4,664 research outputs found
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
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
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 0.1â0.2%. 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
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 -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 -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
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