Coherent phenomena in semiconductors

A review of coherent phenomena in photoexcited semiconductors is presented. In particular, two classes of phenomena are considered: On the one hand the role played by optically-induced phase coherence in the ultrafast spectroscopy of semiconductors; On the other hand the Coulomb-induced effects on the coherent optical response of low-dimensional structures. All the phenomena discussed in the paper are analyzed in terms of a theoretical framework based on the density-matrix formalism. Due to its generality, this quantum-kinetic approach allows a realistic description of coherent as well as incoherent, i.e. phase-breaking, processes, thus providing quantitative information on the coupled ---coherent vs. incoherent--- carrier dynamics in photoexcited semiconductors. The primary goal of the paper is to discuss the concept of quantum-mechanical phase coherence as well as its relevance and implications on semiconductor physics and technology. In particular, we will discuss the dominant role played by optically induced phase coherence on the process of carrier photogeneration and relaxation in bulk systems. We will then review typical field-induced coherent phenomena in semiconductor superlattices such as Bloch oscillations and Wannier-Stark localization. Finally, we will discuss the dominant role played by Coulomb correlation on the linear and non-linear optical spectra of realistic quantum-wire structures.Comment: Topical review in Semiconductor Science and Technology (in press) (Some of the figures are not available in electronic form

Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He

Defects are believed to play a fundamental role in the supersolid state of 4He. We have studied solid 4He in two dimensions (2D) as function of the number of vacancies n_v, up to 30, inserted in the initial configuration at rho = 0.0765 A^-2, close to the melting density, with the exact zero temperature Shadow Path Integral Ground State method. The crystalline order is found to be stable also in presence of many vacancies and we observe two completely different regimes. For small n_v, up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n_v, the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. In the equilibrated state it is no more possible to recognize vacancies because they mainly transform into quantum dislocations and crystalline order is found almost independent on how many vacancies have been inserted in the initial configuration. The one--body density matrix in this latter regime shows a non decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of incommensurate versus commensurate state loses meaning for solid 4He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in presence of up to 100 vacancies

Local search for stable marriage problems

The stable marriage (SM) problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. In the classical formulation, n men and n women express their preferences (via a strict total order) over the members of the other sex. Solving a SM problem means finding a stable marriage where stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. We consider both the classical stable marriage problem and one of its useful variations (denoted SMTI) where the men and women express their preferences in the form of an incomplete preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these lists, an we try to find a stable matching that marries as many people as possible. Whilst the SM problem is polynomial to solve, the SMTI problem is NP-hard. We propose to tackle both problems via a local search approach, which exploits properties of the problems to reduce the size of the neighborhood and to make local moves efficiently. We evaluate empirically our algorithm for SM problems by measuring its runtime behaviour and its ability to sample the lattice of all possible stable marriages. We evaluate our algorithm for SMTI problems in terms of both its runtime behaviour and its ability to find a maximum cardinality stable marriage.For SM problems, the number of steps of our algorithm grows only as O(nlog(n)), and that it samples very well the set of all stable marriages. It is thus a fair and efficient approach to generate stable marriages.Furthermore, our approach for SMTI problems is able to solve large problems, quickly returning stable matchings of large and often optimal size despite the NP-hardness of this problem.Comment: 12 pages, Proc. COMSOC 2010 (Third International Workshop on Computational Social Choice

Transient Rayleigh-Benard-Marangoni Convection due to Evaporation : a Linear Non-normal Stability Analysis

The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wave number and time. The method is applied to transient Rayleigh-Benard-Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.Comment: 31 pages, 8 figure

Strong coupling expansion of chiral models

A general precedure is outlined for an algorithmic implementation of the strong coupling expansion of lattice chiral models on arbitrary lattices. A symbolic character expansion in terms of connected values of group integrals on skeleton diagrams may be obtained by a fully computerized approach.Comment: 2 pages, PostScript file, contribution to conference LATTICE '9

Bose Einstein Condensation in solid 4He

We have computed the one--body density matrix rho_1 in solid 4He at T=0 K using the Shadow Wave Function (SWF) variational technique. The accuracy of the SWF has been tested with an exact projector method. We find that off-diagonal long range order is present in rho_1 for a perfect hcp and bcc solid 4He for a range of densities above the melting one, at least up to 54 bars. This is the first microscopic indication that Bose Einstein Condensation (BEC) is present in perfect solid 4He. At melting the condensate fraction in the hcp solid is 5*10^{-6} and it decreases by increasing the density. The key process giving rise to BEC is the formation of vacancy--interstitial pairs. We also present values for Leggett's upper bound on the superfluid fraction deduced from the exact local density.Comment: 4 pages, 3 figures, accepted for publication as a Rapid Communication in Physical Review