Computational aberration correction for an arbitrary linear imaging system

We show that aberration corrections can be made in any arbitrary linear imaging system provided the aberrations are well characterized and at least one of these aberrations can be independently varied in a well-controlled manner. We derive a generalization of the Schr?dinger equation for wave propagation in aberration space assuming forward scattering. Transport equations in aberration space are derived. A general iterative algorithm which can retrieve the phase, and is robust in the presence of noise, is also derived. This is demonstrated using simulated data pertinent to electron microscopy, from a series of images with differing spherical aberration.     

Emission of a linear current pulse of an arbitrary shape

A general formula is obtained, which makes it possible in some cases to easily calculate the electromagnetic field of a linear current in the wave band. The emission of a linear current pulse of triangular form is considered as an application of the formula.Polytechnical University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 14–18, June, 1992.     

Analytical expression of pulse broadening in an arbitrary linear slow light medium

We derive an analytical expression for the broadening of a Gaussian input pulse in an arbitrary linear slow light medium. The expression consists of two terms, one corresponding to amplitude broadening (low-pass filtering of the pulse bandwidth) and another corresponding to phase broadening (phase dispersion around the resonance). It is shown that for a Lorentzian gain profile, the amplitude broadening is dominant at small fractional delays. However, for large fractional delays, phase broadening is inevitably dominate.     

Nuclear giant resonances and linear response

We search for nonlinear effects in nuclear giant resonances (GRs), in particular the isovector dipole and the isoscalar quadrupole modes. To that end, we employ a spectral analysis of time-dependent Hartree-Fock (TDHF) dynamics using Skyrme forces. Based on TDHF calculations over a wide range of excitation amplitudes, we explore the collectivity and degree of harmonic motion in these modes. Both GR modes turn out to be highly harmonic in heavy nuclei from A = 100 on. There is no trace of a transition to irregular motion and multiple resonances are predicted. Slight anharmonicities are seen for light nuclei, particularly for ¹⁶O. These are mainly caused by the spin-orbit splitting.     

Darboux operators for linear first-order multi-component equations in arbitrary dimensions

We construct Darboux operators for linear, multi-component partial differential equations of first order. The number of variables and the dimension of the matrix coefficients in our equations are arbitrary. The Darboux operator and the transformed equation are worked out explicitly. We present an application of our formalism to the (1+2)-dimensional Weyl equation.     

Nonautonomous solitons of Bose-Einstein condensation in a linear potential with an arbitrary time-dependence

In the presence of a linear potential with an arbitrary time-dependence, Hirota method is developed carefully for applying into the effective mean-field model of quasi-one-dimensional Bose-Einstein condensation with repulsive interaction. We obtain the exact nonautonomous soliton solution (NSS) analytically. These solutions show that the time-dependent potential can affect the velocity of NSS. In some special cases the velocity has the character of both increase and oscillation with time. A detail analysis for the asymptotic behaviour of solutions shows that the collision of two NSSs is elastic.     

Hirota method for the nonlinear Schrödinger equation with an arbitrary linear time-dependent potential

In this paper, a Hirota method is developed for applying to the nonlinear Schrödinger equation with an arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensation. The nonlinear Schrödinger equation is decoupled to two equations carefully. With a reasonable assumption the one- and two-soliton solutions are constructed analytically in the presence of an arbitrary time-dependent linear potential.     

Jacobi fields and linear connections for arbitrary second-order ODEs

We discuss generalisations of Jacobi fields and Raychaudhuri’s equation from the geodesic case to that of an arbitrary system of second-order ODEs. Our results are obtained using a natural choice of linear connection on evolution space.     

A link between scattering resonances and dilation analytic resonances in few body quantum mechanics

We study the (2 cluster)(2 cluster) scattering amplitudes for classes of two, three, and four particle dilation analytic Schrödinger operators whose two-body potentials fall off exponentially. As functions of the energy, these amplitudes are shown to have meromorphic continuations on certain Riemann surfaces. We prove that all poles of these continuations are necessarily bound states or dilation analytic resonances [i.e., eigenvalues ofH() for some ].Supported in part by the National Science Foundation under Grant PHY 78-08066     

End and central plasmon resonances in linear atomic chains

The existence and nature of end and central plasmon resonances in a linear atomic chain, the 1D analog to surface and bulk plasmons in 2D metals, has been predicted by ab initio time-dependent density functional theory. Length dependence of the absorption spectra shows the emergence and development of collectivity of these resonances. It converges to a single resonance in the longitudinal mode, and two transverse resonances, which are localized at the ends and center of the atom chains. These collective modes bridge the gaps, in concept and scale, between the collective excitation of atomic physics and nanoplasmonics. It also outlines a route to atomic-scale engineering of collective excitations.     

QED in arbitrary linear media: Amplifying media

Recently, we have developed a unified approach to QED in arbitrary linearly responding media in equilibrium—media that give rise to absorption [Phys. Rev. A 75, 053813 (2007)]. In the present paper we show that, under appropriate conditions, the theory can be quite naturally generalized to amplifying media the effect of which is described within the framework of linear response theory. We discuss the limits of validity of the generalized theory and make contact with earlier quantization schemes suggested for the case of linearly and locally responding amplifying dielectric-type media. To illustrate the theory, we present the electromagnetic-field correlation functions that determine the Casimir force in the presence of amplifying media.     

Quantum Langevin equation and input-output fields for arbitrary linear response

A retarded quantum Langevin equation is derived for a small subsystem coupled to an arbitrary number of large reservoirs by treating the small back-action on the reservoir within linear response theory. Interpreting the coupling to the reservoirs as input to the small subsyste, and using the advanced quantum Langevin equation to define the corresponding output emitted into the reservoirs, causally connected input and output variables are constructed which are used to set up anS-matrix formalism relating input and output variables in a unitary and causal way. An application to squeezing by subharmonic generation with arbitrary linear response is given.     

Quantum teleportation of an arbitrary two-mode coherent state using only linear optics elements

We propose a linear optics scheme to teleport an arbitrary two-mode coherent state. The devices used are beam-splitters, phase-shifters and ideal photo-detectors capable of distinguishing between even and odd photon numbers. The scheme achieves faithful teleportation with a probability of 1/4. However, with additional use of an appropriate displacement operator, the teleported state can always be made near-faithful.     

Optical arbitrary waveform characterization using linear spectrograms

We demonstrate the first application of linear spectrogram methods based on electro-optic phase modulation to characterize optical arbitrary waveforms generated under spectral line-by-line control. This approach offers both superior sensitivity and self-referencing capability for retrieval of periodic high repetition rate optical arbitrary waveforms.     

Analytic conditions for the existence of localized electron states in a linear chain with an arbitrary number of impurities

The effective Hamiltonian and the negative eigenvalue theorem are used to obtain an analytic formula for the integrated density of electron states in a linear chain with an arbitrary number of impurities within the tight binding approximation. From this formula, the analytic conditions for the existence of localized electron states lying above or below the band of states of host atoms are obtained. The way of obtaining the energies of localized states and the form of eigenvectors are also discussed.