Broken Symmetry and Coherence of Molecular Vibrations in Tunnel Transitions

We examine the Breit-Wigner resonances that ensue from field effects in molecular single electron transistors (SETs). The adiabatic dynamics of a quantum dot elastically attached to electrodes are treated in the Born-Oppenheimer approach. The relation between thermal and shot noise induced by the source-drain voltage $V_{bias}$ is found when the SET operates in a regime tending to thermodynamic equilibrium far from resonance. The equilibration of electron-phonon subsystems produces broadening and doublet splitting of transparency resonances helping to explain a negative differential resistance (NDR)of current versus voltage (I-V) curves. Mismatch between the electron and phonon temperatures brings out the bouncing-ball mode in the crossover regime close to the internal vibrations mode. The shuttle mechanism occurs at a threshold $V_{bias}$ of the order of the Coulomb energy $U_c$. An accumulation of charge is followed by the Coulomb blockade and broken symmetry of a single or double well potential. The Landau bifurcation cures the shuttling instability and the resonance levels of the quantum dot become split because of molecular tunneling. We calculate the tunnel gaps of conductivity and propose a tunneling optical trap (TOT) for quantum dot isolation permitting coherent molecular tunneling by virtue of Josephson oscillations in a charged Bose gas. We discuss experimental conditions when the above theory can be tested.Comment: 45 pages, 18 figures; The talk presented at Workshop "Decoherence, Entanglement and Information Protection in Complex Quantum Systems", Les Houches, April 25 -30, 2004. Corrected typos and minor grammatical and stylistic changes; Editors: V. M. Akulin, A. Sarfati, G. Kurizki and S. Pellegrin Publisher: Kluwer Academic Publisher, Boston / Dordrecht / London: to appear in 2005 (February / March

Scattering of electromagnetic waves by small impedance particles of an arbitrary shape

An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle $D$ of an arbitrary shape. If $a$ is the characteristic size of the particle, $\lambda$ is the wavelength, $a<<\lambda$ and $\zeta$ is the boundary impedance of $D$, $[N,[E,N]]=\zeta [N,H]$ on $S$, where $S$ is the surface of the particle, $N$ is the unit outer normal to $S$, and $E$, $H$ is the EM field, then the scattered field is $E_{sc}=[\nabla g(x,x_1), Q]$. Here $g(x,y)=\frac{e^{ik|x-y|}}{4\pi |x-y|}$, $k$ is the wave number, $x_1\in D$ is an arbitrary point, and $Q=-\frac{\zeta |S|}{i\omega \mu}\tau \nabla \times E_0$, where $E_0$ is the incident field, $|S|$ is the area of $S$, $\omega$ is the frequency, $\mu$ is the magnetic permeability of the space exterior to $D$, and $\tau$ is a tensor which is calculated explicitly. The scattered field is $O(|\zeta| a^2)>> O(a^3)$ as $a\to 0$ when $\lambda$ is fixed and $\zeta$ does not depend on $a$. Thus, $|E_{sc}|$ is much larger than the classical value $O(a^3)$ for the field scattered by a small particle. It is proved that the effective field in the medium, in which many small particles are embedded, has a limit as $a\to 0$ and the number $M=M(a)$ of the particles tends to $\infty$ at a suitable rate. Thislimit solves a linear integral equation. The refraction coefficient of the limiting medium is calculated analytically. This yields a recipe for creating materials with a desired refraction coefficient

Sunquakes: helioseismic response to solar flares

Sunquakes observed in the form of expanding wave ripples on the surface of the Sun during solar flares represent packets of acoustic waves excited by flare impacts and traveling through the solar interior. The excitation impacts strongly correlate with the impulsive flare phase, and are caused by the energy and momentum transported from the energy release sites. The flare energy is released in the form of energetic particles, waves, mass motions, and radiation. However, the exact mechanism of the localized hydrodynamic impacts which generate sunquakes is unknown. Solving the problem of the sunquake mechanism will substantially improve our understanding of the flare physics. In addition, sunquakes offer a unique opportunity for studying the interaction of acoustic waves with magnetic fields and flows in flaring active regions, and for developing new approaches to helioseismic acoustic tomography.Comment: 23 pages, 12 figures, to appear in "Extraterrestrial Seismology", Cambridge Univ. Pres