On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts

In the context of two particularly interesting non-Hermitian models in quantum mechanics we explore the relationship between the original Hamiltonian H and its Hermitian counterpart h, obtained from H by a similarity transformation, as pointed out by Mostafazadeh. In the first model, due to Swanson, h turns out to be just a scaled harmonic oscillator, which explains the form of its spectrum. However, the transformation is not unique, which also means that the observables of the original theory are not uniquely determined by H alone. The second model we consider is the original PT-invariant Hamiltonian, with potential V=igx^3. In this case the corresponding h, which we are only able to construct in perturbation theory, corresponds to a complicated velocity-dependent potential. We again explore the relationship between the canonical variables x and p and the observables X and P.Comment: 9 pages, no figure

Annual banned-substance review: Analytical approaches in human sports drug testing 2019/2020.

Analytical chemistry-based research in sports drug testing has been a dynamic endeavor for several decades, with technology-driven innovations continuously contributing to significant improvements in various regards including analytical sensitivity, comprehensiveness of target analytes, differentiation of natural/endogenous substances from structurally identical but synthetically derived compounds, assessment of alternative matrices for doping control purposes, and so forth. The resulting breadth of tools being investigated and developed by anti-doping researchers has allowed to substantially improve anti-doping programs and data interpretation in general. Additionally, these outcomes have been an extremely valuable pledge for routine doping controls during the unprecedented global health crisis that severely affected established sports drug testing strategies. In this edition of the annual banned-substance review, literature on recent developments in anti-doping published between October 2019 and September 2020 is summarized and discussed, particularly focusing on human doping controls and potential applications of new testing strategies to substances and methods of doping specified the World Anti-Doping Agency's 2020 Prohibited List

Coordinate Singularities in Harmonically-sliced Cosmologies

Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this slicing condition can show pathological behaviour. In this paper, analytic and numerical methods are used to examine harmonic slicings of Kasner and Gowdy cosmological spacetimes. It is shown that in general the slicings are prevented from covering the whole of the spacetimes by the appearance of coordinate singularities. As well as limiting the maximum running times of numerical simulations, the coordinate singularities can lead to features being produced in numerically evolved solutions which must be distinguished from genuine physical effects.Comment: 21 pages, REVTeX, 5 figure

Thermodynamics of Pseudo-Hermitian Systems in Equilibrium

In study of pseudo(quasi)-hermitian operators, the key role is played by the positive-definite metric operator. It enables physical interpretation of the considered systems. In the article, we study the pseudo-hermitian systems with constant number of particles in equilibrium. We show that the explicit knowledge of the metric operator is not essential for study of thermodynamic properties of the system. We introduce a simple example where the physically relevant quantities are derived without explicit calculation of either metric operator or spectrum of the Hamiltonian.Comment: 9 pages, 2 figures, to appear in Mod.Phys.Lett. A; historical part of sec. 2.1 reformulated, references corrected; typos correcte

Fermion-Boson Interactions and Quantum Algebras

Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and bosons interacting via schematic forces. The structure of the proposed su_q(2) Hamiltonians, and the meaning of the corresponding deformation parameters, are discussed.Comment: 20 pages, 10 figures. Physical Review C (in press

Moyal products -- a new perspective on quasi-hermitian quantum mechanics

The rationale for introducing non-hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of Non-Hermitian Operator

Design of a low-noise aeroacoustic wind tunnel facility at Brunel University

This paper represents the design principle of a quiet, low turbulence and moderately high speed aeroacoustic wind tunnel which was recently commissioned at Brunel University. A new hemi-anechoic chamber was purposely built to facilitate aeroacoustic measurements. The wind tunnel can achieve a maximum speed of about 80 ms-1. The turbulence intensity of the free jet in the potential core is between 0.1–0.2%. The noise characteristic of the aeroacoustic wind tunnel was validated by three case studies. All of which can demonstrate a very low background noise produced by the bare jet in comparison to the noise radiated from the cylinder rod/flat plate/airfoil in the air stream.The constructions of the aeroacoustic wind tunnel and the hemi-anechoic chamber are financially supported by the School of Engineering and Design at Brunel University

Carrier multiplication yields in PbS and PbSe nanocrystals measured by transient photoluminescence

We report here an assessment of carrier multiplication (CM) yields in PbSe and PbS nanocrystals (NCs) by a quantitative analysis of biexciton and exciton dynamics in transient photoluminescence decays. Interest in CM, the generation of more than one electron and hole in a semiconductor after absorption of one photon, has renewed in recent years because of reports suggesting greatly increased efficiencies in nanocrystalline materials compared to the bulk form, in which CM was otherwise too weak to be of consequence in photovoltaic energy conversion devices. In our PbSe and PbS NC samples, however, we estimate using transient photoluminescence that at most 0.25 additional e-h pairs are generated per photon even at energies hv > 5Eg, instead of the much higher values reported in the literature. We argue by comparing NC CM estimates and reported bulk values on an absolute energy basis, which we justify as appropriate on physical grounds, that the data reported thus far are inconclusive with respect to the importance of nanoscale-specific phenomena in the CM process.Comment: 10 pages, 7 figure

On the efficient Monte Carlo implementation of path integrals

We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Levy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Levy-Ciesielski implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.

Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations

The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily $\cal PT$-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5; final published versio