Semiclassical Quantum Theory Research Articles

Determination of the Surface Corrugation Amplitude from Classical Atom Scattering

The energy landscape of an atomic or molecular projectile interacting with a surface is often described in terms of a corrugation function that gives the classical turning point as a function of position vector parallel to the surface. It is shown here that the relative height variation of the corrugation function for scattering of atoms under classical conditions can be determined by a measurement of the maximum intensity in energy-resolved scattering spectra as a function of surface temperature. This is demonstrated by developing a semiclassical quantum theory of atomic scattering from corrugated surfaces and then extending the theory to the classical limit of large incident energies and high surface temperatures. Comparisons of calculations with available data for Ar atom scattering determine the corrugation amplitude for a molten In surface to be about 29% of the mean interparticle spacing in the bulk liquid.

Computing the density of paths in complex systems

Trajectories of duration tau joining two points q(0) and q(1) in the configuration space of a classical system satisfy Hamilton's principle: they are stationary points of the classical action. The second variation (fluctuations) of the action around the stationary point signals whether the latter is or not a minimum and delivers the density in trajectory space around the points q(0) and q(1). This concept of density of paths is of great importance in semiclassical quantum theory, where it weights the contribution to the propagator from the single classical trajectories. In this paper, two algorithms based on the concepts of molecular dynamics simulation are introduced for computing the density of paths, also called van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] determinant. Examples for realistic systems are presented, together with a suggestion about possible applications in the field of rare events in physics and chemistry.

Dynamical properties of an asymmetric Josephson junction in Bose-Einstein condensates

Based on the semiclassical quantum theory, we study the dynamical behaviors of Bose-Einstein condensate in an asymmetric Josephson junction. It is shown that the Josephson effect appears in the system when the ratio χ of the difference of two ground state energies to the interaction energies is zero. When χ≠0, the dynamical behavior of the system shows both the macroscopic quantum tunneling and the macroscopic quantum localization.

Simplified formulae system for resonant inverse Compton scattering of a fast electron in an intense magnetic field

We present simple analytical formulae for the emission spectrum and total power of a special kind of resonant inverse Compton scattering (RICS) of a relativistic electron in an intense magnetic field. In contrast with the available formulae system, we obtain a markedly simplified one based on the semiclassical quantum theory, which is more understandable for people who are unfamiliar with quantum electrodynamics. We show that the RICS process, under an appropriate ‘accommodation condition’ derived in this paper, is predominantly much more efficient than the coexistent ordinary inverse Compton scattering, and produces highly beamed high-frequency radiation with moderately good monochromaticity. Our formulae are simple to use — thus offering a lucid physical intuition for the theory — and may find wide applications in hard X-ray and gamma-ray astrophysics.

Semiclassical quantum unimolecular reaction rate theory revisited

We describe a semiclassical quantum unimolecular reaction rate theory derived from the corresponding classical theory developed by Davis, Gray, Rice and Zhao (DGRZ). The analysis retains the intuitively useful mechanistic distinctions between intramolecular energy transfer and reaction, with the consequence that the semiclassical quantum theory version neglects some interference effects in the reaction dynamics. In the limiting case that intramolecular energy transfer is very fast compared to the rate of reaction we show that the DGRZ representation of the rate constant can be transformed, using the Weyl correspondence between quantum operators and classical variables, to the quantum flux–flux correlation function representation of the rate constant. In the more general case that the rate of intramolecular energy transfer influences the reaction dynamics, the semiclassical representation of the Wigner function for a classical system with both quasiperiodic and chaotic motion is used to obtain the reaction rate constant. Our analysis identifies the quantum analogue of the classical bottleneck to intramolecular energy transfer with the scars of unstable periodic orbits; it leads to a flux–flux correlation function representation of the rate constant for intramolecular energy transfer.

Semi-classical quantum theory for cyclotron radiation

A semi-classical quantum theory of the cyclotron radiation of the nonrelativistic thermal electrons in a very strong magnetic field is presented. The basic formulae of the absorption coefficient of cyclotron resonancekvand the absorption (scattering) cross-section of cyclotron resonance σv have been derived under the quadrupole approximation. σv is an important quantity in the study of the “magnetic inverse-Compton scattering”. It is shown that σv is greatly larger than the Thomson cross-sectron σT, which is important in discussing the magnetic inverse-Compton scattering of the relativistic electrons in a very strong magnetic field.

Simplified formulae of quantum cyclotron radiation

Using a semi-classical quantum theory of the cyclotron radiation of a nonrelativistic thermal electron in a very strong magnetic field, we present the simplified formulae of the absorption coefficient of cyclotron resonance k v and the absorption and/or scattering cross section of cyclotron resonance σ v at base frequency ω B ≡ eB m 0c in the quadrupole approximation. The results can be conveniently used for studying the “magnetic inverse-Compton scattering”, an important radiation mechanism in gamma-ray astronomy.

Semiclassical quantum theory and its applications in two dimensions by conformal mapping.

Semiclassical quantum theory and its applications in two dimensions by conformal mapping.

Electromagnetic excitations in metals in strong magnetic fields

A set of experimental characteristics of the microwave quantum magneto-absorption is presented. The measurements, regarding the derivative of the surface impedance as a function of the external magnetic field in single crystals of Bi, are explained in the frame of a semiclassical quantum theory.

Some generalisations of the Poisson summation formula

Some useful generalisations of the Poisson summation formula are presented with proofs. These extend the formula to finite sums over arbitrary intervals and to sums of derivatives. The results are indicated as being of importance in the treatment of scattering in semiclassical quantum theory.

Continuum radiation from partially ionized argon.

Experimental measurements of the total thermal radiation from an argon plasma arc of the wall-stabilized type with Poiseuille flow are compared with theoretical predictions. The magnitude of radiation is of importance both for re-entry calculations and use in the HellerElenbaas energy balance equation when transport properties are to be determined. The experimentally measured radiation (utilizing a carefully calibrated novel radiation meter) has been compared with predictions from semiclassical quantum theory (cum-experimental constants) based on recombination and bremsstrahlung. A simple equation for the total radiated power (in watts per cubic centimeter) as a function of temperature has been developed and corroborated by experiment. Spectrographically determined temperature distributions from a similar arc in the same laboratory were utilized in-making the comparisons. The plasma arc was operated at 1 atm over a range of argon flow rates from 0.02 to 0.415 g/sec and currents from 35 to 500 amp for three different column lengths. Steady-state total radiation as high as 5500 w/cm of column length, representing over 30% of the power input to the arc, was measured.