problem of the computation of a non-analytically reducible integral constraint. We first provide an illustrative example when maximizing an integral constrained likelihood for the stress-strength reliability that confirms the effectiveness of the algorithms. Our results indicate no clear difference in convergence, but we favor the use of the problem approximation strategy styled algorithm as it is less expensive in terms of computing time. Second, we run a classical financial problem such as portfolio optimization, showing the potential of our proposed methods in financial applications
Domain wall partition functions and KP
We observe that the partition function of the six vertex model on a finite
square lattice with domain wall boundary conditions is (a restriction of) a KP
tau function and express it as an expectation value of charged free fermions
(up to an overall normalization).Comment: 16 pages, LaTeX2
Measuring frequency fluctuations in nonlinear nanomechanical resonators
Advances in nanomechanics within recent years have demonstrated an always
expanding range of devices, from top-down structures to appealing bottom-up
MoS and graphene membranes, used for both sensing and component-oriented
applications. One of the main concerns in all of these devices is frequency
noise, which ultimately limits their applicability. This issue has attracted a
lot of attention recently, and the origin of this noise remains elusive up to
date. In this Letter we present a very simple technique to measure frequency
noise in nonlinear mechanical devices, based on the presence of bistability. It
is illustrated on silicon-nitride high-stress doubly-clamped beams, in a
cryogenic environment. We report on the same dependence of the frequency
noise power spectra as reported in the literature. But we also find unexpected
{\it damping fluctuations}, amplified in the vicinity of the bifurcation
points; this effect is clearly distinct from already reported nonlinear
dephasing, and poses a fundamental limit on the measurement of bifurcation
frequencies. The technique is further applied to the measurement of frequency
noise as a function of mode number, within the same device. The relative
frequency noise for the fundamental flexure lies in the range
ppm (consistent with literature for cryogenic MHz devices), and
decreases with mode number in the range studied. The technique can be applied
to {\it any types} of nano-mechanical structures, enabling progresses towards
the understanding of intrinsic sources of noise in these devices.Comment: Published 7 may 201
The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
The longitudinal spin structure factor for the XXZ-chain at small wave-vector
q is obtained using Bethe Ansatz, field theory methods and the Density Matrix
Renormalization Group. It consists of a peak with peculiar, non-Lorentzian
shape and a high-frequency tail. We show that the width of the peak is
proportional to q^2 for finite magnetic field compared to q^3 for zero field.
For the tail we derive an analytic formula without any adjustable parameters
and demonstrate that the integrability of the model directly affects the
lineshape.Comment: 4 pages, 3 figures, published versio
On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
We consider the problem of computing form factors of the massless XXZ
Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit
where the size M of the chain becomes large. For that purpose, we take the
particular example of the matrix element of the third component of spin between
the ground state and an excited state with one particle and one hole located at
the opposite ends of the Fermi interval (umklapp-type term). We exhibit its
power-law decrease in terms of the size of the chain M, and compute the
corresponding exponent and amplitude. As a consequence, we show that this form
factor is directly related to the amplitude of the leading oscillating term in
the long-distance asymptotic expansion of the two-point correlation function of
the third component of spin.Comment: 28 page
On factorizing -matrices in and spin chains
We consider quantum spin chains arising from -fold tensor products of the
fundamental evaluation representations of and .
Using the partial -matrix formalism from the seminal work of Maillet and
Sanchez de Santos, we derive a completely factorized expression for the
-matrix of such models and prove its equivalence to the expression obtained
by Albert, Boos, Flume and Ruhlig. A new relation between the -matrices and
the Bethe eigenvectors of these spin chains is given.Comment: 30 page
Resolution of the Nested Hierarchy for Rational sl(n) Models
We construct Drinfel'd twists for the rational sl(n) XXX-model giving rise to
a completely symmetric representation of the monodromy matrix. We obtain a
polarization free representation of the pseudoparticle creation operators
figuring in the construction of the Bethe vectors within the framework of the
quantum inverse scattering method. This representation enables us to resolve
the hierarchy of the nested Bethe ansatz for the sl(n) invariant rational
Heisenberg model. Our results generalize the findings of Maillet and Sanchez de
Santos for sl(2) models.Comment: 25 pages, no figure
Permutation-type solutions to the Yang-Baxter and other n-simplex equations
We study permutation type solutions to n-simplex equations, that is,
solutions whose R matrix can be written as a product of delta- functions
depending linearly on the indices. With this ansatz the D^{n(n+1)} equations of
the n-simplex equation reduce to an [n(n+1)/2+1]x[n(n+1)/2+1] matrix equation
over Z_D. We have completely analyzed the 2-, 3- and 4-simplex equations in the
generic D case. The solutions show interesting patterns that seem to continue
to still higher simplex equations.Comment: 20 pages, LaTeX2e. to appear in J. Phys. A: Math. Gen. (1997
Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
The Faddeev-Reshetikhin procedure corresponds to a removal of the
non-ultralocality of the classical SU(2) principal chiral model. It is realized
by defining another field theory, which has the same Lax pair and equations of
motion but a different Poisson structure and Hamiltonian. Following earlier
work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible
to alleviate in a similar way the non-ultralocality of symmetric space sigma
models. The equivalence of the equations of motion holds only at the level of
the Pohlmeyer reduction of these models, which corresponds to symmetric space
sine-Gordon models. This work therefore shows indirectly that symmetric space
sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an
integrable potential, have a mild non-ultralocality. The first step needed to
construct an integrable discretization of these models is performed by
determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change
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