Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.

The applicability of using different energy levels in CT imaging for differentiation or identification of dental restorative materials.

PURPOSE The goal of this study was to investigate whether different computed tomography (CT) energy levels could supply additional information for the differentiation of dental materials for forensic investigations. METHODS Nine different commonly used restorative dental materials were investigated in this study. A total of 75 human third molars were filled with the restorative dental materials and then scanned using the forensic reference phantom in singlesource mode. The mean Hounsfield unit values and standard deviations (SDs) of each material were calculated at 120, 80 and 140 kVp. RESULTS Most of the dental materials could be differentiated at 120 kVp. We found that greater X-ray density of a material resulted in higher SDs and that the material volume could influence the measurements. CONCLUSION Differentiation of dental materials in CT was possible in many cases using single-energy CT scans at 120 kVp. Because of the number of dental restorative materials available and scanner and scan parameter dependence, as well as the CT imaging artifacts, the identification (in contrast to differentiation) was problematic.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Simulating Energy Transfer and Upconversion in β-NaYF 4 : Yb 3+ , Tm 3+

The design of upconversion phosphors with higher quantum yield requires a deeper understanding of the detailed energy transfer and upconversion processes between active ions inside the material. Rate equations can model those processes by describing the populations of the energy levels of the ions as a function of time. However, this model presents some drawbacks: energy migration is assumed to be infinitely fast, it does not determine the detailed interaction mechanism (multipolar or exchange), and it only provides the macroscopic averaged parameters of interaction. Hence, a rate equation model with the same parameters cannot correctly predict the time evolution of upconverted emission and power dependence under a wide range of concentrations of active ions. We present a model that combines information about the host material lattice, the concentration of active ions, and a microscopic rate equation system. The extent of energy migration is correctly taken into account because the energy transfer processes are described on the level of the individual ions. This model predicts the decay curves, concentration, and excitation power dependences of the emission. This detailed information can be used to predict the optimal concentration that results in the maximum upconverted emission.

Dual-energy multidetector CT: how does it work, what can it tell us, and when can we use it in abdominopelvic imaging?

Dual-energy CT provides information about how substances behave at different energies, the ability to generate virtual unenhanced datasets, and improved detection of iodine-containing substances on low-energy images. Knowing how a substance behaves at two different energies can provide information about tissue composition beyond that obtainable with single-energy techniques. The term K edge refers to the spike in attenuation that occurs at energy levels just greater than that of the K-shell binding because of the increased photoelectric absorption at these energy levels. K-edge values vary for each element, and they increase as the atomic number increases. The energy dependence of the photoelectric effect and the variability of K edges form the basis of dual-energy techniques, which may be used to detect substances such as iodine, calcium, and uric acid crystals. The closer the energy level used in imaging is to the K edge of a substance such as iodine, the more the substance attenuates. In the abdomen and pelvis, dual-energy CT may be used in the liver to increase conspicuity of hypervascular lesions; in the kidneys, to distinguish hyperattenuating cysts from enhancing renal masses and to characterize renal stone composition; in the adrenal glands, to characterize adrenal nodules; and in the pancreas, to differentiate between normal and abnormal parenchyma.

Varying spin state composition by the choice of capping ligand in a family of molecular chains: detailed analysis of magnetic properties of chromium(III) horseshoes

We report a detailed physical analysis on a family of isolated, antiferro-magnetically (AF) coupled, chromium(III) finite chains, of general formula (Cr(RCO(2))(2)F)(n) where the chain length n = 6 or 7. Additionally, the chains are capped with a selection of possible terminating ligands, including hfac (= 1,1,1,5,5,5-hexafluoropentane-2,4-dionate(1-)), acac (= pentane-2,4-dionate(1-)) or (F)(3). Measurements by inelastic neutron scattering (INS), magnetometery and electron paramagnetic resonance (EPR) spectroscopy have been used to study how the electronic properties are affected by n and capping ligand type. These comparisons allowed the subtle electronic effects the choice of capping ligand makes for odd member spin 3/2 ground state and even membered spin 0 ground state chains to be investigated. For this investigation full characterisation of physical properties have been performed with spin Hamiltonian parameterisation, including the determination of Heisenberg exchange coupling constants and single ion axial and rhombic anisotropy. We reveal how the quantum spin energy levels of odd or even membered chains can be modified by the type of capping ligand terminating the chain. Choice of capping ligands enables Cr-Cr exchange coupling to be adjusted by 0, 4 or 24%, relative to Cr-Cr exchange coupling within the body of the chain, by the substitution of hfac, acac or (F)(3) capping ligands to the ends of the chain, respectively. The manipulation of quantum spin levels via ligands which play no role in super-exchange, is of general interest to the practise of spin Hamilton modelling, where such second order effects are generally not considered of relevance to magnetic properties.

Optical quantum random number generator

A physical random number generator based on the intrinsic randomness of quantum mechanics is described. The random events are realized by the choice of single photons between the two outputs of a beamsplitter. We present a simple device, which minimizes the impact of the photon counters’ noise, dead-time and after pulses.

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

αs from the static energy in QCD

Comparing perturbative calculations with a lattice computation of the static energy in quantum chromodynamics at short distances, we obtain a determination of the strong coupling αS. Our determination is performed at a scale of around 1.5 GeV (the typical distance scale of the lattice data) and, when evolved to the Z-boson mass scale MZ, it corresponds to .