Symmetry-Induced Tunnelling in One-Dimensional Disordered Potentials

A new mechanism of tunnelling at macroscopic distances is proposed for a wave packet localized in one-dimensional disordered potential with mirror symmetry, V(-x)=V(x). Unlike quantum tunnelling through a regular potential barrier, which occurs only at the energies lower then the barrier height, the proposed mechanism of tunnelling exists even for weak white-noise-like scattering potentials. It also exists in classical circuits of resonant contours with random resonant frequencies. The latter property may be used as a new method of secure communication, which does not require coding and decoding of the transmitting signal.Comment: 10 pages, 4 figure

Experimental observation of the mobility edge in a waveguide with correlated disorder

The tight-binding model with correlated disorder introduced by Izrailev and Krokhin [PRL 82, 4062 (1999)] has been extended to the Kronig-Penney model. The results of the calculations have been compared with microwave transmission spectra through a single-mode waveguide with inserted correlated scatterers. All predicted bands and mobility edges have been found in the experiment, thus demonstrating that any wanted combination of transparent and non-transparent frequency intervals can be realized experimentally by introducing appropriate correlations between scatterers.Comment: RevTex, 4 pages including 4 Postscript figure

Parametric instability of linear oscillators with colored time-dependent noise

The goal of this paper is to discuss the link between the quantum phenomenon of Anderson localization on the one hand, and the parametric instability of classical linear oscillators with stochastic frequency on the other. We show that these two problems are closely related to each other. On the base of analytical and numerical results we predict under which conditions colored parametric noise suppresses the instability of linear oscillators.Comment: RevTex, 9 pages, no figure

Enhancement of localization in one-dimensional random potentials with long-range correlations

We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single mode waveguide with 100 tuneable scatterers periodically inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the spacing between each pair of scatterers, we observe a strong decrease of the localization length when white-noise scatterers are replaced by a correlated arrangement of scatterers.Comment: 4 pages, 6 figure

Complexity classification in qualitative temporal constraint reasoning

We study the computational complexity of the qualitative algebra which is a temporal constraint formalism that combines the point algebra, the point-interval algebra and Allen's interval algebra. We identify all tractable fragments and show that every other fragment is NP-complete

The Complexity of General-Valued CSPs

An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. We study, assuming that P ≠ NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language. The case when all allowed functions take values in {0, ∞} corresponds to ordinary CSPs, where one deals only with the feasibility issue and there is no optimization. This case is the subject of the Algebraic CSP Dichotomy Conjecture predicting for which constraint languages CSPs are tractable (i.e. solvable in polynomial time) and for which NP-hard. The case when all allowed functions take only finite values corresponds to finite-valued CSP, where the feasibility aspect is trivial and one deals only with the optimization issue. The complexity of finite-valued CSPs was fully classified by Thapper and Zivny. An algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language was recently given by Kozik and Ochremiak. As our main result, we prove that if a constraint language satisfies this algebraic necessary condition, and the feasibility CSP (i.e. the problem of deciding whether a given instance has a feasible solution) corresponding to the VCSP with this language is tractable, then the VCSP is tractable. The algorithm is a simple combination of the assumed algorithm for the feasibility CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy for ordinary CSPs would imply a dichotomy for general-valued CSPs

Allen Linear (Interval) Temporal Logic --Translation to LTL and Monitor Synthesis--

The relationship between two well established formalisms for temporal reasoning is first investigated, namely between Allen's interval algebra (or Allen's temporal logic, abbreviated \ATL) and linear temporal logic (\LTL). A discrete variant of \ATL is defined, called Allen linear temporal logic (\ALTL), whose models are \omega-sequences of timepoints, like in \LTL. It is shown that any \ALTL formula can be linearly translated into an equivalent \LTL formula, thus enabling the use of \LTL techniques and tools when requirements are expressed in \ALTL. %This translation also implies the NP-completeness of \ATL satisfiability. Then the monitoring problem for \ALTL is discussed, showing that it is NP-complete despite the fact that the similar problem for \LTL is EXPSPACE-complete. An effective monitoring algorithm for \ALTL is given, which has been implemented and experimented with in the context of planning applications