Ensemble-averaged Density Research Articles

Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?

We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined -- i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.

Effective description of the gap fluctuation for chaotic Andreev billiards

An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the numerical calculation for Sinai-Andreev billiards. A systematic linear decrease of the mean field gap with increasing Ehrenfest time $\tau_E$ is observed but its derivative with respect to $\tau_E$ is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is interpreted semi-classically.

Correlated quantum measurement of a solid-state qubit

We propose a solid-state experiment to study the process of continuous quantum measurement of a qubit state. The experiment would verify that an individual qubit stays coherent during the process of measurement (in contrast to the gradual decoherence of the ensemble-averaged density matrix) thus confirming the possibility of the qubit purification by continuous measurement. The experiment can be realized using quantum dots, single-electron transistors, or SQUIDs.

Nanometric Inhomogeneity of Polymer Network Investigated by Scanning Near-Field Optical Microscopy

The structural inhomogeneity of the poly(methyl methacrylate) (PMMA) network was studied by scanning near-field optical microscopy (SNOM), which provides us optical images and spectroscopic information in a local area with a spatial resolution of several tens of nanometers. The optically transparent PMMA network was labeled with fluorescent dyes either at the network chain or at the cross-linking points. The spatial distribution of the chain segments and cross-links could be directly visualized in real space, and the PMMA network was found to have an inhomogeneous structure in a scale of submicrons. Nanosecond dynamics of the energy transfer among the dyes introduced to the side chain was also examined in a nanometric area by the time-correlated photon counting system combined with SNOM. The fluorescence decay through the near-field excitation showed that the local segment density was ca. 10 times higher than the ensemble average density. The local segment density had little correlation with the structure...

On stochastic dynamics of hydrogenic ion transport through solids

We investigate the problem of hydrogenic ion transport through solids. To this end, we consider a system made of a single electron in a given potential and driven by a stochastic force uniformly distributed in time [D.G. Arbò et al., Phys. Rev. A 60 (1999) 1091], and we derive the time evolution equation of the ensemble average density matrix. We show that the random phase approximation of this equation leads to the rate equation model used to describe ion transport [P. Nicolai et al., J. Phys. B 23 (1990) 3609; J.P. Rozet et al., J. Phys. B 22 (1988) 33]. With the help of the Wigner transform, we also demonstrate that both quantum and classical dynamics of an electron under a train of kicks obeys the same equation within the semiclassical approximation. We conclude that seemingly different approaches may be regarded as different approximations of the same quantum problem and we show with a numerical example where differences arise.

Density of states for band random matrices with electric field

We present a long-range hopping tight-binding model in which the ensemble averaged density of states, rho (E), undergoes a gradual transition from a homogeneous form with almost no variation to strongly peaked behaviour as an external electric field grows. The model consists of N*N band random matrices of bandwidth b. The corresponding matrix elements, hij, have all vanishing average except on the diagonal where, (hii)= alpha i. Here, the parameter alpha plays the role of the electric field. We approximate the behaviour of the width, sigma E, of the local density of states, rho L(E), and use it to predict the value of alpha around which the transition is centred.

Lineshapes in Three-Level Spectroscopy with an Intense Laser Field

Effects of an intense saturating radiation on a probe lineshape under Doppler broadening are studied in a three-level system when the frequency of the probe light is higher than that of the saturating light. The problem is analysed in the approximation of weak probe field using an ensemble averaged density matrix. An analytical form of the lineshape is obtained for the resonant saturating field of high intensity at which the Rabi nutation frequency is larger than the Doppler width of the probe transition. The linewidth of probe absorption depends on the Doppler width and the frequency ratio of the probe light to the saturating light. The computer calculation is carried out to find the lineshape in detail at a light intensity where the Rabi nutation frequency is comparable to the Doppler width.

Statistical properties of many-particle spectra

Many-particle eigenvalue densities, generated by k-body interactions in asymptotically large spectroscopic spaces, are studied in terms of the density moments of a Gaussian orthogonal ensemble of such interactions. It is shown that the densities approach Gaussian as particle number increases; the rate of approach is determined, as is the rate of departure from the semicircular form which obtains in the few-particle limit, as well as the low-moment representation for intermediate cases. By considering the variances of the moments it is shown that a convergence in probability of the individual densities to the ensemble-averaged density, first demonstrated by Grenander for the fewparticle limit, is valid in general. In part as a preliminary to a study of the density and spectrum fluctuations, explicit forms are derived for the covariances of low-order moments for arbitrary particle number and of moments of general order in the few-particle and many-particle limits. In the limiting cases the ensemble eigenvalue densities are exhibited in terms of a set of statistically uncorrelated Chebyshev or Hermitepolynomial excitations of the ensemble-averaged densities. Some explicit results for GOE fluctuations are given.

Theory of a three-level gas laser amplifier

A laser amplifier to be treated in this work consists of an ensemble of atoms three energy levels of which form two coupled transitions of arbitrary frequencies. Two classical monochromatic travelling light waves are to be close to resonance with the transitions. The gain profile (or spontaneous emission) on the transition corresponding to the weak “probe” wave, modified by the perturbing field on the other transition, is calculated via a susceptibility. Within this framework, the atoms are described by an ensemble-averaged density matrix with full account of level degeneracies, light polarizations, and inelastic and dephasing collisions; an extension to elastic collisions and disorientation is straightforward. An integration over the thermal velocity distribution gives results applicable to gas discharges: directionally anisotropic narrow structures superimposed on the Doppler-broadened probe-gain profile due to non-linear interference effects in addition to saturation. At alower probe frequency, a peculiar non-Lorentzian signal appears even with transparency on the perturbing transition. At low intensities a distinction is reasonable of frequency correlations due to generalized two-quantum processes, and of a dynamic Stark splitting. These effects permit an information on the linewidth of the third forbidden transition. The connection with numerous related approaches is pointed out.

Wave propagation through an assembly of spheres: III. The density of states in a liquid

The expression for the density of states in a system of non-overlapping potentials by Lloyd in 1966 is investigated by means of a diagrammatic technique for the case where the system under discussion is a liquid. The resulting equations express the ensemble-averaged density of states of such a system in terms of the scattering phase shifts and the probability correlation functions for the positions of the scatterers.