Theoretical analysis of dynamic chemical imaging with lasers using high-order harmonic generation

We report theoretical investigations of the tomographic procedure suggested by Itatani {\it et al.} [Nature, {\bf 432} 867 (2004)] for reconstructing highest occupied molecular orbitals (HOMO) using high-order harmonic generation (HHG). Using the limited range of harmonics from the plateau region, we found that under the most favorable assumptions, it is still very difficult to obtain accurate HOMO wavefunction, but the symmetry of the HOMO and the internuclear separation between the atoms can be accurately extracted, especially when lasers of longer wavelengths are used to generate the HHG. We also considered the possible removal or relaxation of the approximations used in the tomographic method in actual applications. We suggest that for chemical imaging, in the future it is better to use an iterative method to locate the positions of atoms in the molecule such that the resulting HHG best fits the macroscopic HHG data, rather than by the tomographic method.Comment: 13 pages, 14 figure

A Robust Method for Detecting Interdependences: Application to Intracranially Recorded EEG

We present a measure for characterizing statistical relationships between two time sequences. In contrast to commonly used measures like cross-correlations, coherence and mutual information, the proposed measure is non-symmetric and provides information about the direction of interdependence. It is closely related to recent attempts to detect generalized synchronization. However, we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise, and to detect also weak interdependences. We apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies.Comment: 29 pages, 5 figures, paper accepted for publication in Physica

Zeeman smearing of the Coulomb blockade

Charge fluctuations of a large quantum dot coupled to a two-dimensional lead via a single-mode good Quantum Point Contact (QPC) and capacitively coupled to a back-gate, are investigated in the presence of a parallel magnetic field. The Zeeman term induces an asymmetry between transmission probabilities for the spin-up and spin-down channels at the QPC, producing noticeable effects on the quantization of the grain charge already at low magnetic fields. Performing a quantitative analysis, I show that the capacitance between the gate and the lead exhibits - instead of a logarithmic singularity - a reduced peak as a function of gate voltage. Experimental applicability is discussed.Comment: 5 pages, 3 figures (Final version

Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices

Contact matrices provide a coarse grained description of the configuration omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when the distance between the position of the i-th and j-th step are less than or equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with "a" the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n <= 2, but differs for n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is rewritten in a less formal way with the main results explained in simple term

Fractional plateaus in the Coulomb blockade of coupled quantum dots

Ground-state properties of a double-large-dot sample connected to a reservoir via a single-mode point contact are investigated. When the interdot transmission is perfect and the dots controlled by the same dimensionless gate voltage, we find that for any finite backscattering from the barrier between the lead and the left dot, the average dot charge exhibits a Coulomb-staircase behavior with steps of size e/2 and the capacitance peak period is halved. The interdot electrostatic coupling here is weak. For strong tunneling between the left dot and the lead, we report a conspicuous intermediate phase in which the fractional plateaus get substantially altered by an increasing slope.Comment: 6 pages, 4 figures, final versio

Almost formality of manifolds of low dimension

In this paper we introduce the notion of Poincaré DGCAs of Hodge type, which is a subclass of Poincaré DGCAs encompassing the de Rham algebras of closed orientable manifolds. Then we introduce the notion of the small algebra and the small quotient algebra of a Poincaré DGCA of Hodge type. Using these concepts, we investigate the equivalence class of (r-1)-connected (r &gt; 1) Poincaré DGCAs of Hodge type. In particular, we show that an (r-1)-connected Poincar ́e DGCA of Hodge type A* of dimension n &lt;= 5r - 3 is A-infinity-quasi-isomorphic to an A_3-algebra and prove that the only obstruction to the formality of A* is a distinguished Harrison cohomology class [μ3] in Harr^3-1(H*(A*), H*(A*)). Moreover, the cohomology class [μ3] and the DGCA isomorphism class of H*(A*) determine the A-infinity-quasi-isomorphism class of A*. This can be seen as a Harrison cohomology version of the Crowley- Nordstrom results on rational homotopy type of (r - 1)-connected (r &gt; 1) closed manifolds of dimension up to 5r -3. We also derive the almost formality of closed G2 -manifolds, which have been discovered recently by Chan-Karigiannis- Tsang, from our results and the Cheeger-Gromoll splitting theorem

Laser anneal of oxycarbosilane low-k film

Submilisecond laser anneal has been experimentally investigated for porogen removal and its ability to improve the mechanical strength in oxycarbosilane ultra low-k films compromised due to the introduction of porosity. We report the occurrence of extensive bond rearrangements inferred from Fourier-transform infra-red (FTIR) spectroscopy, elastic recoil detection (ERD) and spectroscopic ellipsometry (SE) in the energy range of 1.4-8 eV. The laser anneal affects most notably the organic content of the organosilicate matrix leading to depletion and reorganization. Nevertheless, the tested conditions reveal a processing window which allows for 13% improvement of Young’s modulus as compared to the reference film, annealed in a conventional furnace at 400°C for 2 h, while not impacting the relative dielectric constant of 2.25