Overtones of Isoscalar Giant Resonances in medium-heavy and heavy nuclei

A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly- and doubly-closed-shell nuclei are compared with available experimental data.Comment: 12 pages, 14 figures, submitted to Phys. Rev.

The Harish-Chandra isomorphism for reductive symmetric superpairs

We consider symmetric pairs of Lie superalgebras which are strongly reductive and of even type, and introduce a graded Harish-Chandra homomorphism. We prove that its image is a certain explicit filtered subalgebra of the Weyl invariants on a Cartan subspace whose associated graded is the image of Chevalley's restriction map on symmetric invariants. This generalises results of Harish-Chandra and V. Kac, M. Gorelik.Comment: 43 pages; v2: substantially improved versio

Phonon relaxation of subgap levels in superconducting quantum point contacts

Superconducting quantum point contacts are known to possess two subgap states per each propagating mode. In this note we compute the low-temperature relaxation rate of the upper subgap state into the lower one with the emission of an acoustic phonon. If the reflection in the contact is small, the relaxation time may become much longer than the characteristic lifetime of a bulk quasiparticle.Comment: REVTeX, 4 page

Two-level Hamiltonian of a superconducting quantum point contact

In a superconducting quantum point contact, dynamics of the superconducting phase is coupled to the transitions between the subgap states. We compute this coupling and derive the two-level Hamiltonian of the contact.Comment: REVTeX, 5 pages, reference adde

Shuttle Mechanism for Charge Transfer in Coulomb Blockade Nanostructures

Room-temperature Coulomb blockade of charge transport through composite nanostructures containing organic inter-links has recently been observed. A pronounced charging effect in combination with the softness of the molecular links implies that charge transfer gives rise to a significant deformation of these structures. For a simple model system containing one nanoscale metallic cluster connected by molecular links to two bulk metallic electrodes we show that self-excitation of periodic cluster oscillations in conjunction with sequential processes of cluster charging and decharging appears for a sufficiently large bias voltage. This new `electron shuttle' mechanism of discrete charge transfer gives rise to a current through the nanostructure, which is proportional to the cluster vibration frequency.Comment: 4 pages, 4 figure

Far-infrared induced current in a ballistic channel -- potential barrier structure

We consider electron transport in a ballistic multi-mode channel structure in the presence of a transversely polarized far-infrared (FIR) field. The channel structure consists of a long resonance region connected to an adiabatic widening with a potential barrier at the end. At frequencies that match the mode energy separation in the resonance region we find distinct peaks in the photocurrent, caused by Rabi oscillations in the mode population. For an experimental situation in which the width of the channel is tunable via gates, we propose a method for reconstructing the spectrum of propagating modes, without having to use a tunable FIR source. With this method the change in the spectrum as the gate voltage is varied can be monitored.Comment: Submitted to Phys. Rev.

Electromechanical instability in suspended carbon nanotubes

We have theoretically investigated electromechanical properties of freely suspended carbon nanotubes when a current is injected into the tubes using a scanning tunneling microscope. We show that a shuttle-like electromechanical instability can occur if the bias voltage exceeds a dissipation-dependent threshold value. An instability results in large amplitude vibrations of the carbon nanotube bending mode, which modify the current-voltage characteristics of the system

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic