Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

We calculate the probability distribution of entanglement entropy S across a cut of a finite one dimensional spin chain of length L at an infinite randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L) \sim L^{-\psi(k)}$, where $k = S / \log [L/L_0]$, the large deviation function $\psi(k)$ is found explicitly, and $L_0$ is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix product state (MPS) based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.Comment: 6 pages, 4 figure

Entanglement Entropy and Full Counting Statistics for 2d2d-Rotating Trapped Fermions

We consider $N$ non-interacting fermions in a $2d$ harmonic potential of trapping frequency $\omega$ and in a rotating frame at angular frequency $\Omega$, with $0<\omega - \Omega\ll \omega$. At zero temperature, the fermions are in the non-degenerate lowest Landau level and their positions are in one to one correspondence with the eigenvalues of an $N\times N$ complex Ginibre matrix. For large $N$, the fermion density is uniform over the disk of radius $\sqrt{N}$ centered at the origin and vanishes outside this disk. We compute exactly, for any finite $N$, the R\'enyi entanglement entropy of order $q$, $S_q(N,r)$, as well as the cumulants of order $p$, $\langle{N_r^{p}}\rangle_c$, of the number of fermions $N_r$ in a disk of radius $r$ centered at the origin. For $N \gg 1$, in the (extended) bulk, i.e., for $0 < r/\sqrt{N} < 1$, we show that $S_q(N,r)$ is proportional to the number variance ${\rm Var}\,(N_r)$, despite the non-Gaussian fluctuations of $N_r$. This relation breaks down at the edge of the fermion density, for $r \approx \sqrt{N}$, where we show analytically that $S_q(N,r)$ and ${\rm Var}\,(N_r)$ have a different $r$-dependence.Comment: 6 pages + 7 pages (Supplementary material), 2 Figure

Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a discrete version of the problem in one dimension reveal that particles cluster very strongly: the two point density correlation function scales with the system size with a scaling function which diverges at small argument. Analytic results are obtained for the Sinai problem of random walkers in a quenched random landscape. This equilibrium system too has a singular scaling function which agrees remarkably with that for advected particles.Comment: To be published in Physical Review Letter

HOW VIOLENCE ERUPTED: FRONT PEMBELA ISLAM ACTIVITY IN YOGYAKARTA

Islamic Defender Front/Front Pembela Islam (FPI) is one of the most prominent civil organizations in Indonesia. They also perceived as one of the most radical and violent Islamic organizations in Indonesia especially when dealing with the religious/blasphemy issues towards Islam. On the contrary, the cause of violence in FPI is not always depends on religious issues. They also have another reason in resorting to violence even with their fellow Islamic organizations. This case is often found in their relations with Islamic Jihad Front/Front Jihad Islam (FJI) in the Special Region of Yogyakarta province. This research will try to explain the patterns of violence in FPI’s activities in Yogyakarta, both towards the religious issues or others. The violence of FPI will be explained by the social movement perspective especially with the vigilantism and framing concepts. Framing will explain about the source of legitimation towards the violence. Meanwhile, the vigilantism will explain about the pattern and behavior in the act of violence. One conclusion that can be drawn is FPI act of violence in Yogyakarta is not always related with the religious issues, but also began with their hostility with Front Jihad Islam/FJI. This kind of violence is based on the rivalry between FPI’s leader (Bambang Tedy) and FJI’s leader (Jarot). On the other hand, FPI also have a religious-motivated violence although the scale of this features usually smaller than the hostility with FJI. Keywords: Front Pembela Islam, Front Jihad Islam, violence, vigilantism, framing, social movement

Extremes of 2d2d Coulomb gas: universal intermediate deviation regime

In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint distribution can be interpreted as a $2d$ Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential $v(r) \propto r^2$. We study the statistics of the eigenvalue with the largest modulus $r_{\max}$ in the complex plane. The typical and large fluctuations of $r_{\max}$ around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this "intermediate deviation function" (IDF) and show that it is universal, i.e. independent of the confining potential $v(r)$ as long as it is spherically symmetric and increases faster than $\ln r^2$ for large $r$ with an unbounded support. If the confining potential $v(r)$ has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as $v(r) \sim \ln r^2$ for $r \gg 1$ with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.Comment: 36 pages, 7 figure

Using mobile telephones technology to address functionality of rural water supply systems in Uganda

Uganda’s Ministry of Water and Environment last updated the information on coverage and functionality of the point water sources which lead to the establishment and publication of the 2010 Water Atlas. While the Ministry sees potential benefits from improved information about the state of rural water sources, it also realises that the real benefit for the water user is only achieved when information of a broken water point leads to prompt repair of the source. The challenge with the monitoring system is to improve not only information collection, but its flow that leads to action to improve water services on the basis of information collected. Real time information on functionality of water services is vital if functionality is to be increased and the use of modern technology is critical if this endeavour is to be achieved

Statistics of fermions in a dd-dimensional box near a hard wall

We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth potentials. We compute this $d$ dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.Comment: 5 pages + 14 pages (Supp. Mat.), 6 figure