Relation Between Quantum Speed Limits And Metrics On U(n)

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with 1\le p \le \limitingp induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.Comment: minor amendments, 6 pages, to appear in J.Phys.

Coulomb Driven New Bound States at the Integer Quantum Hall States in GaAs/Al(0.3)Ga(0.7)As Single Heterojunctions

Coulomb driven, magneto-optically induced electron and hole bound states from a series of heavily doped GaAs/Al(0.3)Ga(0.7)As single heterojunctions (SHJ) are revealed in high magnetic fields. At low magnetic fields (nu > 2), the photoluminescence spectra display Shubnikov de-Haas type oscillations associated with the empty second subband transition. In the regime of the Landau filling factor nu < 1 and 1 < nu <2, we found strong bound states due to Mott type localizations. Since a SHJ has an open valence band structure, these bound states are a unique property of the dynamic movement of the valence holes in strong magnetic fields

Forecasting wind speed data by using a combination of ARIMA model with single exponential smoothing

Wind serves as natural resources as the solution to minimize global warming and has been commonly used to produce electricity. Because of their uncontrollable wind characteristics, wind speed forecasting is considered one of the best challenges in developing power generation. The Autoregressive Integrated Moving Average (ARIMA), Simple Exponential Smoothing (SES) and a hybrid model combination of ARIMA and SES will be used in this study to predict the wind speed. The mean absolute percentage error (MAPE) and the root mean square error (RMSE) are used as measurement of efficiency. The hybrid model provides a positive outcome for predicting wind speed compare to the single model of ARIMA and SES

Renormalization of the periodic Anderson model: an alternative analytical approach to heavy Fermion behavior

In this paper a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians is applied to the periodic Anderson model (PAM) with the aim to describe heavy Fermion behavior. In this method high-energetic excitation operators instead of high energetic states are eliminated. We arrive at an effective Hamiltonian for a quasi-free system which consists of two non-interacting heavy-quasiparticle bands. The resulting renormalization equations for the parameters of the Hamiltonian are valid for large as well as small degeneracy $\nu_f$ of the angular momentum. An expansion in $1/\nu_f$ is avoided. Within an additional approximation which adapts the idea of a fixed renormalized \textit{f} level $\tilde{\epsilon}_{f}$, we obtain coupled equations for $\tilde{\epsilon}_{f}$ and the averaged \textit{f} occupation $$. These equations resemble to a certain extent those of the usual slave boson mean-field (SB) treatment. In particular, for large $\nu_f$ the results for the PRM and the SB approach agree perfectly whereas considerable differences are found for small $\nu_f$.Comment: 26 pages, 5 figures included, discussion of the DOS added in v2, accepted for publication in Phys. Rev.

What can Gaussian Processes really tell us about supernova lightcurves? Consequences for Type II(b) morphologies and genealogies

Machine learning has become widely used in astronomy. Gaussian Process (GP) regression in particular has been employed a number of times to fit or re-sample supernova (SN) light-curves, however by their nature typical GP models are not suited to fit SN photometric data and they will be prone to over-fitting. Recently GP re-sampling was used in the context of studying the morphologies of type II and IIb SNe and they were found to be clearly distinct with respect to four parameters: the rise time (t$_{\rm rise}$), the magnitude difference between 40 and 30 days post explosion ($\Delta m_{\rm 40-30}$), the earliest maximum (post-peak) of the first derivative (dm1) and minimum of the second derivative (dm2). Here we take a close look at GP regression and its limitations in the context of SN light-curves in general, and we also discuss the uncertainties on these specific parameters, finding that dm1 and dm2 cannot give reliable astrophysical information. We do reproduce the clustering in t$_{\rm rise}$--$\Delta m_{\rm 40-30}$ space although it is not as clear cut as previously presented. The best strategy to accurately populate the t$_{\rm rise}$-- $\Delta m_{\rm 40-30}$ space will be to use an expanded sample of high quality light-curves (such as those in the ATLAS transient survey) and analytical fitting methods. Finally, using the BPASS fiducial models, we predict that future photometric studies will reveal clear clustering of the type IIb and II light curve morphologies with a distinct continuum of transitional events.Comment: 13 pages, 11 figures, 2 tables, Accepted for publication in MNRA

Dilaton test of connection between AdS_3 X S^3 and 5D black hole

A 5D black hole(M$_5$) is investigated in the type IIB superstring theory compactified on S$^1 \times$T$^4$. This corresponds to AdS$_3 \times$S$^3 \times$T$^4$ in the near horizon with asymptotically flat space. Here the harmonic gauge is introduced to decouple the mixing between the dilaton and others. On the other hand we obtain the BTZ balck hole(AdS$_3\times$S$^3\times$T$^4$) as the non-dilatonic solution. We calculate the greybody factor of the dilaton as a test scalar both for a 5D black hole(M$_5 \times$S$^1 \times$T$^4$) and the BTZ black hole(AdS$_3 \times$S$^3 \times$T$^4$). The result of the BTZ black hole agrees with the greybody factor of the dilaton in the dilute gas approximation of a 5D black hole.Comment: revised version to appear in classical and quantum gravity, 15 pages with RevTe

Condensation in ideal Fermi gases

I investigate the possibility of condensation in ideal Fermi systems of general single particle density of states. For this I calculate the probability $w_{N_0}$ of having exactly $N_0$ particles in the condensate and analyze its maxima. The existence of such maxima at macroscopic values of $N_0$ indicates a condensate. An interesting situation occurs for example in 1D systems, where $w_{N_0}$ may have two maxima. One is at $N_0=0$ and another one may exist at finite $N_0$ (for temperatures bellow a certain condensation temperature). This suggests the existence of a first order phase transition. % The calculation of $w_{N_0}$ allows for the exploration of ensemble equivalence of Fermi systems from a new perspective.Comment: 8 pages with 1 figure. Will appear in J. Phys. A: Math. Gen. Changes (minor): I updated Ref. [9] and its citation in the text. I introduced citation for figure 1 in the tex

Infrared phonons and specific heat in Ba3Cr2O8

We report on the phonon spectrum of Ba3Cr2O8 determined by infrared spectroscopy, and on specific heat measurements across the Jahn-Teller transition in magnetic fields up to 9 T. Phonon modes split below the Jahn-Teller transition, which occurs at T_{JT} = 70 K as detected by specific heat measurements. The field-dependent specific heat data is analyzed in terms of the contributions from lattice, magnetic and orbital degrees of freedom. In contrast to the isostructural compound Sr3Cr2O8 our analysis does not indicate the existence of orbital fluctuations below the Jahn-Teller transition in Ba3Cr2O8.Comment: 5 pages, 4 figure

Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions

The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=\rho a^d$ where $\rho$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated.Comment: Proceedings of the QFS2004 conference in Trento. To appear in JLT