“…Because of this quantization, the zero-bias conductance of the system vanishes, while the current I as the function of the source-drain voltage V shows a threshold behavior. The fine structure of the current-voltage curve is associated with the single-electron levels of the system 3,4 .…”
Trace formulae and the non-linear supersymmetric σ-model are basic analytical tools used successfully in the fields of quantum chaos and disordered systems. Both are designed to treat systems with a small number of degrees of freedom. Hence they are limited in their possibility of analyzing many-body systems where interparticle interactions play an important role, and the number of degrees of freedom is large.On the other hand, many experimental studies of quantum chaos use systems which consist in a large number of interacting particles, for example quantum dots or disordered metallic particles. Having an elaborate single-particle description of these systems, it is of prominent importance to understand the role of interactions, the range of applicability of a single-particle picture, and the interplay between chaos and interparticle interactions.In this respect, an important observation is that strong chaotic dynamics, on the level of non-interacting single-particle description, provides us with the possibility of analyzing interacting many-body systems by a systematic perturbative approach. The small parameter of this perturbation theory is 1/g, where g = t H /t c is the dimensionless conductance, i.e. the ratio of the Heisenberg time, t H (the inverse mean level spacing), to the classical relaxation time, t c .The general form of the interaction Hamiltonian in which particles interact via a two-body potential U(r, r ′ ) iswhere c † iσ and c iσ are the creation and annihilation operators for a particle in state ψ i and spin σ, whileIn other configurations of these devices a gate electrode of ring shape is deposited after flipping the membrane, and the same procedure follows the oxidation of the gate.
“…Because of this quantization, the zero-bias conductance of the system vanishes, while the current I as the function of the source-drain voltage V shows a threshold behavior. The fine structure of the current-voltage curve is associated with the single-electron levels of the system 3,4 .…”
Trace formulae and the non-linear supersymmetric σ-model are basic analytical tools used successfully in the fields of quantum chaos and disordered systems. Both are designed to treat systems with a small number of degrees of freedom. Hence they are limited in their possibility of analyzing many-body systems where interparticle interactions play an important role, and the number of degrees of freedom is large.On the other hand, many experimental studies of quantum chaos use systems which consist in a large number of interacting particles, for example quantum dots or disordered metallic particles. Having an elaborate single-particle description of these systems, it is of prominent importance to understand the role of interactions, the range of applicability of a single-particle picture, and the interplay between chaos and interparticle interactions.In this respect, an important observation is that strong chaotic dynamics, on the level of non-interacting single-particle description, provides us with the possibility of analyzing interacting many-body systems by a systematic perturbative approach. The small parameter of this perturbation theory is 1/g, where g = t H /t c is the dimensionless conductance, i.e. the ratio of the Heisenberg time, t H (the inverse mean level spacing), to the classical relaxation time, t c .The general form of the interaction Hamiltonian in which particles interact via a two-body potential U(r, r ′ ) iswhere c † iσ and c iσ are the creation and annihilation operators for a particle in state ψ i and spin σ, whileIn other configurations of these devices a gate electrode of ring shape is deposited after flipping the membrane, and the same procedure follows the oxidation of the gate.
Kvantovaya Elektron. (Moscow) 20, 113-122 (February 1993) The research-and-development effort on CO lasers and applications of these lasers in Russia are reviewed. Various types of cw, pulsed, and periodic-pulse CO lasers have been developed in various laboratories. Sealed-oif, water-cooled cw CO lasers with an output power of 5-10 W, pumped by a self-sustained electric discharge, are being used successfully in the manufacture of electronic devices and in medicine. The output power of fast-flow cryogenic cw CO lasers with a self-sustained discharge ranges up to ~ 1 kW. The use of electron-beam pumping has made it possible to develop pulsed electron-beamsustained (BBS) CO lasers with an energy up to ~ 1 kJ and also to develop cw and periodicpulse BBS CO lasers with a power of 10 kW and an efficiency up to ~40%. Research on pulsed electron-beam-sustained CO lasers has been the scientific foundation for the construction of CO laser systems of the (master oscillator)-amplifier type and periodicpulse CO lasers. A CO laser system with an output energy ~200 J and an output beam divergence of 2 • 10~4 rad has been developed. Requirements on the effective gain in the active medium and on the transport through atmospheric air of multifrequency output pulses from CO laser with various spectral and temporal characteristics have been formulated. A supersonic BBS CO laser with a peak power ~ 10 5 W and a 10-kW periodicpulse BBS CO laser with subsonic flow have been developed. The latter laser generates pulses with an energy ~ 100 J and a repetition frequency up to 100 Hz. The BBS CO lasers with injection of the laser mixture in the liquid phase are discussed. Lasers using nuclear ionization of the active medium are also discussed.
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