The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data provide stringent limits on deviations from the minimal, six-parameter Λ cold dark matter model. We report these limits and use them to constrain the physics of cosmic inflation via Gaussianity, adiabaticity, the power spectrum of primordial fluctuations, gravitational waves, and spatial curvature. We also constrain models of dark energy via its equation of state, parity-violating interaction, and neutrino properties, such as mass and the number of species. We detect no convincing deviations from the minimal model. The six parameters and the corresponding 68% uncertainties, derived from the WMAP data combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO) in the distribution of galaxies, are: Ω b h 2 = 0.02267+0.00058 –0.00059, Ω c h 2 = 0.1131 ± 0.0034, ΩΛ = 0.726 ± 0.015, ns = 0.960 ± 0.013, τ = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these, we derive σ8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc–1, Ω b = 0.0456 ± 0.0015, Ω c = 0.228 ± 0.013, Ω m h 2 = 0.1358+0.0037 –0.0036, z reion = 10.9 ± 1.4, and t 0 = 13.72 ± 0.12 Gyr. With the WMAP data combined with BAO and SN, we find the limit on the tensor-to-scalar ratio of r 1 is disfavored even when gravitational waves are included, which constrains the models of inflation that can produce significant gravitational waves, such as chaotic or power-law inflation models, or a blue spectrum, such as hybrid inflation models. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and the spatial curvature of the universe: –0.14 < 1 + w < 0.12(95%CL) and –0.0179 < Ω k < 0.0081(95%CL). We provide a set of WMAP distance priors, to test a variety of dark energy models with spatial curvature. We test a time-dependent w with a present value constrained as –0.33 < 1 + w 0 < 0.21 (95% CL). Temperature and dark matter fluctuations are found to obey the adiabatic relation to within 8.9% and 2.1% for the axion-type and curvaton-type dark matter, respectively. The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than –59 < Δα < 24 (95% CL) between the decoupling and the present epoch. We find the limit on the total mass of massive neutrinos of ∑m ν < 0.67 eV(95%CL), which is free from the uncertainty in the normalization of the large-scale structure data. The number of relativistic degrees of freedom (dof), expressed in units of the effective number of neutrino species, is constrained as N eff = 4.4 ± 1.5 (68%), consistent with the standard value of 3.04. Finally, quantitative limits on physically-motivated primordial non-Gaussianity parameters are –9 < f local NL < 111 (95% CL) and –151 < f equil NL < 253 (95% CL) for the local and equilateral models, respectively.

https://iopscience.iop.org/article/10.1088/0067-0049/180/2/330/pdf

Five-year wilkinson microwave anisotropy probe observations: cosmological interpretation

Metal–Organic Frameworks for Separations

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.

/pdf/the-density-matrix-renormalization-group-in-the-age-of-6718dr7b3l.pdf

The density-matrix renormalization group in the age of matrix product states

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.

http://www.physics.udel.edu/~bnikolic/QTTG/NOTES/DMRG/SCHOLLWOCK=RMP_dmrg.pdf

The density-matrix renormalization group

New varieties of quasi-one-dimensional transition metal (M)-halide (X) compounds, $$(\hbox{C}_8\hbox{H}_6\hbox{N}_4)[\hbox{Pt}(\hbox{C}_2\hbox{H}_8\hbox{N}_2)\hbox{Cl}]_2\hbox{Cl}(\hbox{ClO}_4)_3\cdot \hbox{H}_2\hbox{O}$$
 and $$(\hbox{C}_{10}\hbox{H}_8\hbox{N}_2)[\hbox{Pt}(\hbox{C}_4\hbox{H}_{13}\hbox{N}_3)\hbox{Br}]_2\hbox{Br}_4\cdot 2\hbox{H}_2\hbox{O},$$
 comprising two-leg ladders of mixed-valent platinum complexes, are theoretically investigated with particular emphasis on their photoresponses. Observations of the polarized optical conductivity prove the interchain valence arrangement to be in phase in the former but out of phase in the latter. Possible nonlinear lattice relaxation originating with a photogenerated exciton is also simulated in an attempt to further elucidate the contrast between them.

Optical observations of new halogen-bridged platinum complexes assembled within a ladder lattice

A formation and confinement experiment for fast ions is performed using the ion cyclotron range of frequencies (ICRF) minority heating scheme with a proton minority and a deuteron majority in Heliotron J, a low-shear helical-axis heliotron. The effect of the magnetic configuration on the fast-ion confinement is one of the most important issues in helical devices. In this paper, the effect of bumpiness, one of the Fourier components of the field strength, on the trapped fast-ion confinement is clarified by using ICRF minority heating. The role of the bumpiness is a key issue for the design principle of the magnetic field of Heliotron J, where the particle confinement is controlled by the bumpiness. Here, the bumpiness or the bumpy ripple is defined by the Fourier harmonic ratio eb ≡ B04/B00 in (Mizuuchi T et al 2006 Fusion Sci. Technol. 50 352), where B04 is the bumpy component and B00 is the averaged magnetic field strength. The proper bumpiness causes deeply trapped particles to be confined in the small grad-B region. High-energy ions are produced up to 10 keV by injecting an ICRF pulse into an electron cyclotron heating target plasma where ion temperature at the centre Ti(0) = 0.2 keV, electron temperature at the centre Te(0) = 0.8 keV and line-averaged electron density . For the study of the configuration dependence of the fast particle confinement, three configurations are selected; the bumpy ripples are 0.01, 0.06 and 0.15 at the normalized minor radius ρ = 0.67. The measured tail temperatures by using a charge-exchange neutral energy analyser are 1.10 keV, 0.88 keV and 0.50 keV for the ripples of 0.15, 0.06 and 0.01, respectively. The heating efficiency of the bulk ion is also better in the high bumpy case. A Monte-Carlo analysis also indicates good confinement of the high energy ions in the high bumpy case although the difference is not very large compared with the experiment.

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Dependence of the confinement of fast ions generated by ICRF heating on the field configuration in heliotron J

Employing the one-dimensional single-band extended Peierls-Hubbard model, we investigate optical conductivity for solitonic excitations in halogen-bridged binuclear metal $(MMX)$ complexes. Photoinduced soliton absorption spectra for $MMX$ chains possibly split into two bands, forming a striking contrast to those for conventional mononuclear metal $(MX)$ analogs, due to the broken electron-hole symmetry combined with relevant Coulomb and∕or electron-phonon interactions.

Soliton-induced optical absorption of halogen-bridged mixed-valence binuclear metal complexes

Based on a symmetry argument, we study the ground-state properties of halogen-bridged binuclear metal chain complexes. We systematically derive commensurate density-wave solutions from a relevant two-band Peierls-Hubbard model and numerically draw the the ground-state phase diagram as a function of electron-electron correlations, electron-phonon interactions, and doping concentration within the Hartree-Fock approximation. The competition between two types of charge-density-wave states, which has recently been reported experimentally, is demonstrated.

Competing Ground States of the New Class of Halogen-Bridged Metal Complexes

Motivated by recent stimulative observations in halogen (X)-bridged binuclear transition-metal (M) complexes, which are referred to as MMX chains, we study solitons in a one-dimensional three-quarter-filled charge-density-wave system with both intrasite and intersite electron-lattice couplings. Two distinct ground states of MMX chains are reproduced and the soliton excitations on them are compared. In the weak-coupling region, all the solitons are degenerate to each other and are uniquely scaled by the band gap, whereas in the strong-coupling region, they behave differently deviating from the scenario in the continuum limit. The soliton masses are calculated and compared with those for conventional mononuclear MX chains.

Shoji Yamamoto

Papers

Optical observations of new halogen-bridged platinum complexes assembled within a ladder lattice

Dependence of the confinement of fast ions generated by ICRF heating on the field configuration in heliotron J

Soliton-induced optical absorption of halogen-bridged mixed-valence binuclear metal complexes

Competing Ground States of the New Class of Halogen-Bridged Metal Complexes

Soliton Excitations in Halogen-Bridged Mixed-Valence Binuclear Metal Complexes