The Scaling Behavior of Classical Wave Transport in Mesoscopic Media at the Localization Transition

The propagation of classical wave in disordered media at the Anderson localization transition is studied. Our results show that the classical waves may follow a different scaling behavior from that for electrons. For electrons, the effect of weak localization due to interference of recurrent scattering paths is limited within a spherical volume because of electron-electron or electron-phonon scattering, while for classical waves, it is the sample geometry that determine the amount of recurrent scattering paths that contribute. It is found that the weak localization effect is weaker in both cubic and slab geometry than in spherical geometry. As a result, the averaged static diffusion constant D(L) scales like ln(L)/L in cubic or slab geometry and the corresponding transmission follows ~ln L/L^2. This is in contrast to the behavior of D(L)~1/L and ~1/L^2 obtained previously for electrons or spherical samples. For wave dynamics, we solve the Bethe-Salpeter equation in a disordered slab with the recurrent scattering incorporated in a self-consistent manner. All of the static and dynamic transport quantities studied are found to follow the scaling behavior of D(L). We have also considered position-dependent weak localization effects by using a plausible form of position-dependent diffusion constant D(z). The same scaling behavior is found, i.e., ~ln L/L^2.Comment: 11 pages, 12 figures. Submitted to Phys. Rev. B on 3 May 200

What is the Thouless Energy for Ballistic Systems?

The Thouless energy, \Ec characterizes numerous quantities associated with sensitivity to boundary conditions in diffusive mesoscopic conductors. What happens to these quantities if the disorder strength is decreased and a transition to the ballistic regime takes place? In the present analysis we refute the intuitively plausible assumption that \Ec loses its meaning as an inverse diffusion time through the system at hand, and generally disorder independent scales take over. Instead we find that a variety of (thermodynamic) observables are still characterized by the Thouless energy.Comment: 4 pages REVTEX, uuencoded file. To appear in Physical Review Letter

Landau diamagnetism and magnetization of interacting diffusive conductors

We show how the orbital magnetization of an interacting disordered diffusive electron gas can be simply related to the magnetization of the non-interacting system having the same geometry. This result is applied to the persistent current of a mesoscopic ring and to the relation between Landau diamagnetism and the interaction correction to the magnetization of diffusive systems. The field dependence of this interaction contribution can be deduced directly from the de Haas-van Alphen oscillations of the free electron gas. Known results for the free orbital magnetism of finite systems can be used to derive the interaction contribution in the diffusive regime in various geometries.Comment: 4 pages, 2 figure

Improved algorithm for quantum separability and entanglement detection

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm' for solving the quantum separability problem which follows from the definition of a separable state. By exploiting specific properties of the set of separable states, we introduce a new classical algorithm that solves the problem significantly faster than the `basic algorithm', allowing a feasible separability test where none previously existed e.g. in 3-by-3-dimensional systems. Our algorithm also provides a novel tool in the experimental detection of entanglement.Comment: 4 pages, revtex4, no figure

Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems

A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the contribution of the respective transfer matrix to the decay of correlations is considered only as far as the ratio of its two largest eigenvalues, allowing an economical calculation of a configuration-averaged correlation length. Standard phenomenological-renormalisation procedures are then used to analyse aspects of the phase boundary which are difficult to assess accurately by alternative methods. For magnetic site concentration $p$ close to $p_c$, the extent of exponential behaviour of the $T_c \times p$ curve is clearly seen for over two decades of variation of $p - p_c$. Close to the pure-system limit, the exactly-known reduced slope is reproduced to a very good approximation, though with non-monotonic convergence. The averaged correlation lengths are inserted into the exponent-amplitude relationship predicted by conformal invariance to hold at criticality. The resulting exponent $\eta$ remains near the pure value (1/4) for all intermediate concentrations until it crosses over to the percolation value at the threshold.Comment: RevTeX 3, 11 pages +5 figures, uuencoded, to appear in Phys. Rev. B (1994), PUC/RJ preprin

Correlations and fluctuations of a confined electron gas

The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their autocorrelation as a function of $\mu$, $x$ and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive and integrable motions are investigated, and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.

Topological Orthoalgebras

We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show that a compact TOA in which 0 is an isolated point is atomic and of finite height. We identify and study a particularly tractable class of TOAs, which we call {\em stably ordered}: those in which the upper-set generated by an open set is open. This includes all topological OMLs, and also the projection lattices of Hilbert spaces. Finally, we obtain a topological version of the Foulis-Randall representation theory for stably ordered TOAsComment: 16 pp, LaTex. Minor changes and corrections in sections 1; more substantial corrections in section

Successful strategies for engaging Chinese breast cancer survivors in a randomized controlled trial

This is the author accepted manuscript. The final version is available from the American Psychological Association via the DOI in this record.Chinese immigrant breast cancer survivors face various challenges due to cultural and socioecological factors. Research efforts to develop culturally sensitive interventions have been limited by lack of knowledge regarding successful recruitment and implementation practices among Chinese immigrant populations. This paper documents strategies utilized during the development and implementation of a randomized controlled trial of a culturally sensitive psychosocial intervention for Chinese immigrant breast cancer survivors. In partnership with a community agency, we developed culturally and linguistically appropriate research materials, recruited participants from community channels, and conducted longitudinal data collection. Key strategies include building equitable research partnerships with community agencies to engage participants; being responsive to the needs of community agencies and participants; considering within-group diversity of the research population; utilizing recruitment as an opportunity for relationship-building with participants; and developing key strategies to promote retention. Successful participant engagement in cancer intervention research is the result of collaboration among breast cancer survivors, community leaders and agencies, and academic researchers. The engagement process for this study is novel because we have emphasized cultural factors in the process and taken a relational approach to recruitment and retention

Phi_0 - Periodic Aharonov-Bohm Oscillations Survive Ensemble Averaging

We have demonstrated that Phi_0 periodic Aharonov--Bohm oscillations measured in a ensemble of rings may survive after ensemble averaging procedure. The central point is the difference between the preparation stage of the ensemble and the subsequent measurement stage. The robustness of the effect under finite temperature and non--zero charging energy of rings is discussed.Comment: 11 pages, 2 figures, RevTex 3.0,WIS-93/84/Aug.-P