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

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

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

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

Marketing Strategy Suggestion of the Commway Program in Bank Commonwealth

The issue with Bank Commonwealth is its brand. To overcome this, the company had run a program named Commway. However, the program only generated a low increase of brand improvement. The purpose of this study was to identify the brand condition of Bank Commonwealth and the solutions to improve its brand effectively by finding out the customer\u27s perception. In these matters, the management should make improvement regarding the marketing program. The qualitative research methodologies are used in this study. The qualitative research data is acquired by questionnaires. 130 questionnaires were given to Bank Commonwealth customers in Bandung, varying in backgrounds. With 100% respond rate, all of them were responded. The data then would be analyzed using the Importance-Performance Analysis (IPA). The result revealed that people were not well informed with the Bank Commonwealth and its program. The correspondents mentioned that the program is considered to be not special. The author recommends that management within Bank Commonwealth reevaluate their practices and started from introducing their company. It is recommended that Bank Commonwealth conducts efforts with synergized marketing strategy which is more relevant to the company situation and its need. The marketing strategy required by Bank Commonwealth should include broad audience and show something edgy and memorable, focusing in captivating the target\u27s attention

Faktor-Faktor yang Mempengaruhi Nilai Impor Pesawat Boeing Amerika Serikat 1990-2010

The value of imports plane made by PT. Garuda Indonesia Airlines had made the country foreign exchange reserves to the deficit. On the other hand, the country has PT. Dirgantara Indonesia for development and production of the plane. Resources and expensive cost of research into the company to import plane. This research using secondary data and using analysis of multiple linear. The aim of this research, (1) if the demand, inflation, dollar rate of United States, reserves simultaneously and partial influence significantly towards the United States imported the plane by a Boeing company. Garuda Indonesia Airlines, (2) to know the most dominant variable effect on imports Boeing aircraft United States. The result that the number of requests, inflation dollar exchange rate and and reserves directly affect the import value the Boeing company Garuda Indonesia Airlines 1990-2010 period. Besides, the request and would not affect the partial on imports and dollar exchange reserves have negative and positive impact. The variables is the dominant foreign exchange reserves

Persistence of a Continuous Stochastic Process with Discrete-Time Sampling

We introduce the concept of `discrete-time persistence', which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n \Delta T. For a Gaussian Markov process with relaxation rate \mu, we show that the persistence (no crossing) probability decays as \rho(a)^n for large n, where a = \exp(-\mu \Delta T), and we compute \rho(a) to high precision. We also define the concept of `alternating persistence', which corresponds to a1, corresponding to motion in an unstable potential (\mu<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.Comment: 5 pages, some minor change