Matrix Product States Algorithms and Continuous Systems

A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be applied to a wide variety of situations. As a first test, we show how it provides reliable results in the computation of fundamental properties of a chain of quantum harmonic oscillators achieving off-critical and critical relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use it to study the ground state properties of the quantum rotor model in one spatial dimension, a model that can be mapped to the Mott insulator limit of the 1-dimensional Bose-Hubbard model. At the quantum critical point, the central charge associated to the underlying conformal field theory can be computed with good accuracy by measuring the finite-size corrections of the ground state energy. Examples of MPS-computations both in the finite-size regime and in the thermodynamic limit are given. The precision of our results are found to be comparable to those previously encountered in the MPS studies of, for instance, quantum spin chains. Finally, we present a spin-off application: an iterative technique to efficiently get numerical solutions of partial differential equations of many variables. We illustrate this technique by solving Poisson-like equations with precisions of the order of 10^(-7).Comment: 22 pages, 14 figures, final versio

Tweet2Vec: Learning Tweet Embeddings Using Character-level CNN-LSTM Encoder-Decoder

We present Tweet2Vec, a novel method for generating general-purpose vector representation of tweets. The model learns tweet embeddings using character-level CNN-LSTM encoder-decoder. We trained our model on 3 million, randomly selected English-language tweets. The model was evaluated using two methods: tweet semantic similarity and tweet sentiment categorization, outperforming the previous state-of-the-art in both tasks. The evaluations demonstrate the power of the tweet embeddings generated by our model for various tweet categorization tasks. The vector representations generated by our model are generic, and hence can be applied to a variety of tasks. Though the model presented in this paper is trained on English-language tweets, the method presented can be used to learn tweet embeddings for different languages.Comment: SIGIR 2016, July 17-21, 2016, Pisa. Proceedings of SIGIR 2016. Pisa, Italy (2016

Response of finite spin-S Heisenberg chains to local perturbations

We consider the properties of finite isotropic antiferromagnetic Heisenberg chains with S=1/2, 1, 3/2 spins when a weak magnetic field is applied on a few sites, using White's density matrix renormalization group (DMRG) method. For the S=1 chain there exists only one length scale in the system which determines the behavior of the one- and two-point correlation functions both around the local perturbation and near the free boundary. For the critical, half-odd-integer spin cases the exponent of the spin-spin correlation function was found to be $\eta=1$, and the exponent of the decay of the site magnetization around the perturbed site is $x_m =\eta /2$. Close to a free boundary, however, the behavior is completely different for S=1/2 and $S > 1/2$.Comment: 13 pages, 7 figure

Universal Features of Terahertz Absorption in Disordered Materials

Using an analytical theory, experimental terahertz time-domain spectroscopy data and numerical evidence, we demonstrate that the frequency dependence of the absorption coupling coefficient between far-infrared photons and atomic vibrations in disordered materials has the universal functional form, C(omega) = A + B*omega^2, where the material-specific constants A and B are related to the distributions of fluctuating charges obeying global and local charge neutrality, respectively.Comment: 5 pages, 3 fig

Single Production of Fourth Family Sneutrino via RPV Couplings at Linear Colliders

The single production of fourth family sneutrino $\tilde{\nu}_{4}$ via R-parity violating interactions in electron-positron collisions has been investigated. We study the decays of $\tilde{\nu}_{4}$ into different flavor dilepton $e^{\pm}\mu^{\mp}$ via R-parity violation. It is shown that R-parity violating couplings $(\lambda_{411},\lambda_{412})$ down to 0.001 will be reachable at future linear colliders which would provide better accuracy comparing to the indirect measurements as complementary to the LHC results.Comment: 11 pages, 6 figure

Characteristics of Cherenkov Radiation in Naturally Occuring Ice

We revisit the theory of Cherenkov radiation in uniaxial crystals. Historically, a number of flawed attempts have been made at explaining this radiation phenomenon and a consistent error-free description is nowhere available. We apply our calculation to a large modern day telescope - IceCube. Being located at the Antarctica, this detector makes use of the naturally occuring ice as a medium to generate Cherenkov radiation. However, due to the high pressure at the depth of the detector site, large volumes of hexagonal ice crystals are formed. We calculate how this affects the Cherenkov radiation yield and angular dependence. We conclude that the effect is small, at most about a percent, and would only be relevant in future high precision instruments like e.g. Precision IceCube Next Generation Upgrade (PINGU). For radio-Cherenkov experiments which use the presence of a clear Cherenkov cone to determine the arrival direction, any variation in emission angle will directly and linearly translate into a change in apparent neutrino direction. In closing, we also describe a simple experiment to test this formalism, and calculate the impact of anisotropy on light-yields from lead tungstate crystals as used, for example, in the CMS calorimeter at the CERN LHC

The optical-ultraviolet continuum of Seyfert 2 galaxies

This paper aims to understand the continuum of Seyfert 2 galaxies. By fitting the single galaxies in the sample of Heckman et al. (1995) with composite models (shock+ photoionization from the active center), we show that five main components characterize the SED of the continuum. Shocks play an important role since they produce a high temperature zone where soft X-rays are emitted. We show that in the optical-UV range, the slope of the NLR emission reproduces the observed values, and may be the main component of the featureless continuum. The presence of star forming regions cannot be excluded in the circumnuclear region of various Seyfert galaxies. An attempt is made to find their fingerprints in the observed AGN spectra. Finally, it is demonstrated that multi-cloud models are necessary to interpret the spectra of single objects, even in the global investigation of a sample of galaxies.Comment: 26 pages, LaTeX (including 5 Tables) + 17 PostScript figures. To appear in "The Astrophysical Journal