Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems

Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems may be treated in a similar framework as quasi/pseudo and/or PT-symmetric systems, which have recently attracted much attention. For a newly proposed deformation of exponential type we compute the minimal uncertainty and minimal length, which are essential in almost all approaches to quantum gravity

Strings from position-dependent noncommutativity

We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PTlike symmetries, i.e.antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two dimensional space is string like, i.e.having a fundamental length in one direction beyond which a resolution is impossible. Subsequently we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.Comment: 11 pages, Late

Dibaryons as axially symmetric skyrmions

Dibaryons configurations are studied in the framework of the bound state soliton model. A generalized axially symmetric ansatz is used to determine the soliton background. We show that once the constraints imposed by the symmetries of the lowest energy torus configuration are satisfied all spurious states are removed from the dibaryon spectrum. In particular, we show that the lowest allowed state in the $S=-2$ channel carries the quantum numbers of the H particle. We find that, within our approximations, this particle is slightly bound in the model. We discuss, however, that vacuum effects neglected in the present calculation are very likely to unbind the H.Comment: 24 pages, LaTeX, TAN-FNT-93-12 (it replaces old version which was truncated

Influence of nanoparticle encapsulation and encoding on the surface chemistry of polymer carrier beads

Surface-functionalized polymer beads encoded with molecular luminophores and nanocrystalline emitters such as semiconductor nanocrystals, often referred to as quantum dots (QDs), or magnetic nanoparticles are broadly used in the life sciences as reporters and carrier beads. Many of these applications require a profound knowledge of the chemical nature and total number of their surface functional groups (FGs), that control bead charge, colloidal stability, hydrophobicity, and the interaction with the environment and biological systems. For bioanalytical applications, also the number of groups accessible for the subsequent functionalization with, e.g., biomolecules or targeting ligands is relevant. In this study, we explore the influence of QD encoding on the amount of carboxylic acid (COOH) surface FGs of 2 µm polystyrene microparticles (PSMPs). This is done for frequently employed oleic acid and oleylamine stabilized, luminescent core/shell CdSe QDs and two commonly used encoding procedures. This included QD addition during bead formation by a thermally induced polymerization reaction and a post synthetic swelling procedure. The accessible number of COOH groups on the surface of QD-encoded and pristine beads was quantified by two colorimetric assays, utilizing differently sized reporters and electrostatic and covalent interactions. The results were compared to the total number of FGs obtained by a conductometric titration and Fourier transform infrared spectroscopy (FTIR). In addition, a comparison of the impact of QD and dye encoding on the bead surface chemistry was performed. Our results demonstrate the influence of QD encoding and the QD-encoding strategy on the number of surface FG that is ascribed to an interaction of the QDs with the carboxylic acid groups on the bead surface. These findings are of considerable relevance for applications of nanoparticle-encoded beads and safe-by-design concepts for nanomaterials

Influence of nanoparticle encapsulation and encoding on the surface chemistry of polymer carrier beads

Surface-functionalized polymer beads encoded with molecular luminophores and nanocrystalline emitters such as semiconductor nanocrystals, often referred to as quantum dots (QDs), or magnetic nanoparticles are broadly used in the life sciences as reporters and carrier beads. Many of these applications require a profound knowledge of the chemical nature and total number of their surface functional groups (FGs), that control bead charge, colloidal stability, hydrophobicity, and the interaction with the environment and biological systems. For bioanalytical applications, also the number of groups accessible for the subsequent functionalization with, e.g., biomolecules or targeting ligands is relevant. In this study, we explore the influence of QD encoding on the amount of carboxylic acid (COOH) surface FGs of 2 µm polystyrene microparticles (PSMPs). This is done for frequently employed oleic acid and oleylamine stabilized, luminescent core/shell CdSe QDs and two commonly used encoding procedures. This included QD addition during bead formation by a thermally induced polymerization reaction and a post synthetic swelling procedure. The accessible number of COOH groups on the surface of QD-encoded and pristine beads was quantified by two colorimetric assays, utilizing differently sized reporters and electrostatic and covalent interactions. The results were compared to the total number of FGs obtained by a conductometric titration and Fourier transform infrared spectroscopy (FTIR). In addition, a comparison of the impact of QD and dye encoding on the bead surface chemistry was performed. Our results demonstrate the influence of QD encoding and the QD-encoding strategy on the number of surface FG that is ascribed to an interaction of the QDs with the carboxylic acid groups on the bead surface. These findings are of considerable relevance for applications of nanoparticle-encoded beads and safe-by-design concepts for nanomaterials

Non-Hermitian Hamiltonians of Lie algebraic type

We analyse a class of non-Hermitian Hamiltonians, which can be expressed bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of Lie algebraic type. Demanding a real spectrum and the existence of a well defined metric, we systematically investigate the constraints these requirements impose on the coupling constants of the model and the parameters in the metric operator. We compute isospectral Hermitian counterparts for some of the original non-Hermitian Hamiltonian. Alternatively we employ a generalized Bogoliubov transformation, which allows to compute explicitly real energy eigenvalue spectra for these type of Hamiltonians, together with their eigenstates. We compare the two approaches.Comment: 27 page

't Hooft-Polyakov monopoles in non-Hermitian quantum field theory

We construct exact ’t Hooft-Polyakov monopole solutions in a non-Hermitian field theory with local non- Abelian SU(2) gauge symmetry and a modified antilinear CPT symmetry. The solutions are obtained in a fourfold Bogomolny-Prasad-Sommerfield scaling limit giving rise to two different types of monopole masses that saturate the lower energy bound. These two masses only coincide in the Hermitian limit and in the limit in which the symmetry breaking vacuum tends to the trivial symmetry preserving vacuum. In the two theories corresponding to the two known Dyson maps these two masses are exchanged, unlike the Higgs and the gauge masses, which remain the same in both theories. We identify three separate regions in parameter space bounded by different types of exceptional points. In the first region the monopole masses are finite and tend both to zero at the boundary exceptional point, in the second the monopole masses become complex and in the third only one of the monopole masses becomes zero at the boundary exceptional point, whereas the other tends to infinity. We find a self-dual point in parameter space at which the gauge mass becomes exactly identical to the monopole mass

Invertebrate neurophylogeny: suggested terms and definitions for a neuroanatomical glossary

<p>Abstract</p> <p>Background</p> <p>Invertebrate nervous systems are highly disparate between different taxa. This is reflected in the terminology used to describe them, which is very rich and often confusing. Even very general terms such as 'brain', 'nerve', and 'eye' have been used in various ways in the different animal groups, but no consensus on the exact meaning exists. This impedes our understanding of the architecture of the invertebrate nervous system in general and of evolutionary transformations of nervous system characters between different taxa.</p> <p>Results</p> <p>We provide a glossary of invertebrate neuroanatomical terms with a precise and consistent terminology, taxon-independent and free of homology assumptions. This terminology is intended to form a basis for new morphological descriptions. A total of 47 terms are defined. Each entry consists of a definition, discouraged terms, and a background/comment section.</p> <p>Conclusions</p> <p>The use of our revised neuroanatomical terminology in any new descriptions of the anatomy of invertebrate nervous systems will improve the comparability of this organ system and its substructures between the various taxa, and finally even lead to better and more robust homology hypotheses.</p

Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type

We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra

Unmanned Aerial Systems for Investigating the Polar Atmospheric Boundary Layer—Technical Challenges and Examples of Applications

Unmanned aerial systems (UAS) fill a gap in high-resolution observations of meteorological parameters on small scales in the atmospheric boundary layer (ABL). Especially in the remote polar areas, there is a strong need for such detailed observations with different research foci. In this study, three systems are presented which have been adapted to the particular needs for operating in harsh polar environments: The fixed-wing aircraft M2AV with a mass of 6 kg, the quadrocopter ALICE with a mass of 19 kg, and the fixed-wing aircraft ALADINA with a mass of almost 25 kg. For all three systems, their particular modifications for polar operations are documented, in particular the insulation and heating requirements for low temperatures. Each system has completed meteorological observations under challenging conditions, including take-offand landing on the ice surface, low temperatures (down to-28 °C), icing, and, for the quadrocopter, under the impact of the rotor downwash. The influence on the measured parameters is addressed here in the form of numerical simulations and spectral data analysis. Furthermore, results from several case studies are discussed: With the M2AV, low-level flights above leads in Antarctic sea ice were performed to study the impact of areas of open water within ice surfaces on the ABL, and a comparison with simulations was performed. ALICE was used to study the small-scale structure and short-term variability of the ABL during a cruise of RV Polarstern to the 79° N glacier in Greenland. With ALADINA, aerosol measurements of different size classes were performed in Ny-Alesund, Svalbard, in highly complex terrain. In particular, very small, freshly formed particles are difficult to monitor and require the active control of temperature inside the instruments. The main aim of the article is to demonstrate the potential of UAS for ABL studies in polar environments, and to provide practical advice for future research activities with similar systems. © 2020 by the authors