Search Results (8 total)

The regimes of growing phases (for electron numbers N≈0–8) that pass into regions of self-returning phases (for N>8), found recently in quantum dot conductances by Heiblum and co-workers are accounted for by an elementary Green’s function formalism, appropriate to an equi-spaced ladder structure (with at least three rungs) of electronic levels in the quantum dot. The key features of the theory are physically a dissipation rate that increases linearly with the level number (and is tentatively linked to coupling to longitudinal optical phonons) and a set of Fano-like metastable levels, which disturb the unitarity, and mathematically the changeover of the position of the complex transmission amplitude zeros from the upper half in the complex gap-voltage plane to the lower half of that plane. The two regimes are identified with (respectively) the Blaschke term and the Kramers-Kronig integral term in the theory of complex variables.

We report experimental studies of the spectral linewidth and chirp characteristics of the mm-wave rf radiation of the Israeli Electrostatic-Accelerator free electron laser (EA-FEL), along with theory and numerical simulations. The simulations, matching the experimental data, were carried out using a space-frequency-domain model. EA-FELs have the capacity to generate long pulses of tens microseconds and more, that in principle can be elongated indefinitely (cw operation). Since a cold beam FEL is by nature a “homogeneously broadened laser,” EA-FEL can operate, unlike other kinds of FELs, at a single longitudinal mode (single frequency). This allows the generation of very coherent radiation. The current status of the Israeli Tandem Electrostatic-Accelerator FEL, which is based on an electrostatic Van de Graaff accelerator, allows the generation of pulses of tens microseconds duration. It has been operated recently past saturation, and produced single-mode coherent radiation of record narrow inherent relative linewidth ∼Δf/f=10^-6 at frequencies near 100 GHz. A frequency chirp was observed during the pulses of tens of microseconds (0.3–0.5  MHz/ms). This is essentially a drifting “frequency-pulling effect,” associated with the accelerator voltage drop during the pulse. Additionally, damped relaxation of the FEL oscillator was experimentally measured at the beginning and the end of the lasing pulse, in good correspondence to our theory and numerical simulations. We propose using the chirped signal of the pulsed EA-FEL for single pulse sweep spectroscopy of very fine resolution. The characteristics of this application are analyzed based on the experimental data.

The principle of operation of intense radiation devices such as microwave tubes, free-electron lasers, and masers, is based on a distributed interaction between an electron beam and electromagnetic radiation. Some of the effects emerging during the interaction involve a continuum of frequencies in their broadband spectrum. We developed a three-dimensional, space-frequency theory for the analysis and simulation of radiation excitation and propagation in electron devices and free-electron lasers operating in an ultrawide range of frequencies. The total electromagnetic field (radiation and space-charge waves) is presented in the frequency domain as an expansion in terms of transverse eigenmodes of the (cold) cavity, in which the field is excited and propagates. The mutual interaction between the electron beam and the electromagnetic field is fully described by coupled equations, expressing the evolution of mode amplitudes and electron beam dynamics. The approach is applied in a numerical particle code WB3D, simulating wideband interactions in free-electron lasers operating in the linear and nonlinear regimes.

We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the lowest pair of electronic states, approximate “vibronic” (vibration-electronic) ground-state wave functions are constructed having the form of simple, closed expressions. The basis of the method is to regard electronic density operators as classical variables. It extends an earlier “guessed solution,” devised for the dynamical Jahn-Teller effect in cubic symmetry, to situations having lower (e.g., dihedral) symmetry or having no symmetry at all. While the proposed solution is expected to be quite close to the exact one, its formal simplicity allows straightforward calculations of several interesting quantities, like energies and vibronic reduction (or Ham) factors. We calculate for dihedral symmetry two different q factors (“q_z” and “q_x”) and a p factor. In simplified situations we obtain p=q_z+q_x−1. The formalism enables quantitative estimates to be made for the dynamical narrowing of hyperfine lines in the observed electron spin resonance spectrum of the dihedral cyclobutane radical cation.

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the “factorization” of the density. Only the “kinetic energy” appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the least dissipation function condition of Rayleigh-Onsager and in practical applications is flexible. The variational proposal is tested on a two-level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.

We derive a general expression for the expectation value of the phase acquired by a time dependent wave function in a multicomponent system, as excursions are made in its coordinate space. We then obtain the mean phase for the (linear dynamic E⊗ε) Jahn-Teller situation in an electronically degenerate system. We interpret the phase-change as an observable measure of the effective nodal structure of the wave function.

Recent mesoscopic two-arm experiments involving quantum dots, electron interferometry, and Aharonov-Bohm effects have enabled measurements of both electron transmission probabilities and phases. Unexpected features in the phases as function of the gap voltage U have stimulated several theoretical works. It is shown in this paper that the phases (f ) and conductances (|C|), appearing both in the experimental and in theoretical studies, are interrelated through integral expressions, causing f and ln(|C|) to be Hilbert transforms. The empirically found interrelations imply certain analytical properties of the U dependence of wave functions in mesoscopic systems.

For time (t)-dependent wave functions, we derive rigorous conjugate relations between analytic decompositions (in the complex t plane) of phases and log moduli. We then show that reciprocity, taking the form of Kramers-Kronig integral relations (but in the time domain), holds between observable phases and moduli in several physically important instances. These include the nearly adiabatic (slowly varying) case, a class of cyclic wave functions, wave packets, and noncyclic states in an “expanding potential”. The results define a unique phase through its analyticity properties, and exhibit the interdependence of geometric phases and related decay probabilities. Several known quantum-mechanical applications possess the reciprocity property obtained in the paper.