Half-Cycle Pulse Acting on a One-Dimensional Rydberg Atom: Semiclassical Transition Amplitudes in Action and Angle Variables

In this paper we derive the expression for the transition coefficient used in the preceding paper [C. D. Schwieters and J. B. Delos, Phys. Rev. A 51, 1023 (1995)] for principal-quantum-number transitions in one-dimensional hydrogen caused by half-cycle pulses. We briefly review the methods of Miller [Adv. Chem. Phys. 25, 69 (1974)] and Marcus [Chem. Phys. Lett. 7, 525 (1970); J. Chem. Phys. 54, 3965 (1971)], and then derive the result using the methods of Maslov and Fedoriuk [Semi-Classical Approximation in Quantum Mechanics, (Reidel, Dordrecht, 1981)]. Also, we examine the approximate reduction of hydrogen from three to one dimension and we find a hitherto unknown correction due to the residual motion of one of the ignored degrees of freedom. We discuss the regime of validity of this one-dimensional approximation

Semiclassical Treatment of a Half-Cycle Pulse Acting on a One-Dimensional Rydberg Atom

The final-state distribution of hydrogen, acted upon by a 1/2-cycle pulse, has been calculated semiclassically for a proposed one-dimensional experiment. This work was motivated by the recent experimental realization of half-cycle pulses by Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] in which preliminary studies of ionization and state redistribution for hydrogenlike atoms were carried out. To simplify the situation theoretically, an experiment is proposed in which an additional weak static electric field is imposed and approximately one-dimensional states are selected. Within this one-dimensional approximation the transition probability to various n states (n is the principal quantum number) has been calculated as a function of the amplitude of the half-cycle pulse, using a semiclassical formula due to Miller [Adv. Chem. Phys. 25, 69 (1974)]. A complete derivation of this formula and a discussion of approximations are made in the following paper. We have found that an even number of trajectories always contributes to the transition probability and leads to observable interference effects. In addition, we find that bifurcations of these trajectories can occur, resulting in resonances and more complicated interference structures

Semiclassical Scattering in a Circular Semiconductor Microstructure

The conductance of a microscopic junction shows fluctuations caused by quantum interference of waves that follow different paths between the leads. We give a semiclassical formula for these fluctuations. The theory utilizes trajectories which travel between the centers of the lead apertures; it also incorporates diffraction at these apertures. We extend the theory to include ‘‘ghost paths,’’ which scatter diffractively off the lead mouths. Semiclassical S-matrix elements are computed for a circular junction over a range of Fermi wave numbers, and the large-scale structure of these matrix elements shows good agreement with quantum results. Finally, we propose a hypothesis about the effect of the quantum coherence length on the S matrix and on the semiclassical sum. © 1996 The American Physical Society

Excitation of weakly bound Rydberg electrons by half-cycle pulses

The interaction of a weakly bound Rydberg electron with an electromagnetic half-cycle pulse (HCP) is described with the help of a multidimensional semiclassical treatment. This approach relates the quantum evolution of the electron to its underlying classical dynamics. The method is nonperturbative and is valid for arbitrary spatial and temporal shapes of the applied HCP. On the basis of this approach angle- and energy-resolved spectra resulting from the ionization of Rydberg atoms by HCPs are analyzed. The different types of spectra obtainable in the sudden-impact approximation are characterized in terms of the appearing semiclassical scattering phenomena. Typical modifications of the spectra originating from finite pulse effects are discussed.Comment: Submitted to Phys. Rev.

Estimation of interdomain flexibility of N-terminus of factor H using residual dipolar couplings

Characterization of segmental flexibility is needed to understand the biological mechanisms of the very large category of functionally diverse proteins, exemplified by the regulators of complement activation, that consist of numerous compact modules or domains linked by short, potentially flexible, sequences of amino acid residues. The use of NMR-derived residual dipolar couplings (RDCs), in magnetically aligned media, to evaluate interdomain motion is established but only for two-domain proteins. We focused on the three N-terminal domains (called CCPs or SCRs) of the important complement regulator, human factor H (i.e. FH1-3). These domains cooperate to facilitate cleavage of the key complement activation-specific protein fragment, C3b, forming iC3b that no longer participates in the complement cascade. We refined a three-dimensional solution structure of recombinant FH1-3 based on nuclear Overhauser effects and RDCs. We then employed a rudimentary series of RDC datasets, collected in media containing magnetically aligned bicelles (disk-like particles formed from phospholipids) under three different conditions, to estimate interdomain motions. This circumvents a requirement of previous approaches for technically difficult collection of five independent RDC datasets. More than 80% of conformers of this predominantly extended three-domain molecule exhibit flexions of < 40 °. Such segmental flexibility (together with the local dynamics of the hypervariable loop within domain 3), could facilitate recognition of C3b via initial anchoring and eventual reorganization of modules to the conformation captured in the previously solved crystal structure of a C3b:FH1-4 complex

Diffraction and boundary conditions in semi-classical open billiards

The conductance through open quantum dots or quantum billiards shows fluctuations, that can be explained as interference between waves following different paths between the leads of the billiard. We examine such systems by the use of a semi-classical Green's functions. In this paper we examine how the choice of boundary conditions at the lead mouths affect the diffraction. We derive a new formula for the S-matrix element. Finally we compare semi-classical simulations to quantum mechanical ones, and show that this new formula yield superior results.Comment: 7 pages, 4 figure

Negative length orbits in normal-superconductor billiard systems

The Path-Length Spectra of mesoscopic systems including diffractive scatterers and connected to superconductor is studied theoretically. We show that the spectra differs fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path-lengths should arise in the spectra as opposed to normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the Path-Length Spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.Comment: 4 pages, 4 figures include

Optical creation of vibrational intrinsic localized modes in anharmonic lattices with realistic interatomic potentials

Using an efficient optimal control scheme to determine the exciting fields, we theoretically demonstrate the optical creation of vibrational intrinsic localized modes (ILMs) in anharmonic perfect lattices with realistic interatomic potentials. For systems with finite size, we show that ILMs can be excited directly by applying a sequence of femtosecond visible laser pulses at THz repetition rates. For periodic lattices, ILMs can be created indirectly via decay of an unstable extended lattice mode which is excited optically either by a sequence of pulses as described above or by a single picosecond far-infrared laser pulse with linearly chirped frequency. In light of recent advances in experimental laser pulse shaping capabilities, the approach is experimentally promising.Comment: 20 pages, 7 eps figures. Accepted, Phys. Rev.

Microwave study of quantum n-disk scattering

We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin 2-D microwave cavities. Two, three, and four-disk scattering are investigated in detail. The experiments, which are able to probe the stationary Green's function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, non-universal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include

Conductance of Open Quantum Billiards and Classical Trajectories

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S-matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S-matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.Comment: 19 pages, 6 figures (jpg), 2 table