On polynomial variance functions

Summary Let be a natural exponential family on and (V, ) be its variance function. Here, is the mean domain of andV, defined on , is the variance of . A problem of increasing interest in the literature is the following: Given an open interval and a functionV defined on , is the pair (V, ) a variance function of some natural exponential family? Here, we consider the case whereV is a polynomial. We develop a complex-analytic approach to this problem and provide necessary conditions for (V, ) to be such a variance function. These conditions are also sufficient for the class of third degree polynomials and certain subclasses of polynomials of higher degree.     

Nonlinear optical properties of confined excitons in clusters

Size effects in femtosecond photon echo spectroscopy of neat clusters are calculated using a quasiparticle representation of the nonlinear response. We extend our previous study of cooperative effects on the nonlinear response of assemblies of two level molecules [J. A. Leegwater and S. Mukamel, Phys. Rev. A46, 452 (1992)] to allow for nuclear motion and to have an s-p model of polarizable atoms. Photon echos in Benzene/Argon clusters are calculated using a semiclassical phase averaging procedure [L. E. Fried and S. Mukamel, Adv. Chem. Phys. (in Press)].     

Zero-Range Process with Open Boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density ρ_c. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters.     

Investigation of electronic coupling in semiconductor double quantum wells using coherent optical two-dimensional Fourier transform spectroscopy

We investigate electronic coupling in asymmetric semiconductor double quantum wells using a new spectroscopy method, optical two-dimensional Fourier transform (2D-FT) spectroscopy. Measurements on two samples with different barrier thicknesses show drastically different 2D-FT spectra. We compare these measurements to conventional one-dimensional four-wave-mixing measurements, highlighting the unique advantages of the 2D-FT spectroscopy. An oscillatory behavior in the intensity of the cross peaks as a function of the mixing time is observed. This oscillation is attributed to interference between different quantum mechanical pathways, and its features are determined by the non-radiative Raman coherence between dipole-forbidden states.     

Modeling the Ultrafast Response of Two‐Magnon Raman Excitations in Antiferromagnets on the Femtosecond Timescale

Illuminating a magnetic material with femtosecond laser pulses induces complex ultrafast dynamical processes. The resulting optically detectable response usually contains contributions from both the optical properties and the magnetic degrees of freedom. Disentangling all the different components concurring to the generation of the total signal is a major challenge of contemporary experimental solid‐state physics. Here, this problem is tackled, addressing the purely optical, nonmagnetic artifacts on the time resolved two‐magnon stimulated Raman spectrum of an antiferromagnet, rationalizing the recent observation on the exchange energy modification upon photo‐excitation. It is demonstrated how the genuine dynamics of the magnetic eigenmode can be disentangled from the nonlinear optical effects, generated by cross phase modulation, on the femtosecond timescale. The introduced approach can be extended for the investigation of <100 fs dynamic processes by means of coherent Raman scattering.     

An exact solution of a one-dimensional asymmetric exclusion model with open boundaries

A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state is known for all system sizes less thanN, then our equation (8) gives the steady state for sizeN. Using this recursion, we obtain closed expressions (48) for the average occupations of all sites. The results are compared to the predictions of a mean field theory. In particular, for infinitely large systems, the effect of the boundary decays as the distance to the power –1/2 instead of the inverse of the distance, as predicted by the mean field theory.     

Breaking of ergodicity and long relaxation times in systems with long-range interactions

The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.