A generalized Kac-Ward formula

The Kac-Ward formula allows to compute the Ising partition function on a planar graph G with straight edges from the determinant of a matrix of size 2N, where N denotes the number of edges of G. In this paper, we extend this formula to any finite graph: the partition function can be written as an alternating sum of the determinants of 2^{2g} matrices of size 2N, where g is the genus of an orientable surface in which G embeds. We give two proofs of this generalized formula. The first one is purely combinatorial, while the second relies on the Fisher-Kasteleyn reduction of the Ising model to the dimer model, and on geometric techniques. As a consequence of this second proof, we also obtain the following fact: the Kac-Ward and the Fisher-Kasteleyn methods to solve the Ising model are one and the same.Comment: 23 pages, 8 figures; minor corrections in v2; to appear in J. Stat. Mech. Theory Ex

Static and Dynamic Chain Structures in the Mean-Field Theory

We give a brief overview of recent work examining the presence of $\alpha$-clusters in light nuclei within the Skyrme-force Hartree-Fock model. Of special significance are investigations into $\alpha$-chain structures in carbon isotopes and $^{16}$O. Their stability and possible role in fusion reactions are examined in static and time-dependent Hartree-Fock calculations. We find a new type of shape transition in collisions and a centrifugal stabilization of the $4\alpha$ chain state in a limited range of angular momenta. No stabilization is found for the $3\alpha$ chain.Comment: Fusionn 11 Conference, St. Malo, France, 201

Single-particle dissipation in TDHF studied from a phase-space perspective

We study dissipation and relaxation processes within the time-dependent Hartree-Fock approach using the Wigner distribution function. On the technical side we present a geometrically unrestricted framework which allows us to calculate the full six-dimensional Wigner distribution function. With the removal of geometrical constraints, we are now able to extend our previous phase-space analysis of heavy-ion collisions in the reaction plane to unrestricted mean-field simulations of nuclear matter on a three-dimensional Cartesian lattice. From the physical point of view we provide a quantitative analysis on the stopping power in TDHF. This is linked to the effect of transparency. For the medium-heavy $^{40}$Ca+$^{40}$Ca system we examine the impact of different parametrizations of the Skyrme force, energy-dependence, and the significance of extra time-odd terms in the Skyrme functional.Comment: 7 pages, 4 figures, 2 videos. arXiv admin note: substantial text overlap with arXiv:1201.526

Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

Calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in time-dependent Hartree-Fock during a heavy-ion collision. We compare the Wigner distribution function with the smoothed Husimi distribution function. Observables are defined to give a quantitative measure for local and global equilibration. We present different reaction scenarios by analyzing central and non-central $^{16}O+$$^{16}O$ and $^{96}Zr+$$^{132}Zn$ collisions. It is shown that the initial phase-space volumes of the fragments barely merge. The mean values of the observables are conserved in fusion reactions and indicate a "memory effect" in time-dependent Hartree-Fock. We observe strong dissipation but no evidence for complete equilibration.Comment: 12 pages, 10 figure

Optically driving the radiative Auger transition

In a radiative Auger process, optical decay is accompanied by simultaneous excitation of other carriers. The radiative Auger process gives rise to weak red-shifted satellite peaks in the optical emission spectrum. These satellite peaks have been observed over a large spectral range: in the X-ray emission of atoms; close to visible frequencies on donors in semiconductors and quantum emitters; and at infrared frequencies as shake-up lines in two-dimensional systems. So far, all the work on the radiative Auger process has focussed on detecting the spontaneous emission. However, the fact that the radiative Auger process leads to photon emission suggests that the transition can also be optically excited. In such an inverted radiative Auger process, excitation would correspond to simultaneous photon absorption and electronic de-excitation. Here, we demonstrate optical driving of the radiative Auger transition on a trion in a semiconductor quantum dot. The radiative Auger and the fundamental transition together form a $\Lambda$-system. On driving both transitions of this $\Lambda$-system simultaneously, we observe a reduction of the fluorescence signal by up to $70\%$. Our results demonstrate a type of optically addressable transition connecting few-body Coulomb interactions to quantum optics. The results open up the possibility of carrying out THz spectroscopy on single quantum emitters with all the benefits of optics: coherent laser sources, efficient and fast single-photon detectors. In analogy to optical control of an electron spin, the $\Lambda$-system between the radiative Auger and the fundamental transitions allows optical control of the emitters' orbital degree of freedom.Comment: 8 pages, 6 figure

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-

Wafer-scale epitaxial modulation of quantum dot density

Precise control of the properties of semiconductor quantum dots (QDs) is vital for creating novel devices for quantum photonics and advanced opto-electronics. Suitable low QD-densities for single QD devices and experiments are challenging to control during epitaxy and are typically found only in limited regions of the wafer. Here, we demonstrate how conventional molecular beam epitaxy (MBE) can be used to modulate the density of optically active QDs in one- and two- dimensional patterns, while still retaining excellent quality. We find that material thickness gradients during layer-by-layer growth result in surface roughness modulations across the whole wafer. Growth on such templates strongly influences the QD nucleation probability. We obtain density modulations between 1 and 10 QDs/µm2 and periods ranging from several millimeters down to at least a few hundred microns. This method is universal and expected to be applicable to a wide variety of different semiconductor material systems. We apply the method to enable growth of ultra-low noise QDs across an entire 3-inch semiconductor wafer

Smart garment for trunk posture monitoring: A preliminary study

© 2008 Wong and Wong; licensee BioMed Central Ltd

The Potential and Challenges of Nanopore Sequencing

A nanopore-based device provides single-molecule detection and analytical capabilities that are achieved by electrophoretically driving molecules in solution through a nano-scale pore. The nanopore provides a highly confined space within which single nucleic acid polymers can be analyzed at high throughput by one of a variety of means, and the perfect processivity that can be enforced in a narrow pore ensures that the native order of the nucleobases in a polynucleotide is reflected in the sequence of signals that is detected. Kilobase length polymers (single-stranded genomic DNA or RNA) or small molecules (e.g., nucleosides) can be identified and characterized without amplification or labeling, a unique analytical capability that makes inexpensive, rapid DNA sequencing a possibility. Further research and development to overcome current challenges to nanopore identification of each successive nucleotide in a DNA strand offers the prospect of ‘third generation’ instruments that will sequence a diploid mammalian genome for ~$1,000 in ~24 h.Molecular and Cellular BiologyPhysic