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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Singularities caused by coalesced complex eigenvalues of an effective hamilton operator
Разночтения заглавия :авие SCOPUS: Singularities caused by coalesced complex eigenvalues of an effective Hamilton operator
Место публикации : Int. J. Theor. Phys.: SPRINGER/PLENUM PUBLISHERS, 2007. - Vol. 46: 25th International Colloquium on Group Theoretical Methods in Physics (AUG 02-06, 2004, Cocoyoc, MEXICO), Is. 8. - P1914-1928. - ISSN 0020-7748, DOI 10.1007/s10773-006-9328-4
Примечания : Cited References: 38
Предметные рубрики: UNIMOLECULAR REACTION-RATES
EXCEPTIONAL POINTS
OVERLAPPING RESONANCES
NUCLEAR REACTIONS
QUANTUM-SYSTEMS
UNIFIED THEORY
S-MATRIX
CONTINUUM
PHASE
DEGENERACY
Ключевые слова (''Своб.индексиров.''): effective hamilton--complex eigenvalue--quantum dots--branch points--branch points--complex eigenvalue--effective hamilton--quantum dots
Аннотация: The S matrix theory with use of the effective Hamiltonian is sketched and applied to the description of the transmission through double quantum dots. The effective Hamilton operator is non-hermitian, its eigenvalues are complex, the eigenfunctions are bi-orthogonal. In this theory, singularities occur at points where two (or more) eigenvalues of the effective Hamiltonian coalesce. These points are physically meaningful: they separate the scenario of avoided level crossings from that without any crossings in the complex plane. They are branch points in the complex plane. Their geometrical features are different from those of the diabolic points.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sadreev A. F., Berggren K. F.
Заглавие : Signatures of quantum chaos in complex wavefunctions describing open billiards
Место публикации : J. Phys. A. - 2005. - Vol. 38, Is. 49. - P.10787-10804. - ISSN 0305-4470, DOI 10.1088/0305-4470/38/49/019
Примечания : Cited References: 103
Предметные рубрики: TIME-REVERSAL SYMMETRY
RANDOM-MATRIX
STATISTICAL-THEORY
ENERGY-LEVELS
S-MATRIX
CHARACTERISTIC VECTORS
PHASE SINGULARITIES
INFINITE DIMENSIONS
BORDERED MATRICES
NUCLEAR REACTIONS
Аннотация: We discuss signatures of quantum chaos in open chaotic billiards. Solutions for such a system are given by complex scattering wavefunctions psi = u + iv when a steady current flows through the billiard. For slightly opened chaotic billiards the current distributions are simple and universal. It is remarkable that the resonant transmission through integrable billiards also gives the universal current distribution. Cur-rents induced by the Rashba spin-orbit interaction can flow even in closed billiards. Wavefunction and current distributions for a chaotic billiard with weak and strong spin-orbit interactions have been derived and compared with numerics. Similarities with classical waves are considered. In particular we propose that the networks of electric resonance RLC circuits may be used to study wave chaos. However, being different from quantum billiards, there is a resistance from the inductors which gives rise to heat power and decoherence.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Avoided level crossings, diabolic points, and branch points in the complex plane in an open double quantum dot
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2005. - Vol. 71, Is. 3. - Ст.36227. - ISSN 1063-651X, DOI 10.1103/PhysRevE.71.036227
Примечания : Cited References: 49
Предметные рубрики: BERRY TOPOLOGICAL PHASE
EXCEPTIONAL POINTS
GEOMETRIC PHASES
NUCLEAR REACTIONS
RESONANCE STATES
UNIFIED THEORY
S-MATRIX
CONTINUUM
REPULSION
INTERFEROMETER
Ключевые слова (''Своб.индексиров.''): branch points in the complex plane (bpcp)--diabolic points (dp)--geometric phases--riemann sheets--eigenvalues and eigenfunctions--electron energy levels--functions--hamiltonians--quantum theory--resonance--topology--semiconductor quantum dots
Аннотация: We study the spectrum of an open double quantum dot as a function of different system parameters in order to receive information on the geometric phases of branch points in the complex plane (BPCP). We relate them to the geometrical phases of the diabolic points (DPs) of the corresponding closed system. The double dot consists of two single dots and a wire connecting them. The two dots and the wire are represented by only a single state each. The spectroscopic values follow from the eigenvalues and eigenfunctions of the Hamiltonian describing the double dot system. They are real when the system is closed, and complex when the system is opened by attaching leads to it. The discrete states as well as the narrow resonance states avoid crossing. The DPs are points within the avoided level crossing scenario of discrete states. At the BPCP, width bifurcation occurs. Here, different Riemann sheets evolve and the levels do not cross anymore. The BPCP are physically meaningful. The DPs are unfolded into two BPCP with different chirality when the system is opened. The geometric phase that arises by encircling the DP in the real plane, is different from the phase that appears by encircling the BPCP. This is found to be true even for a weakly opened system and the two BPCP into which the DP is unfolded.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sadreev A. F., Bulgakov E. N., Rotter I.
Заглавие : Trapping of an electron in the transmission through two quantum dots coupled by a wire
Место публикации : JETP Letters. - 2005. - Vol. 82, Is. 8. - P.498-503. - ISSN 0021-3640, DOI 10.1134/1.2150869
Примечания : Cited References: 32
Предметные рубрики: NUCLEAR REACTIONS
CIRCULAR BENDS
UNIFIED THEORY
WAVE-GUIDES
S-MATRIX
STATES
BILLIARD
SYSTEMS
Аннотация: We consider single-channel transmission through a double quantum dot that consists of two identical single dots coupled by a wire. The numerical solution for the scattering wave function shows that the resonance width of a few of the states may vanish when the width (or length) of the wire and the energy of the incident particle each take a certain value. In such a case, a particle is trapped inside the wire as the numerical visualization of the scattering wave function shows. To understand these numerical results, we explore a simple model with a small number of states, which allows us to consider the problem analytically. If the eigenenergies of the closed system cross the energies of the transmission zeroes, the wire effectively decouples from the rest of the system and traps the particle. (C) 2005 Pleiades Publishing, Inc.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Influence of branch points in the complex plane on the transmission through double quantum dots
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2004. - Vol. 69, Is. 6. - Ст.66201. - ISSN 1539-3755, DOI 10.1103/PhysRevE.69.066201
Примечания : Cited References: 25
Предметные рубрики: ELECTRON-ATOM SCATTERING
S-MATRIX
DOUBLE POLES
CONTINUUM
SYSTEM
MODEL
Ключевые слова (''Своб.индексиров.''): eigenvalues and eigenfunctions--hamiltonians--mathematical models--matrix algebra--probability--resonance--scattering--wave propagation--branch points--open quantum systems--propagating modes--quantum computing devices--semiconductor quantum dots
Аннотация: We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows one to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Luna-Acosta G. A., Mendez-Bermudez J. A., Seba P., Pichugin K. N.
Заглавие : Classical versus quantum structure of the scattering probability matrix: Chaotic waveguides
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2002. - Vol. 65, Is. 4. - Ст.46605. - ISSN 1539-3755, DOI 10.1103/PhysRevE.65.046605
Примечания : Cited References: 47
Предметные рубрики: SEMICLASSICAL CROSS-SECTION
CONDUCTANCE FLUCTUATIONS
S-MATRIX
BALLISTIC-TRANSPORT
WEAK-LOCALIZATION
CAVITIES
COLLISIONS
MICROSTRUCTURES
DENSITY
CHANNEL
Ключевые слова (''Своб.индексиров.''): chaos theory--matrix algebra--optical waveguides--quantum theory--scattering--wave equations--chaotic cavities--chaotic waveguides--quantum structure--scattering probability matrix--quantum optics
Аннотация: The purely classical counterpart of the scattering probability matrix (SPM) \S(n,m)\(2) of the quantum scattering matrix S is defined for two-dimensional quantum waveguides for an arbitrary number of propagating modes M. We compare the quantum and classical structures of \S(n,m)\(2) for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincare maps.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Rotter I., Sadreev A. F.
Заглавие : Phase rigidity and avoided level crossings in the complex energy plane
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2006. - Vol. 74, Is. 5. - Ст.56204. - ISSN 1539-3755, DOI 10.1103/PhysRevE.74.056204
Примечания : Cited References: 40
Предметные рубрики: OPEN QUANTUM-SYSTEMS
FANO RESONANCES
S-MATRIX
DOT
CONTINUUM
TRANSMISSION
COHERENCE
TRANSPORT
BILLIARDS
PROBE
Ключевые слова (''Своб.индексиров.''): eigenvalues and eigenfunctions--hamiltonians--resonance--rigidity--semiconductor quantum dots--biorthogonal eigenfunctions--open quantum system--phase rigidity--quantum theory
Аннотация: We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)parallel to phi(lambda))/phi(lambda)parallel to phi(lambda) that characterizes the phase rigidity of the eigenfunctions phi(lambda). In the scenario with avoided level crossings, r(lambda) varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r(lambda) is an internal property of an open quantum system. In the literature, the phase rigidity rho of the scattering wave function Psi(E)(C) is considered. Since Psi(E)(C) can be represented in the interior of the system by the phi(lambda), the phase rigidity rho of the Psi(E)(C) is related to the r(lambda) and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity rho to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity rho and transmission numerically for small open cavities.
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