Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space

In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is $\frak{so}(3,1)$ and the SGA is $\frak{so}(4,2)$. We start with a representation of $\frak{so}(4,2)$ by functions on a realization of the Lobachevski space given by a two sheeted hyperboloid, where the Lie algebra commutators are the usual Poisson-Dirac brackets. Then, introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and "naive" ladder operators are identified. The previously defined "naive" ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non self-adjoint function of a linear combination of the ladder operators which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of two sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.Comment: 23 page

Magnetic and electric dipole moments of the H 3Δ1H\ {}^3\Delta_1 state in ThO

The metastable $H \ {}^3\Delta_1$ state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a CP-violating permanent electric dipole moment of the electron (eEDM). The magnetic dipole moment $\mu_H$ and the molecule-fixed electric dipole moment $D_H$ of this state are measured in preparation for a search for the eEDM. The small magnetic moment $\mu_H = 8.5(5) \times 10^{-3} \ \mu_B$ displays the predicted cancellation of spin and orbital contributions in a ${}^3 \Delta_1$ paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields ($<$ 10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment.Comment: 4 pages, 3 figure

Quantum-Classical Correspondence of Dynamical Observables, Quantization and the Time of Arrival Correspondence Problem

We raise the problem of constructing quantum observables that have classical counterparts without quantization. Specifically we seek to define and motivate a solution to the quantum-classical correspondence problem independent from quantization and discuss the general insufficiency of prescriptive quantization, particularly the Weyl quantization. We demonstrate our points by constructing time of arrival operators without quantization and from these recover their classical counterparts

Radiative decays of quarkonium states, momentum operator expansion and nilpotent operators

We present the method of calculation of radiative decays of composite quark-antiquark systems with different J^{PC}: (Q\bar Q)_{in} -> gamma (Q\bar Q)_{out}. The method is relativistic invariant, it is based on the double dispersion relation integrals over the masses of composite mesons, it can be used for the high spin particles and provides us with the gauge invariant transition amplitudes. We apply this method to the case when the photon is emitted by a constituent in the intermediate state (additive quark model). We perform the momentum operator expansion of the spin amplitudes for the decay processes. The problem of nilpotent spin operators is discussed.Comment: 21 pages, 1 figur

Relativistic Quantum Thermodynamics of Ideal Gases in 2 Dimensions

In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.Comment: 6 pages, 1 figur

Neurotensin(8–13) analogs as dual NTS1 and NTS2 receptor ligands with enhanced effects on a mouse model of Parkinson's disease

: The modulatory interactions between neurotensin (NT) and the dopaminergic neurotransmitter system in the brain suggest that NT may be associated with the progression of Parkinson's disease (PD). NT exerts its neurophysiological effects by interactions with the human NT receptors type 1 (hNTS1) and 2 (hNTS2). Therefore, both receptor subtypes are promising targets for the development of novel NT-based analogs for the treatment of PD. In this study, we used a virtually guided molecular modeling approach to predict the activity of NT(8-13) analogs by investigating the docking models of ligands designed for binding to the human NTS1 and NTS2 receptors. The importance of the residues at positions 8 and/or 9 for hNTS1 and hNTS2 receptor binding affinity was experimentally confirmed by radioligand binding assays. Further in vitro ADME profiling and in vivo studies revealed that, compared to the parent peptide NT(8-13), compound 10 exhibited improved stability and BBB permeability combined with a significant enhancement of the motor function and memory in a mouse model of PD. The herein reported NTS1/NTS2 dual-specific NT(8-13) analogs represent an attractive tool for the development of therapeutic strategies against PD and potentially other CNS disorders

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We have promoted a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw's particles with the same chirality which spectrum is a vacuum-like one. As another conflictive result we have proved that a Wess-Zumino term used in the literature consists of the scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system.Comment: 6 pages, Revtex. Final version to appear in Physical Review

Hamilton-Jacobi treatment of a non-relativistic particle on a curved space

In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.Comment: 10 pages, LaTe

Spin physics with antiprotons

New possibilities arising from the availability at GSI of antiproton beams, possibly polarised, are discussed. The investigation of the nucleon structure can be boosted by accessing in Drell-Yan processes experimental asymmetries related to cross-sections in which the parton distribution functions (PDF) only appear, without any contribution from fragmentation functions; such processes are not affected by the chiral suppression of the transversity function $h_1(x)$. Spin asymmetries in hyperon production and Single Spin Asymmetries are discussed as well, together with further items like electric and magnetic nucleonic form factors and open charm production. Counting rates estimations are provided for each physical case. The sketch of a possible experimental apparatus is proposed.Comment: Presented for the proceedings of ASI "Spin and Symmetry", Prague, July 5-10, 2004, to be published in Czech. J. Phys. 55 (2005

Исследование аномально высокого времени релаксации фототока в диодах Шоттки на основе a-Ga2O3

Ga2O3 is an ultra-wideband material with excellent optical characteristics. It is a promising material for power applications and optoelectronics because of its high electrical breakdown voltage and radiation hardness. It is optically transparent for visible light and UVA but UVC-sensitive. One of the main disadvantages of this material is the anomalous slow photoeffect: photoconductivity rise and decay characteristic times can be more than hundreds of seconds long. This "slow" photoconductivity effect severely limits the utilisation of the Ga2O3-based devices. The aim of this work is the investigation of the nature of this effect. The results of the photoinduced current rise and decay under 530 nm and 259 nm LED are measured in the HVPE-grown α-Ga2O3-based Schottky diode. Upon UV-illumination the photocurrent rise consists of three parallel processes: fast signal growth, slow growth and very slow decay with characteristic times near 70 ms, 40 s and 300 s respectively. Subsequent 530 nm LED illumination resulted in photoinduced current rise consisting of two mechanisms with characterisatic times 130 ms and 40 s on which a very slow decrease of the photocurrent amplitude with characteristic time of 1500 s was superimposed. 530 nm illumination stimulates this process. Protoinduced current relaxation analysis shows the presence of the deep levels with energies (EC - 0.17 eV). It is suggested that extremely slow relaxations can be associated with potential fluctuations near the Schottky barrier.Ga2O3 — широкозонный материал с рядом уникальных характеристик, которые делают его перспективным материалом фотоники: он оптически прозрачен для оптического и ближнего ультрафиолетового излучения, обладает высокими значениями пробивных напряжений и высокой радиационной стойкостью. Одним из недостатков, которые в настоящее время препятствуют использованию данного материала в солнечно-слепых фотодетекторах, является аномально большое время нарастания и спада фотопроводимости, которое может достигать сотен секунд. Такая «замедленная» фотопроводимость существенно ограничивает область применения этих материалов. Проведены исследования природы этого эффекта. Выполнены измерения времени нарастания и спада фотоиндуцированного тока в диодах Шотки на основе α-Ga2O3, выращенных методом HVPE на сапфире, при засветке светодиодами с длиной волны 259 и 530 нм. При засветке ультрафиолетовым излучением рост тока через фоточувствительную структуру из двух встречных диодов происходил в три этапа: достаточно быстрое нарастание с характерным временем 70 мс, медленный рост с характерным временем 40 с и затянутый спад с характерным временем порядка 300 с. При последующей засветке излучением зеленого цвета рост тока с характерным временем 130 мс и 40 с накладывался на стимулируемый засветкой медленный спад амплитуды максимального тока с характерным временем порядка 1500 с. Анализ релаксации тока показал наличие глубоких центров с энергией (EC – 0,17 эВ). Существенное замедление релаксации фотоиндуцированного тока можно связать с флуктуациями потенциала вблизи барьера Шотки