Zeta-Regularization of the O(N) Non-Linear Sigma Model in D dimensions

The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M \times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$ correspond to flat space, a torus and a sphere, respectively. Using zeta regularization and the $1/N$ expansion, the corresponding partition functions and the gap equations are obtained. Numerical solutions of the gap equations at the critical coupling constants are given, for several values of $D$. The properties of the partition function and its asymptotic behaviour for large $D$ are discussed. In a similar way, a higher-derivative non-linear sigma model is investigated too. The physical relevance of our results is discussed.Comment: 26 page

First steps towards the certification of an ARM simulator using Compcert

The simulation of Systems-on-Chip (SoC) is nowadays a hot topic because, beyond providing many debugging facilities, it allows the development of dedicated software before the hardware is available. Low-consumption CPUs such as ARM play a central role in SoC. However, the effectiveness of simulation depends on the faithfulness of the simulator. To this effect, we propose here to prove significant parts of such a simulator, SimSoC. Basically, on one hand, we develop a Coq formal model of the ARM architecture while on the other hand, we consider a version of the simulator including components written in Compcert-C. Then we prove that the simulation of ARM operations, according to Compcert-C formal semantics, conforms to the expected formal model of ARM. Size issues are partly dealt with using automatic generation of significant parts of the Coq model and of SimSoC from the official textual definition of ARM. However, this is still a long-term project. We report here the current stage of our efforts and discuss in particular the use of Compcert-C in this framework.Comment: First International Conference on Certified Programs and Proofs 7086 (2011

The Infrared Extinction Law at Extreme Depth in a Dark Cloud Core

We combined sensitive near-infrared data obtained with ground-based imagers on the ESO NTT and VLT telescopes with space mid-infrared data acquired with the IRAC imager on the Spitzer Space Telescope to calculate the extinction law A_\lambda/A_K as a function of \lambda between 1.25 and 7.76 micron to an unprecedented depth in Barnard 59, a star forming, dense core located in the Pipe Nebula. The ratios A_\lambda/A_K were calculated from the slopes of the distributions of sources in color-color diagrams \lambda-K vs. H-K. The distributions in the color-color diagrams are fit well with single slopes to extinction levels of A_K ~ 7 (A_V ~ 59 mag). Consequently, there appears to be no significant variation of the extinction law with depth through the B59 line of sight. However, when slopes are translated into the relative extinction coefficients A_\lambda/A_K, we find an extinction law which departs from the simple extrapolation of the near-infrared power law extinction curve, and agrees more closely with a dust extinction model for a cloud with a total to selective absorption R_V=5.5 and a grain size distribution favoring larger grains than those in the diffuse ISM. Thus, the difference we observe could be possibly due to the effect of grain growth in denser regions. Finally, the slopes in our diagrams are somewhat less steep than those from the study of Indebetouw et al. (2005) for clouds with lower column densities, and this indicates that the extinction law between 3 and 8 micron might vary slightly as a function of environment.Comment: 22 pages manuscript, 4 figures (2 multipart), 1 tabl

The influence of local field corrections on Thomson scattering in non-ideal two-component plasmas

Thomson scattering in non-ideal (collision-dominated) two-component plasmas is calculated accounting for electron-ion collisions as well as electron-electron correlations. This is achieved by using a novel interpolation scheme for the electron-electron response function generalizing the traditional Mermin approach. Also, ions are treated as randomly distributed inert scattering centers. The collision frequency is taken as a dynamic and complex quantity and is calculated from a microscopic quantum-statistical approach. Implications due to different approximations for the electron-electron correlation, i.e. different forms of the OCP local field correction, are discussed

Neural-Network Quantum States, String-Bond States, and Chiral Topological States

Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dimensions. In particular we demonstrate that short-range Restricted Boltzmann Machines are Entangled Plaquette States, while fully connected Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry and low bond dimension. These results shed light on the underlying architecture of Restricted Boltzmann Machines and their efficiency at representing many-body quantum states. String-Bond States also provide a generic way of enhancing the power of Neural-Network Quantum States and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of Tensor Networks and the efficiency of Neural-Network Quantum States into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional Tensor Networks, we show that Neural-Network Quantum States and their String-Bond States extension can describe a lattice Fractional Quantum Hall state exactly. In addition, we provide numerical evidence that Neural-Network Quantum States can approximate a chiral spin liquid with better accuracy than Entangled Plaquette States and local String-Bond States. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine-learning applications.Comment: 15 pages, 7 figure

Survey of finance companies, 1996

Finance companies are major suppliers of credit to consumers and businesses. The sector is made up of roughly 1,250 nondepository financial institutions, with 20 firms accounting for three-fourths of the receivables. The Federal Reserve System has been surveying the assets and liabilities of finance companies, typically at five-year intervals, since June 1955. This article summarizes the results of the 1996 survey. Special features of that survey are a breakdown of automobile leases into consumer and business components and, relative to previous surveys, greater detail on the composition of real estate credit and more information on securitized loans and leases.Finance companies

Sommerfeld's quantum condition of action and the spectra of Schwarzschild black hole

If the situation of quantum gravity nowadays is nearly the same as that of the quantum mechanics in it's early time of Bohr and Sommerfeld, then a first step study of the quantum gravity from Sommerfeld's quantum condition of action might be helpful. In this short paper the spectra of Schwarzschild black hole(SBH) in quasi-classical approach of quantum mechanics is given. We find the quantum of area, the quantum of entropy and the Hawking evaporation will cease as the black hole reaches its ground state.Comment: 7 pages, no figures, submitted to Classical and Quantum Gravit

Menyetarakan Nilai Suara: Jumlah dan Alokasi Kursi DPR ke Provinsi

Salah satu prinsip pemilihan umum yang demokratis adalah equality atau kesetaraan. Maksudnya kesetaraan suara yang biasa diungkapkan dengan istilah OPOVOV: one person, one vote, one value. Prinsip ini menegaskan bahwa nilai suara yang dimiliki setiap pemilih adalah sama dalam satu pemilihan. Dalam perspektif hak warga negara, kesetaraan suara adalah perwujudan asas persamaan kedudukan warga negara dalam hukum dan pemerintahan. UUD 1945 mengakui bahwa “Segala warga negara bersamaan kedudukannya dalam hukum dan pemerintahan dan wajib menjunjung hukum dan pemerintahan itu dengan tidak ada kecualinya.

Membangun Sistem Kepartaian Pluralisme Moderat: Menyederhanakan Jumlah Partai Politik

Sistem kepartaian macam apakah yang senyatanya berlangsung di Indonesia dewasa ini? Setelah tiga kali pemilihan umum Pasca Orde Baru tampaknya sistem kepartaian yang berlangsung selama ini masih lebih banyak sebagai sumber masalah daripada solusi. Setidak-tidaknya terdapat sejumlah permasalahan yang berkaitan dengan sistem kepartaian di Indonesia yang berimbas terhadap fungsi sistem perwakilan rakyat dan efektivitas pemerintahan baik pada tingkat nasional maupun daerah