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Sadreev, A. F.
S-matrix formalism of transmission through two quantum billiards coupled by a waveguide / A. F. Sadreev, E. N. Bulgakov, I. . Rotter // J. Phys. A. - 2005. - Vol. 38, Is. 49. - P. 10647-10661, DOI 10.1088/0305-4470/38/49/012. - Cited References: 32 . - ISSN 0305-4470

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
CIRCULAR BENDS
   DOTS
   TRANSPORT
   CONTINUUM
   SYSTEMS
   STATES
Аннотация: We consider a system that consists of two single-quantum billiards (QBs) coupled by a waveguide and study the transmission through this system as a function of length and width of the waveguide. To interpret the numerical results for the transmission, we explore a simple model with a small number of states which allows us to consider the problem analytically. The transmission is described in the S-matrix formalism by using the non-Hermitian effective Hamilton operator for the open system. The coupling of the single QBs to the internal waveguide characterizes the 'internal' coupling strength u of the states of the system while that of the system as a whole to the attached leads determines the 'external' coupling strength v of the resonance states via the continuum (waves in the leads). The transmission is resonant for all values of v/u in relation to the effective Hamiltonian. It depends strongly on the ratio u/u via the eigenvalues and eigenfunctions of the effective Hamiltonian. The results obtained are compared qualitatively with those from simulation calculations for larger systems. Most interesting is the existence of resonance states with vanishing widths that may appear at all values of v/u. They cause zeros in the transmission through the double QB due to trapping of the particle in the waveguide.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
ИФ СО РАН
Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, S-581 83 Linkoping, Sweden
Max-Planck-Institut fur Physik Komplexer Systeme, D-01187 Dresden, Germany

Доп.точки доступа:
Bulgakov, E. N.; Булгаков, Евгений Николаевич; Rotter, I.; Садреев, Алмаз Фаттахович
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Bulgakov, E. N.
Electric circuit networks equivalent to chaotic quantum billiards / E. N. Bulgakov, D. N. Maksimov, A. F. Sadreev // Phys. Rev. E. - 2005. - Vol. 71, Is. 4. - Ст. 46205, DOI 10.1103/PhysRevE.71.046205. - Cited References: 31 . - ISSN 1063-651X

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
TIME-REVERSAL SYMMETRY
   CONDUCTANCE FLUCTUATIONS
   STATISTICS
   SYSTEMS
   EIGENFUNCTIONS
   DOTS
Кл.слова (ненормированные):
Chaotic quantum billiards -- Electric resonance circuits (ERC) -- Resonance networks -- Wave functions -- Boundary conditions -- Capacitors -- Chaos theory -- Eigenvalues and eigenfunctions -- Electric inductors -- Natural frequencies -- Quantum theory -- Resonance -- Statistical mechanics -- Networks (circuits)
Аннотация: We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.

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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
Astafev Pedag Univ, Krasnoyarsk 660049, Russia
ИФ СО РАН
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation
Dept. of Physics and Measurement, Technology Linkoping University, 5-557 83 Linkoping, Sweden
Astaf'Ev Pedagogical University, 89, Krasnoyarsk, 660049 Lebedeva, Russian Federation

Доп.точки доступа:
Maksimov, D. N.; Максимов, Дмитрий Николаевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Булгаков, Евгений Николаевич
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Conductance of open quantum billiards and classical trajectories / R. G. Nazmitdinov [et al.] // Phys. Rev. B. - 2002. - Vol. 66, Is. 8. - Ст. 85322, DOI 10.1103/PhysRevB.66.085322. - Cited References: 46 . - ISSN 1098-0121

РУБ Physics, Condensed Matter
Рубрики:
BALLISTIC MICROSTRUCTURES
   CHAOTIC SCATTERING
   FLUCTUATIONS
   DOTS
   TRANSPORT
   DYNAMICS
   STATES
   MAGNETOTRANSPORT
   STATISTICS
   RESONANCES
Аннотация: We analyze the transport phenomena of two-dimensional quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner in which the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes and bouncing ball modes. In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.

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Держатели документа:
Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany
Joint Inst Nucl Res, Dubna 141980, Russia
Acad Sci Czech Republ, Inst Phys, Prague 16253, Czech Republic
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Univ Hradec Kralove, Dept Phys, Hradec Kralove 50003, Czech Republic
ИФ СО РАН

Доп.точки доступа:
Nazmitdinov, R. G.; Pichugin, K. N.; Пичугин, Константин Николаевич; Rotter, I.; Seba, P.
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    Atypical quantum confinement effect in silicon nanowires / P. B. Sorokin [et al.] // J. Phys. Chem. A. - 2008. - Vol. 112, Is. 40. - P9955-9964, DOI 10.1021/jp805069b. - Cited Reference Count: 25. - Гранты: This work was in part partially supported by a CREST (Core Research for Evolutional Science and Technology) grant in the Area of High Performance Computing for Multiscale and Multiphysics Phenomena from the Japan Science and Technology Agency (JST) as well as by Russian Fund of Basic Researches (grant 08-02-01096) (L.A.C.). P.V.A. acknowledges the encouragement of Dr. Keiji Morokuma, Research Leader at Fukui Institute for Fundamental Chemistry. The geometry of all presented structures was visualized by ChemCraft software.SUP25/SUP L.A.C. acknowledges I. V. Stankevich for help and fruitful discussions. P.B.S. is grateful to the Joint Supercomputer Center of the Russian Academy of Sciences for access to a cluster computer for quantum-chemical calculations. - Финансирующая организация: Japan Science and Technology Agency (JST); Russian Fund of Basic Researches [08-02-01096] . - OCT 9. - ISSN 1089-5639
Рубрики:
ELECTRONIC-STRUCTURE
   OPTICAL-PROPERTIES
   SI
   DENSITY
   WIRES
   EXCHANGE
   ATOMS
   DOTS
Кл.слова (ненормированные):
Electric wire -- Energy gap -- Gallium alloys -- Mathematical models -- Nanostructured materials -- Nanostructures -- Nanowires -- Quantum confinement -- Quantum electronics -- Semiconductor quantum dots -- Silicon -- Ami methods -- Band gaps -- Blue shifts -- Dinger equations -- Linear junctions -- Monotonic decreases -- Quantum confinement effects -- Quantum dots -- Semiempirical -- Silicon nanowires -- System sizes -- Theoretical models -- Nanocrystalline silicon -- nanowire -- quantum dot -- silicon -- article -- chemistry -- electron -- quantum theory -- Electrons -- Nanowires -- Quantum Dots -- Quantum Theory -- Silicon
Аннотация: The quantum confinement effect (QCE) of linear junctions of silicon icosahedral quantum dots (IQD) and pentagonal nanowires (PNW) was studied using DFT and semiempirical AM1 methods. The formation of complex IQD/PNW structures leads to the localization of the HOMO and LUMO on different parts of the system and to a pronounced blue shift of the band gap; the typical QCE with a monotonic decrease of the band gap upon the system size breaks down. A simple one-electron one-dimensional Schrodinger equation model is proposed for the description and explanation of the unconventional quantum confinement behavior of silicon IQD/PNW systems. On the basis of the theoretical models, the experimentally discovered deviations from the typical QCE for nanocrystalline silicon are explained.

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Держатели документа:
Siberian Fed Univ, Krasnoyarsk 660041, Russia
LV Kirenskii Inst Phys, SB RAS, Krasnoyarsk 660036, Russia
RAS, N M Emanuel Inst Biochem Phys, Moscow 119334, Russia
Kyoto Univ, Fukui Inst Fundamental Chem, Kyoto 6068103, Japan
Natl Inst Adv Ind Sci & Technol, Res Inst Computat Sci, Tsukuba, Ibaraki 3058568, Japan

Доп.точки доступа:
Sorokin, P. B.; Ovchinnikov, S. G.; Овчинников, Сергей Геннадьевич; Avramov, P. V.; Chernozatonskii, L.A.; Fedorov, D.G.
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