Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phy

Statistical distribution of quantum entanglement for a random bipartite state

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the associated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachement of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of some of these results appeared recently in Phys. Rev. Lett. {\bf 104}, 110501 (2010).Comment: 7 figure

Ultrafast long-range energy transport via light-matter coupling in organic semiconductor films

The formation of exciton-polaritons allows the transport of energy over hundreds of nanometres at velocities up to 10^6 m s^-1 in organic semiconductors films in the absence of external cavity structures

Unsupervised machine learning applied to scanning precession electron diffraction data

Scanning precession electron diffraction involves the acquisition of a two-dimensional precession electron diffraction pattern at every probe position in a two-dimensional scan. The data typically comprise many more diffraction patterns than the number of distinct microstructural volume elements (e.g. crystals) in the region sampled. A dimensionality reduction, ideally to one representative diffraction pattern per distinct element, may then be sought. Further, some diffraction patterns will contain contributions from multiple crystals sampled along the beam path, which may be unmixed by harnessing this oversampling. Here, we report on the application of unsupervised machine learning methods to achieve both dimensionality reduction and signal unmixing. Potential artefacts are discussed and precession electron diffraction is demonstrated to improve results by reducing the impact of bending and dynamical diffraction so that the data better approximate the case in which each crystal yields a given diffraction pattern

Crystallographic relationships of T-/S-phase aggregates in an Al–Cu–Mg–Ag alloy

T-(Al20Cu2Mn3) phase dispersoids are important for limiting recovery and controlling grain growth in Al-Cu alloys. However, these dispersoids can also reduce precipitation hardening by acting as heterogeneous nucleation sites and may lead to increased susceptibility towards pitting corrosion when galvanically coupled with S-(Al2CuMg) phase precipitates. The interplay between T- and S-phases is therefore important for understanding their effect on the mechanical and electrochemical properties of Al-Cu-Mg alloys. Here, the crystallographic relationships between the T-phase, S-phase, and surrounding Al matrix were investigated in an Al-1.31Cu-1.14Mg-0.13Ag-0.10Fe-0.28Mn (at.%) alloy by combining scanning precession electron diffraction with misorientation analysis in 3-dimensional axis-angle space and high-resolution transmission electron microscopy. Orientation relationships are identified between all three phases, revealing S-T orientation relationships for the first time. Differences in S-Al orientation relationships for precipitates formed at T phase interfaces compared to their non-interfacial counterparts were also identified. These insights provide a comprehensive assessment of the crystallographic relationships in T-/S-phase aggregates, which may guide future alloy design

Nanocrystal segmentation in scanning precession electron diffraction data

Scanning precession electron diffraction (SPED) enables the local crystallography of materials to be probed on the nanoscale by recording a two‐dimensional precession electron diffraction (PED) pattern at every probe position as a dynamically rocking electron beam is scanned across the specimen. SPED data from nanocrystalline materials commonly contain some PED patterns in which diffraction is measured from multiple crystals. To analyse such data, it is important to perform nanocrystal segmentation to isolate both the location of each crystal and a corresponding representative diffraction signal. This also reduces data dimensionality significantly. Here, two approaches to nanocrystal segmentation are presented, the first based on virtual dark‐field imaging and the second on non‐negative matrix factorization. Relative merits and limitations are compared in application to SPED data obtained from partly overlapping nanoparticles, and particular challenges are highlighted associated with crystals exciting the same diffraction conditions. It is demonstrated that both strategies can be used for nanocrystal segmentation without prior knowledge of the crystal structures present, but also that segmentation artefacts can arise and must be considered carefully. The analysis workflows associated with this work are provided open‐source