555 research outputs found
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
When several inequivalent supercharges form a closed superalgebra in Quantum
Mechanics it entails the appearance of hidden symmetries of a
Super-Hamiltonian. We examine this problem in one-dimensional QM for the case
of periodic potentials and potentials with finite number of bound states. After
the survey of the results existing in the subject the algebraic and analytic
properties of hidden-symmetry differential operators are rigorously elaborated
in the Theorems and illuminated by several examples
Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
Resolutions of identity for certain non-Hermitian Hamiltonians constructed
from biorthogonal sets of their eigen- and associated functions are given for
the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under
consideration possess the continuous spectrum and the following peculiarities
are investigated: (1) the case when there is an exceptional point of arbitrary
multiplicity situated on a boundary of continuous spectrum; (2) the case when
there is an exceptional point situated inside of continuous spectrum. The
reductions of the derived resolutions of identity under narrowing of the
classes of employed test functions are revealed. It is shown that in the case
(1) some of associated functions included into the resolution of identity are
normalizable and some of them may be not and in the case (2) the bounded
associated function corresponding to the exceptional point does not belong to
the physical state space. Spectral properties of a SUSY partner Hamiltonian for
the Hamiltonian with an exceptional point are examined
Perfectly conducting incompressible fluid model of a wire array implosion
An incompressible perfectly conducting magnetohydrodynamic model is applied to describe a multiwire array implosion on the (r,θ)(r,θ) plane using the theory of analytic functions. The plasma columns emerging from the electrical explosion of individual wires move and change the shape of their cross section in the magnetic field produced by the currents flowing on the surfaces of the columns and closing through a cylindrical return current can. Geometry of both the “global” and “private” magnetic fields and self-consistent distributions of the electric currents on the conducting surfaces are determined for any wire array configuration including nested wire arrays, wires close to the return current can, etc. The coupled equations of motion and magnetostatics for an essentially two-dimensional problem are reduced to one-dimensional parametric governing equations, written for the boundary of the fluid contours. The implosion dynamics is shown to be driven by a competition between the implosion pressure, making the array converge to the axis as a set of individual plasma columns, and the tidal pressure that makes the wires merge, forming an annular conducting shell. Their relative roles are determined by the gap-to-diameter ratio πRc(t)/NRw(t).πRc(t)/NRw(t). If this ratio is large at early time, then the array implodes as a set of individual plasma columns. Otherwise, when the ratio is about π or less, the tidal forces prevail, and the plasma columns tend to form a shell-like configuration before they start converging to the axis of the array. The model does not allow the precursor plasma streams to be ejected from the wires to the axis, indicating that this process is governed by the finite plasma conductivity and could only be described with a proper conductivity model. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70839/2/PHPAEN-9-4-1366-1.pd
Relaxation Properties of Small-World Networks
Recently, Watts and Strogatz introduced the so-called small-world networks in
order to describe systems which combine simultaneously properties of regular
and of random lattices. In this work we study diffusion processes defined on
such structures by considering explicitly the probability for a random walker
to be present at the origin. The results are intermediate between the
corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure
Bound-state beta-decay of a neutron in a strong magnetic field
The beta-decay of a neutron into a bound state and an antineutrino
in the presence of a strong uniform magnetic field ( G) is
considered. The beta-decay process is treated within the framework of the
standard model of weak interactions. A Bethe-Salpeter formalism is employed for
description of the bound system in a strong magnetic field. For the
field strengths G G the estimate for the
ratio of the bound-state decay rate and the usual (continuum-state) decay
rate is derived. It is found that in such strong magnetic fields . This is in contrast to the field-free case, where [J. N. Bahcall, Phys. Rev. {\bf 124}, 495 (1961); L.
L. Nemenov, Sov. J. Nucl. Phys. {\bf 15}, 582 (1972); X. Song, J. Phys. G:
Nucl. Phys. {\bf 13}, 1023 (1987)]. The dependence of the ratio on
the magnetic field strength exhibits a logarithmic-like behavior. The
obtained results can be important for applications in astrophysics and
cosmology.Comment: 22 pages (revtex4), 1 figure; v2: more detailed discussion on
astrophysical applications in conclusion section, accepted for publication in
Phys. Rev.
Modeling of the Lattice Dynamics in Strontium Titanate Films of Various Thicknesses: Raman Scattering Studies
This paper is partly based upon COST (European Cooperation in Science and Technology) Action 18234 (E.A.K., M.S., and V.K.) and financially supported by FLAG-ERA JTC project To2Dox (Y.A.M). The Institute of Solid State Physics, University of Latvia (Latvia), as the Centre of Excellence has received funding from the European Union’s Horizon 2020 Frame-work Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase2 under grant agreement No. 739508, project CAMART2. The computer resources were provided by the High-Performance Computing Centre Stuttgart (HLRS project DEFTD 12939). In addition, the research of V.K. and A.P. was partly supported by the RADON project (GA 872494) within the H2020-MSCA-RISE-2019 call.While the bulk strontium titanate (STO) crystal characteristics are relatively well known, ultrathin perovskites’ nanostructure, chemical composition, and crystallinity are quite complex and challenging to understand in detail. In our study, the DFT methods were used for modelling the Raman spectra of the STO bulk (space group I4/mcm) and 5–21-layer thin films (layer group p4/mbm) in tetragonal phase with different thicknesses ranging from ~0.8 to 3.9 nm. Our calculations revealed features in the Raman spectra of the films that were absent in the bulk spectra. Out of the seven Raman-active modes associated with bulk STO, the frequencies of five modes (2Eg, A1g, B2g, and B1g) decreased as the film thickness increased, while the low-frequency B2g and higher-frequency Eg modes frequencies increased. The modes in the films exhibited vibrations with different amplitudes in the central or surface parts of the films compared to the bulk, resulting in frequency shifts. Some peaks related to bulk vibrations were too weak (compared to the new modes related to films) to distinguish in the Raman spectra. However, as the film thickness increased, the Raman modes approached the frequencies of the bulk, and their intensities became higher, making them more noticeable in the Raman spectrum. Our results could help to explain inconsistencies in the experimental data for thin STO films, providing insights into the behavior of Raman modes and their relationship with film thickness. © 2023 by the authors. --//-- Krasnenko V., Platonenko A., Liivand A., Rusevich L.L., Mastrikov Y.A., Zvejnieks G., Sokolov M., Kotomin E.A.; Modeling of the Lattice Dynamics in Strontium Titanate Films of Various Thicknesses: Raman Scattering Studies; (2023) Materials, 16 (18), art. no. 6207; DOI: 10.3390/ma16186207; https://www.scopus.com/inward/record.uri?eid=2-s2.0-85172725318&doi=10.3390%2fma16186207&partnerID=40&md5=32f343f9cb8da145c6647566cb534c32. Published under the CC BY 4.0 license.COST Action 18234 and FLAG-ERA JTC project To2Dox. The Institute of Solid State Physics, University of Latvia (Latvia), as the Centre of Excellence has received funding from the European Union’s Horizon 2020 Frame-work Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase2 under grant agreement No. 739508, project CAMART2. HLRS project DEFTD 12939. RADON project (GA 872494) within the H2020-MSCA-RISE-2019 call
Quantum transport on two-dimensional regular graphs
We study the quantum-mechanical transport on two-dimensional graphs by means
of continuous-time quantum walks and analyse the effect of different boundary
conditions (BCs). For periodic BCs in both directions, i.e., for tori, the
problem can be treated in a large measure analytically. Some of these results
carry over to graphs which obey open boundary conditions (OBCs), such as
cylinders or rectangles. Under OBCs the long time transition probabilities
(LPs) also display asymmetries for certain graphs, as a function of their
particular sizes. Interestingly, these effects do not show up in the marginal
distributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.
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