Unsupervised vector-based classification of single-molecule charge transport data

The stochastic nature of single-molecule charge transport measurements requires collection of large data sets to capture the full complexity of a molecular system. Data analysis is then guided by certain expectations, for example, a plateau feature in the tunnelling current distance trace, and the molecular conductance extracted from suitable histogram analysis. However, differences in molecular conformation or electrode contact geometry, the number of molecules in the junction or dynamic effects may lead to very different molecular signatures. Since their manifestation is a priori unknown, an unsupervised classification algorithm, making no prior assumptions regarding the data is clearly desirable. Here we present such an approach based on multivariate pattern analysis and apply it to simulated and experimental single-molecule charge transport data. We demonstrate how different event shapes are clearly separated using this algorithm and how statistics about different event classes can be extracted, when conventional methods of analysis fail

Ground State Energy of the One-Component Charged Bose Gas

The model considered here is the `jellium' model in which there is a uniform, fixed background with charge density $-e\rho$ in a large volume $V$ and in which $N=\rho V$ particles of electric charge $+e$ and mass $m$ move --- the whole system being neutral. In 1961 Foldy used Bogolubov's 1947 method to investigate the ground state energy of this system for bosonic particles in the large $\rho$ limit. He found that the energy per particle is $-0.402 r_s^{-3/4} {me^4}/{\hbar^2}$ in this limit, where $r_s=(3/4\pi \rho)^{1/3}e^2m/\hbar^2$. Here we prove that this formula is correct, thereby validating, for the first time, at least one aspect of Bogolubov's pairing theory of the Bose gasComment: 38 pages latex. Typos corrected.Lemma 6.2 change

Lasing mechanisms in organic photonic crystal lasers with two-dimensional distributed feedback

We present a detailed experimental and theoretical investigation of the lasing characteristics of organic photonic crystal lasers. These lasers are based on strongly modulated two-dimensional polymer surface relief structures on which thin films of optically active organic materials have been deposited. We determine the in-plane photonic band structure of the corresponding quasiguided modes within an effective two-dimensional model. In addition, we calculate the total (three-dimensional) losses associated with these modes. This allows us to identify the lasing thresholds for square lattice geometries and to understand the emission pattern

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres

Multi-qubit gate with trapped ions for microwave and laser-based implementation

A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups

Fabrication and evaluation of a nickel shim for large-area hot embossing of plant surface structures

Petal textures exhibit outstanding broadband and omnidirectional light harvesting properties on solar cells [1,2] + by choice of low surface energy materials their self-cleaning properties can be harnessed [3]. A hot embossing routine via robust nickel embossing tools has been developed for a large area fabrication of such textures

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is extensively applied to the calculations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that has been tested in the mean-field calculations. By comparing the RPA results with those obtained by several other available methods for Ca isotopes, using a density-dependent contact interaction and the Woods-Saxon single-particle states, we confirm that energies, transition strengths and widths of their distribution are described by the GEM bases to good precision, for the $1^-$, $2^+$ and $3^-$ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the $E1$ response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in $^{60}$Ca are argued in some detail.Comment: 30 pages including 12 figure

A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

An algebraic approach to laying a ghost to rest

In the recent literature there has been a resurgence of interest in the fourth-order field-theoretic model of Pais-Uhlenbeck \cite {Pais-Uhlenbeck 50 a}, which has not had a good reception over the last half century due to the existence of {\em ghosts} in the properties of the quantum mechanical solution. Bender and Mannheim \cite{Bender 08 a} were successful in persuading the corresponding quantum operator to `give up the ghost'. Their success had the advantage of making the model of Pais-Uhlenbeck acceptable to the physical community and in the process added further credit to the cause of advancement of the use of ${\cal PT}$ symmetry. We present a case for the acceptance of the Pais-Uhlenbeck model in the context of Dirac's theory by providing an Hamiltonian which is not quantum mechanically haunted. The essential point is the manner in which a fourth-order equation is rendered into a system of second-order equations. We show by means of the method of reduction of order \cite {Nucci} that it is possible to construct an Hamiltonian which gives rise to a satisfactory quantal description without having to abandon Dirac.Comment: 8 page