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Man'ko S.S.,Ivan Franko National University of Lviv
Journal of Physics A: Mathematical and Theoretical | Year: 2010

We discuss the potential scattering on the noncompact star graph. The Schrödinger operator with the short-range potential localized in a neighborhood of the graph vertex is considered. We study the asymptotic behavior of the corresponding scattering matrix in the zero-range limit. It has been known for a long time that in dimension 1 there is no non-trivial Hamiltonian with the distributional potential δ', i.e. the δ' potential acts as a totally reflecting wall. Several authors have, in recent years, studied the scattering properties of the regularizing potentials αε -2Q(x/ε) approximating the first derivative of the Dirac delta function. A non-zero transmission through the regularized potential has been shown to exist as ε → 0. We extend these results to star graphs with the point interaction, which is an analog of the δ' potential on the line. We prove that generically such a potential on the graph is opaque. We also show that there exists a countable set of resonant intensities for which a partial transmission through the potential occurs. This set of resonances is referred to as the resonant set and is determined as the spectrum of an auxiliary Sturm-Liouville problem associated with Q on the graph. © 2010 IOP Publishing Ltd.


Rovenchak A.,Ivan Franko National University of Lviv
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2014

A two-parameter fractional statistics is proposed, which can be used to model a weakly interacting Bose system. It is shown that the parameters of the introduced weakly nonadditive Polychronakos statistics can be linked to the effects of interactions as well as to finite-size corrections. Calculations are made of the specific heat and condensate fraction of the model system corresponding to harmonically trapped Rb-87 atoms. The behavior of the specific heat of three-dimensional isotropic harmonic oscillators with respect tothe statistics parameters is studied in the temperature domain including the BEC-like phase-transition point. © 2014 American Physical Society.


Gnatenko K.P.,Ivan Franko National University of Lviv
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2013

The motion of a composite system made of N particles is examined in a space with a canonical noncommutative algebra of coordinates. It is found that the coordinates of the center-of-mass position satisfy noncommutative algebra with effective parameter. Therefore, the upper bound of the parameter of noncommutativity is re-examined. We conclude that the weak equivalence principle is violated in the case of a non-uniform gravitational field and propose the condition for the recovery of this principle in noncommutative space. Furthermore, the same condition is derived from the independence of kinetic energy on the composition. © 2013 Elsevier B.V.


Rovenchak A.,Ivan Franko National University of Lviv
Journal of Physics: Conference Series | Year: 2012

A generalization of quantum statistics is proposed in a fashion similar to the suggestion of Polychronakos [Phys. Lett. B 365, 202 (1996)] with the parameter α varying between -1 (fermionic case) and +1 (bosonic case). However, unlike the original formulation, it is suggested that intermediate values are located on the unit circle in the complex plane. In doing so one can avoid the case α = 0 corresponding to the Boltzmann statistics, which is not a quantum one. The limits of α → +1 and α → -1 reproducing small deviations from the Bose and Fermi statistics, respectively, are studied in detail. The equivalence between the statistics parameter and a possible dissipative part of the excitation spectrum is established. The case of a non-conserving number of excitations is analyzed. It is defined from the condition that the real part of the chemical potential equals zero. Thermodynamic quantities of a model system of two-dimensional harmonic oscillators are calculated. © Published under licence by IOP Publishing Ltd.


Tkachuk V.M.,Ivan Franko National University of Lviv
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2012

Studies in string theory and quantum gravity lead to the generalized uncertainty principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. The first look on the classical motion of bodies in a space with corresponding deformed Poisson brackets in a uniform gravitational field can give an impression that bodies of different mass fall in different ways and, thus, the equivalence principle is violated. Analyzing the kinetic energy of a composite body, we find that the motion of its center of mass in the deformed space depends on some effective parameter of deformation. It gives a possibility to recover the equivalence principle in the space with deformed Poisson brackets and, thus, GUP is reconciled with the equivalence principle. We also show that the independence of kinetic energy on composition leads to the recovering of the equivalence principle in the space with deformed Poisson brackets. © 2012 American Physical Society.


Rovenchak A.,Ivan Franko National University of Lviv
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2014

A system of isotropic harmonic oscillators obeying the Polychronakos fractional statistics with a complex parameter in a space having the dimension D>1 is studied. Temperature dependences of the thermodynamic functions are analyzed in different temperature domains. The nature of the observed phase transitions is clarified. Both numerical and analytical estimates for the critical temperature are made depending on the number of particles, space dimensionality, and statistics parameter. Approximate correspondence with some other fractional statistics types is established. © 2013 Elsevier B.V. All rights reserved.


Stetsko M.M.,Ivan Franko National University of Lviv
International Journal of Modern Physics A | Year: 2013

We investigate a microscopic black hole in the case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that the incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole. Minimal temperature gives rise to appearance of a phase transition. Emission rate equation and black hole's evaporation time are also obtained. © World Scientific Publishing Company.


Olenych I.B.,Ivan Franko National University of Lviv
Ukrainian Journal of Physical Optics | Year: 2011

Using photoluminescence and infrared spectroscopy techniques, we have investigated the influence of surface molecular composition of porous silicon (PS) on the character of its photoluminescence spectra. The main absorption bands of PS in the infrared spectral range are found to be caused by hydride passivation of silicon nanocrystals, adsorption of water molecules and hydroxyl groups during the process of PS formation, as well as by the adsorption of oxygen and carbon due to oxidation of PS. Additional absorption bands found for PS-polyaniline composites are caused by oscillations of molecules that make up the structural polymer chains. The physical and chemical conditions needed for improving photoluminescence stability by means of passivating the PS surface by oxygen and polymer films are substantiated.


Quesne C.,Free University of Colombia | Tkachuk V.M.,Ivan Franko National University of Lviv
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2010

For composite systems made of N different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first order in the deformation parameters. Such operators satisfy the deformed algebra with effective deformation parameters. As a consequence, a two-particle system can be reduced to a one-particle problem for the internal motion. As an example, the correction to the hydrogen atom nS energy levels is re-evaluated. Comparison with high-precision experimental data leads to an upper bound of the minimal length for the electron equal to 3.3×10-18 m. The effective Hamiltonian describing the center-of-mass motion of a macroscopic body in an external potential is also found. For such a motion, the effective deformation parameter is substantially reduced due to a factor 1/N2. This explains the strangely small result previously obtained for the minimal length from a comparison with the observed precession of the perihelion of Mercury. From our study, an upper bound of the minimal length for quarks equal to 2.4×10-17 m is deduced, which appears close to that obtained for electrons. © 2010 The American Physical Society.


Makitrynskyy R.,Ivan Franko National University of Lviv
Open biology | Year: 2013

Unlike the majority of actinomycete secondary metabolic pathways, the biosynthesis of peptidoglycan glycosyltransferase inhibitor moenomycin in Streptomyces ghanaensis does not involve any cluster-situated regulators (CSRs). This raises questions about the regulatory signals that initiate and sustain moenomycin production. We now show that three pleiotropic regulatory genes for Streptomyces morphogenesis and antibiotic production-bldA, adpA and absB-exert multi-layered control over moenomycin biosynthesis in native and heterologous producers. The bldA gene for tRNA(Leu)UAA is required for the translation of rare UUA codons within two key moenomycin biosynthetic genes (moe), moeO5 and moeE5. It also indirectly influences moenomycin production by controlling the translation of the UUA-containing adpA and, probably, other as-yet-unknown repressor gene(s). AdpA binds key moe promoters and activates them. Furthermore, AdpA interacts with the bldA promoter, thus impacting translation of bldA-dependent mRNAs-that of adpA and several moe genes. Both adpA expression and moenomycin production are increased in an absB-deficient background, most probably because AbsB normally limits adpA mRNA abundance through ribonucleolytic cleavage. Our work highlights an underappreciated strategy for secondary metabolism regulation, in which the interaction between structural genes and pleiotropic regulators is not mediated by CSRs. This strategy might be relevant for a growing number of CSR-free gene clusters unearthed during actinomycete genome mining.

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