Positive contraction mappings for classical and quantum Schrodinger systems

The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior, and the law dictates a controlled path that abides by the specified marginals. Schrodinger proved that the optimal steering of the density between the two end points is effected by a multiplicative functional transformation of the prior; this transformation represents an automorphism on the space of probability measures and has since been studied by Fortet, Beurling and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins with the problem of steering a Markov chain between given marginals. Our approach is based on the Hilbert metric and leads to an alternative proof which, however, is constructive. More specifically, we show that the solution to the Schrodinger bridge is provided by the fixed point of a contractive map. We approach in a similar manner the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map, but only for the case of uniform marginals. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.Comment: 27 page

Longitudinal magnon in the tetrahedral spin system Cu2Te2O5Br2 near quantum criticality

We present a comprehensive study of the coupled tetrahedra-compound Cu2Te2O5Br2 by theory and experiments in external magnetic fields. We report the observation of a longitudinal magnon in Raman scattering in the ordered state close to quantum criticality. We show that the excited tetrahedral-singlet sets the energy scale for the magnetic ordering temperature T_N. This energy is determined experimentally. The ordering temperature T_N has an inverse-log dependence on the coupling parameters near quantum criticality

Dynamical lattice instability versus spin liquid state in a frustrated spin chain system

The low-dimensional s=1/2 compound (NO)[Cu(NO3)3] has recently been suggested to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system shows unbound spinon excitations and a resonating valence bond ground state due spin frustration. Our Raman scattering study demonstrates phonon anomalies as well as the suppression of a broad magnetic scattering continuum for temperatures below a characteristic temperature, T<T*=100K. We interpret these effects as evidence for a dynamical interplay of spin and lattice degrees of freedom that might lead to a further transition into a dimerized or structurally distorted phase at lower temperatures.Comment: 5 pages, 6 figure

Rural electrification in Indonesia : the role of micro hydro power in shaping forest conservation behavior

It is reported that villagers at the villages electrified by micro hydro power (MHP) show more favorable attitudes, intentions, and behaviors toward forest conservation. They initiated a community-based agreement regulating forest cutting, reduced trees chopped from the forests, reduced intention toward forest cutting, and even participated in reforestation. The present study is supposed to test this phenomenon and to find out which variables are determining intentions to behave more favorably toward forest conservation. The Theory of Planned Behavior (TPB) is applied to explain the behavior in question. TPB suggests that intention is the best predictor of behavior and it is determined by attitudes toward the behavior, subjective norms, and perceived behavioral control. These concepts, together with descriptive norms and past behavior, are compared between participants from a village with MHP and participants from a village with no electricity. A comparison between participants from another village with MHP and those from a village with grid electricity is also conducted. The results reveal that MHP inconsistently predicted participants’ beliefs, attitudes, norms, perceived control, intention, and behavior toward forest conservation. Participants from the village electrified by MHP for 4 years showed more concern toward forest conservation than participants from the village without electricity. However, participants from the villages electrified by MHP for a year showed less concern toward forest conservation than participants from the village, which has been grid electrified for 10 years. Regrouping the villages into electrified and non electrified villages gave evidence that rural electrification, regardless of its sources, positively shaped participants’ beliefs, attitudes, norms, perceived control, intention, and behavior toward forest conservation. Regression analyses showed that intentions to behave toward forest conservation were determined by subjective norms, past behavior and educational background

Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer Compound SrCu2(BO3)2

We present a Raman light scattering study of the two-dimensional quantum spin system SrCu2(BO3)2 and show that the magnetic excitation spectrum has a rich structure, including several well-defined bound state modes at low temperature, and a scattering continuum and quasielastic light scattering contributions at high temperature. The key to the understanding of the unique features of SrCu2(BO3)2 is the presence of strong interactions between well-localized triplet excitations in the network of orthogonal spin dimers realized in this compound. Based on our analysis of the Heisenberg model relevant for this material, we argue that the collective excitations involving two and three-particle singlet bound states have large binding energies and are observed as well-defined peaks in the Raman spectrum.Comment: 5 pages, 2 figures. Revised version, to appear in Phys. Rev. Lett. (2000

Ground state order and spin-lattice coupling in tetrahedral spin systems Cu2Te2O5X2

High-resolution ac susceptibility and thermal conductivity measurement on Cu2Te2O5X2(X=Br,Cl) single crystals are reported. For Br-sample, sample dependence prevents to distinguish between possibilities of magnetically ordered and spin-singlet ground states. In Cl-sample a three-dimensional transition at 18.5 K is accompanied by almost isotropic behavior of susceptibility and almost switching behavior of thermal conductivity. Thermal conductivity studies suggest the presence of a tremendous spin-lattice coupling characterizing Cl- but not Br-sample. Below the transition Cl-sample is in a complex magnetic state involving AF order but also the elements consistent with the presence of a gap in the excitation spectrum.Comment: version accepted for publication in Phys.Rev.B-Rapid Communicatio

Bulk antiferromagnetism in Na0.82CoO2\bf Na_{0.82}CoO_2 single crystals

Susceptibility, specific heat, and muon spin rotation measurements on high-quality single crystals of $\rm Na_{0.82}CoO_2$ have revealed bulk antiferromagnetism with N\'{e}el temperature $\rm T_N = 19.8 \pm 0.1$ K and an ordered moment perpendicular to the $\rm CoO_2$ layers. The magnetic order encompasses nearly 100% of the crystal volume. The susceptibility exhibits a broad peak around 30 K, characteristic of two-dimensional antiferromagnetic fluctuations. The in-plane resistivity is metallic at high temperatures and exhibits a minimum at $\rm T_N$.Comment: published versio

Magnetism of a tetrahedral cluster spin-chain

We discuss the magnetic properties of a dimerized and completely frustrated tetrahedral spin-1/2 chain. Using a combination of exact diagonalization and bond-operator theory the quantum phase diagram is shown to incorporate a singlet-product, a dimer, and a Haldane phase. In addition we consider one-, and two-triplet excitations in the dimer phase and evaluate the magnetic Raman cross section which is found to be strongly renormalized by the presence of a two-triplet bound state. The link to a novel tellurate materials is clarified.Comment: 8 pages, 8 figure