``Critical'' phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams

The phonon modes of the Frenkel-Kontorova model are studied both at the pinning transition as well as in the pinned (cantorus) phase. We focus on the minimal frequency of the phonon spectrum and the corresponding generalized eigenfunction. Using an exact decimation scheme, the eigenfunctions are shown to have nontrivial scaling properties not only at the pinning transition point but also in the cantorus regime. Therefore the phonons defy localization and remain critical even where the associated area-preserving map has a positive Lyapunov exponent. In this region, the critical scaling properties vary continuously and are described by a line of renormalization limit cycles. Interesting renormalization bifurcation diagrams are obtained by monitoring the cycles as the parameters of the system are varied from an integrable case to the anti-integrable limit. Both of these limits are described by a trivial decimation fixed point. Very surprisingly we find additional special parameter values in the cantorus regime where the renormalization limit cycle degenerates into the above trivial fixed point. At these ``degeneracy points'' the phonon hull is represented by an infinite series of step functions. This novel behavior persists in the extended version of the model containing two harmonics. Additional richnesses of this extended model are the one to two-hole transition line, characterized by a divergence in the renormalization cycles, nonexponentially localized phonons, and the preservation of critical behavior all the way upto the anti-integrable limit.Comment: 10 pages, RevTeX, 9 Postscript figure

Rician MIMO Channel- and Jamming-Aware Decision Fusion

In this manuscript we study channel-aware decision fusion (DF) in a wireless sensor network (WSN) where: (i) the sensors transmit their decisions simultaneously for spectral efficiency purposes and the DF center (DFC) is equipped with multiple antennas; (ii) each sensor-DFC channel is described via a Rician model. As opposed to the existing literature, in order to account for stringent energy constraints in the WSN, only statistical channel information is assumed for the non-line-of sight (scattered) fading terms. For such a scenario, sub-optimal fusion rules are developed in order to deal with the exponential complexity of the likelihood ratio test (LRT) and impractical (complete) system knowledge. Furthermore, the considered model is extended to the case of (partially unknown) jamming-originated interference. Then the obtained fusion rules are modified with the use of composite hypothesis testing framework and generalized LRT. Coincidence and statistical equivalence among them are also investigated under some relevant simplified scenarios. Numerical results compare the proposed rules and highlight their jammingsuppression capability.Comment: Accepted in IEEE Transactions on Signal Processing 201

Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems

Incommensurate structures can be described by the Frenkel Kontorova model. Aubry has shown that, at a critical value K_c of the coupling of the harmonic chain to an incommensurate periodic potential, the system displays the analyticity breaking transition between a sliding and pinned state. The ground state equations coincide with the standard map in non-linear dynamics, with smooth or chaotic orbits below and above K_c respectively. For the standard map, Greene and MacKay have calculated the value K_c=.971635. Conversely, evaluations based on the analyticity breaking of the modulation function have been performed for high commensurate approximants. Here we show how the modulation function of the infinite system can be calculated without using approximants but by Taylor expansions of increasing order. This approach leads to a value K_c'=.97978, implying the existence of a golden invariant circle up to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation provided; Revised version, accepted for publication in Europhysics Letter

Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing

In this paper we theoretically discuss how quantum simulators based on trapped cold bosons in optical lattices can explore the grand-canonical phase diagram of homogeneous lattice boson models, via control of the trapping potential independently of all other experimental parameters (trap squeezing). Based on quantum Monte Carlo, we establish the general scaling relation linking the global chemical potential to the Hamiltonian parameters of the Bose-Hubbard model in a parabolic trap, describing cold bosons in optical lattices; we find that this scaling relation is well captured by a modified Thomas-Fermi scaling behavior - corrected for quantum fluctuations - in the case of high enough density and/or weak enough interactions, and by a mean-field Gutzwiller Ansatz over a much larger parameter range. The above scaling relation allows to control experimentally the chemical potential, independently of all other Hamiltonian parameters, via trap squeezing; given that the global chemical potential coincides with the local chemical potential in the trap center, measurements of the central density as a function of the chemical potential gives access to the information on the bulk compressibility of the Bose-Hubbard model. Supplemented with time-of-flight measurements of the coherence properties, the measurement of compressibility enables one to discern among the various possible phases realized by bosons in an optical lattice with or without external (periodic or random) potentials -- e.g. superfluid, Mott insulator, band insulator, and Bose glass. We theoretically demonstrate the trap-squeezing investigation of the above phases in the case of bosons in a one-dimensional optical lattice, and in a one-dimensional incommensurate superlattice.Comment: 27 pages, 26 figures. v2: added references and further discussion of the local-density approximation

Ground state wavefunction of the quantum Frenkel-Kontorova model

The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wavefunction crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.Comment: 5 Europhys pages, 3 EPS figures, accepted for publication in Europhys. Letter

(In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite

The scaling of friction with the contact size $A$ and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size ($A^0$) and two commensurate ones which scale differently (with $A^{1/2}$ and $A$) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found ($A^{1/4}, A^{3/4}, A$). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed

Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

We study a real, massive Klein-Gordon field in the Poincar\'e fundamental domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincar\'e fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.Comment: 12 pages, 1 figure. In V3: refs. added, introduction and conclusions expande