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Quantum stress in chaotic billiards / K. F. Berggren [et al.] // Phys. Rev. E. - 2008. - Vol. 77, Is. 6. - Ст. 66209, DOI 10.1103/PhysRevE.77.066209. - Cited References: 43 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
MICROWAVE CAVITIES
   WAVE-FUNCTIONS
   STATISTICAL PROPERTIES
   SYSTEMS
   FIELDS
Кл.слова (ненормированные):
Computer networks -- Electric fields -- Electroacupuncture -- Electromagnetic field theory -- Electromagnetic fields -- Electromagnetism -- Function evaluation -- Functions -- Gaussian distribution -- Image segmentation -- Magnetism -- Mathematical models -- Microwaves -- Modal analysis -- Nematic liquid crystals -- Numerical analysis -- Random processes -- Stresses -- Tensors -- Trellis codes -- Two dimensional -- Wave functions -- Waves -- abiotic and biotic stress -- e ,2e theory -- p ,p ,t measurements -- American Physical Society (APS) -- Analytic expressions -- Current flowing -- Dinger equation -- Experimental studies -- Gaussian random fields -- net flows -- Plane waves -- Quantum billiards -- Quantum-mechanical (QM) -- Scattering wave functions -- Sinai billiard (SB) -- Statistical distributions -- Stress tensors -- Two-dimensional (2D) -- Chaotic systems
Аннотация: This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T(alpha beta)(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u + iv. With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T(alpha beta). The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrodinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T(alpha beta)(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

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Держатели документа:
[Berggren, Karl-Fredrik
Sadreev, Almas F.] Linkoping Univ, IFM Theory & Modeling, S-58183 Linkoping, Sweden
[Maksimov, Dmitrii N.
Sadreev, Almas F.] LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
[Hoehmann, Ruven
Kuhl, Ulrich
Stoeckmann, Hans-Joergen] Univ Marburg, Fachbereich Phys, AG Quantenchaos, D-35032 Marburg, Germany
ИФ СО РАН
IFM-Theory and Modeling, Linkoping University, S-581 83 Linkoping, Sweden
L.V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russian Federation
AG Quantenchaos, Fachbereich Physik der Philipps-Universitat Marburg, Renthof 5, D-35032 Marburg, Germany

Доп.точки доступа:
Berggren, K. F.; Maksimov, D. N.; Максимов, Дмитрий Николаевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Hohmann, R.; Kuhl, U.; Stockmann, H. J.
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Sadreev, A. F.
Signatures of quantum chaos in complex wavefunctions describing open billiards / A. F. Sadreev, K. F. Berggren // J. Phys. A. - 2005. - Vol. 38, Is. 49. - P. 10787-10804, DOI 10.1088/0305-4470/38/49/019. - Cited References: 103 . - ISSN 0305-4470

РУБ Physics, Multidisciplinary + Physics, Mathematical
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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Держатели документа:
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Linkoping Univ, Dept Phys & Measurement Technol, SE-58183 Linkoping, Sweden
ИФ СО РАН
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation
Department of Physics and Measurement Technology, Linkoping University, SE-581 83 Linkoping, Sweden

Доп.точки доступа:
Berggren, K. F.; Садреев, Алмаз Фаттахович
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Sadreev, A. F.
Current statistics for wave transmission through an open Sinai billiard: Effects of net currents / A. F. Sadreev, K. F. Berggren // Phys. Rev. E. - 2004. - Vol. 70, Is. 2. - Ст. 26201, DOI 10.1103/PhysRevE.70.026201. - Cited References: 27 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
EIGENVECTOR STATISTICS
   OPEN SYSTEMS
   EIGENFUNCTIONS
   CHAOS
   FLUCTUATIONS
   CROSSOVER
   ELECTRONS
   INTENSITY
Кл.слова (ненормированные):
Acoustic wave transmission -- Boundary conditions -- Computer simulation -- Continuum mechanics -- Current density -- Fermi level -- Mathematical transformations -- Microwaves -- Probability density function -- Quantum theory -- Random processes -- Reverberation -- Statistical methods -- Surface waves -- Waveguides -- Microwave cavities -- Poynting vector -- Sinai billiard -- Wave functions -- Cavity resonators
Аннотация: Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector) flowing through an open ballistic Sinai billiard to which two opposite leads/wave guides are attached. We show that if the net probability current is small, the scattering wave function inside the billiard is well approximated by a Gaussian random complex field. In this case, the current statistics are universal and obey simple analytic forms. For larger net currents, these forms still apply over several orders of magnitudes. However, small characteristic deviations appear in the tail regions. Although the focus is on electron and microwave billiards, the analysis is relevant also to other classical wave cavities as, for example, open planar acoustic reverberation rooms, elastic membranes, and water surface waves in irregularly shaped vessels.

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Держатели документа:
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Astafev Krasnoyarsk Pedag Univ, Krasnoyarsk 660049, Russia
ИФ СО РАН
Department of Physics, Linkoping University, S-581 83 Linkoping, Sweden
Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation
Astaf'ev Krasnoyarsk Pedagogical U., 660049 Lebedeva, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Berggren, K. F.; Садреев, Алмаз Фаттахович
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Starikov, A. A.
Scenario for the 0.7-conductance anomaly in quantum point contacts / A. A. Starikov, I. I. Yakimenko, K. F. Berggren // Phys. Rev. B. - 2003. - Vol. 67, Is. 23. - Ст. 235319, DOI 10.1103/PhysRevB.67.235319. - Cited References: 23 . - ISSN 1098-0121

РУБ Physics, Condensed Matter
Рубрики:
2-DIMENSIONAL ELECTRON-GAS
   SPIN POLARIZATION
   CONDUCTANCE
   WIRES
   STATE
Аннотация: Effects of spontaneous spin polarization in quantum point contacts (QPC's) are investigated for a realistic semiconductor device structure using the Kohn-Sham local spin-density formalism. At maximal polarization in the contact area, there is a bifurcation into ground-state and metastable solutions. The conduction associated with the metastability is lower than for the normal state. With increasing temperature, the conductance should therefore show an anomalous behavior as observed. For the present device we do not recover resonance or quasibound states.

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Держатели документа:
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН

Доп.точки доступа:
Yakimenko, I. I.; Berggren, K. F.
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Berggren, K. F.
Crossover from regular to irregular behavior in current flow through open billiards / K. F. Berggren, A. F. Sadreev, A. A. Starikov // Phys. Rev. E. - 2002. - Vol. 66, Is. 1. - Ст. 16218, DOI 10.1103/PhysRevE.66.016218. - Cited References: 36 . - ISSN 1539-3755

РУБ Physics, Fluids & Plasmas + Physics, Mathematical
Рубрики:
PHASE SINGULARITIES
   NODAL POINTS
   WAVE-FIELDS
   QUANTUM
   STREAMLINES
   CONDUCTANCE
   VORTICES
   CHAOS
Кл.слова (ненормированные):
Eigenvalues and eigenfunctions -- Mathematical models -- Networks (circuits) -- Random processes -- Resonance -- Signal processing -- Spurious signal noise -- Bursting time series -- Coherence resonance -- Power spectrum -- Stochastic resonance -- Chaos theory
Аннотация: We discuss signatures of quantum chaos in terms of distributions of nodal points, saddle points, and streamlines for coherent electron transport through two-dimensional billiards, which are either nominally integrable or chaotic. As typical examples of the two cases we select rectangular and Sinai billiards. We have numerically evaluted distribution functions for nearest distances between nodal points and found that there is a generic form for open chaotic billiards through which a net current is passed. We have also evaluated the distribution functions for nodal points with specific vorticity (winding number) as well as for saddle points. The distributions may be used as signatures of quantum chaos in open systems. All distributions are well reproduced using random complex linear combinations of nearly monochromatic states in nominally closed billiards. In the case of rectangular billiards with simple sharp-cornered leads the distributions have characteristic features related to order among the nodal points. A flaring or rounding of the contact regions may, however, induce a crossover to nodal point distributions and current flow typical for quantum chaos. For an irregular arrangement of nodal points, as for example in the Sinai billiard, the quantum flow lines become very complex and volatile, recalling chaos among classical trajectories. Similarities with percolation are pointed out.

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Держатели документа:
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
ИФ СО РАН
Dept. of Phys. and Msrmt. Technology, Linkoping University, S-581 83 Linkoping, Sweden
Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadreev, A. F.; Садреев, Алмаз Фаттахович; Starikov, A. A.
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Signatures of quantum chaos in the nodal points and streamlines in electron transport through billiards / K. F. Berggren [et al.] // JETP Letters. - 1999. - Vol. 70, Is. 6. - P. 403-409, DOI 10.1134/1.568188. - Cited References: 13 . - ISSN 0021-3640

РУБ Physics, Multidisciplinary
Рубрики:

Аннотация: Streamlines and the distributions of nodal points are used as signatures of chaos in coherent electron transport through three types of billiards: Sinai, Bunimovich, and rectangular. Numerical averaged distribution functions of the nearest distances between nodal points are presented. We find the same form for the Sinai and Bunimovich billiards and suggest that there is a universal form that can be used as a signature of quantum chaos for electron transport in open billiards. The universal distribution function is found to be insensitive to the way the averaging is performed (over the positions of the leads, over an energy interval with a few conductance fluctuations, or both). The integrable rectangular billiard, on the other hand, displays a nonuniversal distribution with a central peak related to partial order of nodal points for the case of symmetric attachment of the leads. However, cases with asymmetric leads tend to the universal form. Also, it is shown how nodal points in the rectangular billiard can lead to "channeling of quantum flows," while disorder in the nodal points in the Sinai billiard gives rise to unstable irregular behavior of the flow. (C) 1999 American Institute of Physics. [S0021- 3640(99)00718-5].

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Держатели документа:
Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden
LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia
Acad Sci Czech Republic, Inst Phys, Prague 16000, Czech Republic
ИФ СО РАН

Доп.точки доступа:
Berggren, K. F.; Pichugin, K. N.; Пичугин, Константин Николаевич; Sadreev, A. F.; Садреев, Алмаз Фаттахович; Starikov, A. A.
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