1,045 research outputs found
Surface Phonons and Other Localized Excitations
The diatomic linear chain of masses coupled by harmonic springs is a
textboook model for vibrational normal modes (phonons) in crystals. In addition
to propagating acoustic and optic branches, this model is known to support a
``gap mode'' localized at the surface, provided the atom at the surface has
light rather than heavy mass. An elementary argument is given which explains
this mode and provides values for the frequency and localization length. By
reinterpreting this mode in different ways, we obtain the frequency and
localization lengths for three other interesting modes: (1) the surface
vibrational mode of a light mass impurity at the surface of a monatomic chain;
(2) the localized vibrational mode of a stacking fault in a diatomic chain; and
(3) the localized vibrational mode of a light mass impurity in a monatomic
chain.Comment: 5 pages with 4 embedded postscript figures. This paper will appear in
the American Journal of Physic
Shot noise in the interacting resonance level model
The shot noise power and the Fano factor of a spinless resonant level model
is calculated. The Coulomb interaction which in this model acts between the
lead electron and the impurity is considered in the first order approximation.
The logarithmic divergencies which appeared in the expressions for shot noise
and the transport current are removed by renormalization group analysis. It is
shown that Keldysh technique gives an adequate description of perturbation
theory results. By passing to the bosonized form of the resonance model it is
proven that in the strong interaction limit the tunnelling becomes irrelevant
and decreases.Comment: 4 pages, 2 figure
Localized Modes in Open One-Dimensional Dissipative Random Systems
We consider, both theoretically and experimentally, the excitation and
detection of the localized quasi-modes (resonances) in an open dissipative 1D
random system. We show that even though the amplitude of transmission drops
dramatically so that it cannot be observed in the presence of small losses,
resonances are still clearly exhibited in reflection. Surprisingly, small
losses essentially improve conditions for the detection of resonances in
reflection as compared with the lossless case. An algorithm is proposed and
tested to retrieve sample parameters and resonances characteristics inside the
random system exclusively from reflection measurements.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let
On the almost sure central limit theorem for ARX processes in adaptive tracking
The goal of this paper is to highlight the almost sure central limit theorem
for martingales to the control community and to show the usefulness of this
result for the system identification of controllable ARX(p,q) process in
adaptive tracking. We also provide strongly consistent estimators of the even
moments of the driven noise of a controllable ARX(p,q) process as well as
quadratic strong laws for the average costs and estimation errors sequences.
Our theoretical results are illustrated by numerical experiments
Phase randomness in a one-dimensional disordered absorbing medium
Analytical study of the distribution of phase of the transmission coefficient
through 1D disordered absorbing system is presented. The phase is shown to obey
approximately Gaussian distribution. An explicit expression for the variance is
obtained, which shows that absorption suppresses the fluctuations of the phase.
The applicability of the random phase approximation is discussed.Comment: submitted to Phys.Rev.
Average Case Tractability of Non-homogeneous Tensor Product Problems
We study d-variate approximation problems in the average case setting with
respect to a zero-mean Gaussian measure. Our interest is focused on measures
having a structure of non-homogeneous linear tensor product, where covariance
kernel is a product of univariate kernels. We consider the normalized average
error of algorithms that use finitely many evaluations of arbitrary linear
functionals. The information complexity is defined as the minimal number n(h,d)
of such evaluations for error in the d-variate case to be at most h. The growth
of n(h,d) as a function of h^{-1} and d depends on the eigenvalues of the
covariance operator and determines whether a problem is tractable or not. Four
types of tractability are studied and for each of them we find the necessary
and sufficient conditions in terms of the eigenvalues of univariate kernels. We
illustrate our results by considering approximation problems related to the
product of Korobov kernels characterized by a weights g_k and smoothnesses r_k.
We assume that weights are non-increasing and smoothness parameters are
non-decreasing. Furthermore they may be related, for instance g_k=g(r_k) for
some non-increasing function g. In particular, we show that approximation
problem is strongly polynomially tractable, i.e., n(h,d)\le C h^{-p} for all d
and 0<h<1, where C and p are independent of h and d, iff liminf |ln g_k|/ln k
>1. For other types of tractability we also show necessary and sufficient
conditions in terms of the sequences g_k and r_k
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