scholarly journals Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity

Author(s):  
Boris F. Samsonov

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Mehmet Sahin ◽  
Manaf Dzh. Manafov

We study some spectral problems for a second-order differential operator with periodic potential. Notice that the given potential is a sum of zero- and first-order generalized functions. It is shown that the spectrum of the investigated operator consists of infinite number of gaps whose length limit unlike the classic case tends to nonzero constant in some place and to infinity in other place.


2020 ◽  
Vol 310 ◽  
pp. 00010
Author(s):  
Iveta Hegedüsová ◽  
Sergej Priganc

The subject matter of the contribution is findings obtained from a parametric simulation of ceiling panels behaviour under a change of determined parameters. The optional parameters included concrete strength, reinforcement cross-section area, and concrete covering. The experiment investigated an impact of the given parameters changes onto the element resistance which was evaluated on the basis of the ultimate state of usability, namely from the point of view of crack checking and deflection measuring. Panel behaviour was presented by a load-deflection relation and crack topography


Author(s):  
Ирина Викторовна Евстафьева

В статье исследуются вопросы попечительства в отношении несовершеннолетних, отбывающих наказание в виде лишения свободы. Проблема, поднимаемая автором настоящей статьи, многогранна, касается различных аспектов отбывания наказания несовершеннолетними в воспитательных колониях и требует комплексного исследования, способного ответить на определенно значимый вопрос: является ли колония законным представителем находящихся в ней несовершеннолетних со всеми вытекающими из статуса законных представителей последствиями. При этом необходимо обращать внимание на специфику правового статуса лиц, отбывающих наказание в воспитательных колониях, которые, во-первых, являются несовершеннолетними, то есть не обладают дееспособностью в полном объеме и нуждаются в особой заботе, защите и представительстве, а во-вторых, осуждены за совершение тяжкого или особо тяжкого преступления, влекущего изоляцию от общества и определенные ограничения и лишения. Отечественное законодательство достаточно детально регламентирует особенности режима отбывания наказания в виде лишения свободы несовершеннолетними, не определяя при этом статуса воспитательных колоний, кем они являются: воспитателями, попечителями или исключительно учреждениями исполнения наказаний. Между тем правильное понимание значения и роли воспитательной колонии в жизни находящихся в ней несовершеннолетних преступников, по мнению автора, поможет избежать ряда проблем, объективно складывающихся в учреждениях подобного рода. С этой точки зрения предлагаемая тема представляет интерес не только для ученых-теоретиков, но и для практиков - сотрудников соответствующих учреждений. Особо следует подчеркнуть, что исследований по данной тематике в специальной литературе нет. Отдельные исследования, встречающиеся в современной литературе, касаются исключительно общего гражданско-правового статуса несовершеннолетних осужденных. Однако это обстоятельство может свидетельствовать только о новизне данной темы, но никак не об отсутствии самой проблемы. The article analyzes the issues of the status of educational colonies as guardians of minors serving a sentence of imprisonment. In fact, the problem raised by the author of this article is multifaceted, concerns various aspects of the serving of punishment by minors in educational colonies and requires a comprehensive study that can answer, it seems, a definitely significant question: whether the colony is the legal representative of the minors in it with all the consequences arising from the status of legal representatives in the form of duties and responsibilities. At the same time, it seems, it is necessary to pay attention to the specifics of the legal status of citizens serving sentences in educational colonies, who, firstly, are minors, i.e. do not have full legal capacity and need special care, protection and representation, and, secondly, are convicted of committing a serious or particularly serious crime, entailing isolation from society and certain restrictions and deprivation. Domestic legislation regulates in sufficient detail the peculiarities of the regime of serving sentences in the form of deprivation of liberty by minors, without determining the status of educational colonies. Who are they: educators, Trustees or only institutions of execution of punishments. Meanwhile, the correct understanding of the importance and role of the educational colony in the life of juvenile offenders in it, according to the author, will help to avoid a number of problems that objectively develop in institutions of this kind. From this point of view, the proposed topic is of interest not only for theoretical scientists, but for practitioners-employees of relevant institutions. It should be emphasized that there are no studies on this subject in the special literature. However, this circumstance can testify only about novelty of the given subject, but in any way about absence of the problem. It seems that the relevance and importance of a problem is not always measured by the number of studies devoted to it. Sometimes these its traits are manifest only under particularly careful consideration.


Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 755
Author(s):  
Grebenikov Viktor ◽  
Oleksandr Dobzhanskyi ◽  
Gamaliia Rostislav ◽  
Rupert Gouws

This paper presents analysis and study of the single-phase transverse-flux machine. The finite element method results of the machine are compared with the laboratory measurements to confirm the accuracy of the computer model. This computer model is then used to investigate the effect of the machine’s geometry on its output characteristics. Parametric analysis of the machine is carried out to find the optimal air-gap diameter at which the cogging torque of the machine is minimal. In addition, the influence of the coil cross-section on the torque and output power characteristics of the machine is investigated and discussed.


2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.


2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.


2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryuya Namba

AbstractModerate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.


Author(s):  
Jean Vignon Hounguevou ◽  
Daniel Sabi Takou ◽  
Gabriel Y. H. Avossevou

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.


2019 ◽  
Vol 23 (01) ◽  
pp. 1950080
Author(s):  
D. I. Borisov ◽  
P. Exner

We present a new method of gap control in two-dimensional periodic systems with the perturbation consisting of a second-order differential operator and a family of narrow potential “walls” separating the period cells in one direction. We show that under appropriate assumptions one can open gaps around points determined by dispersion curves of the associated “waveguide” system, in general any finite number of them, and to control their widths in terms of the perturbation parameter. Moreover, a distinctive feature of those gaps is that their edge values are attained by the corresponding band functions at internal points of the Brillouin zone.


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