Orientation (vector space)

About: Orientation (vector space) is a research topic. Over the lifetime, 2531 publications have been published within this topic receiving 73256 citations.

Dynamics of the dissipative two-state system

Abstract: This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For $sl1$ the system is localized at zero temperature, and at finite $T$ relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For $sg2$ it undergoes underdamped coherent oscillations for all relevant temperatures, while for $1lsl2$ there is a crossover from coherent oscillation to overdamped relaxation as $T$ increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case, $s=1$, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature $T$: over most of the ($\ensuremath{\alpha}$,$T$) plane (including the whole region $\ensuremath{\alpha}g1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low $T$ and $0l\ensuremath{\alpha}l\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.

Effect of quantum-well structures on the thermoelectric figure of merit.

Abstract: Currently the materials with the highest thermoelectric figure of merit Z are ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ alloys. Therefore these compounds are the best thermoelectric refrigeration elements. However, since the 1960s only slow progress has been made in enhancing Z, either in ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ alloys or in other thermoelectric materials. So far, the materials used in applications have all been in bulk form. In this paper, it is proposed that it may be possible to increase Z of certain materials by preparing them in quantum-well superlattice structures. Calculations have been done to investigate the potential for such an approach, and also to evaluate the effect of anisotropy on the figure of merit. The calculations show that layering has the potential to increase significantly the figure of merit of a highly anisotropic material such as ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$, provided that the superlattice multilayers are made in a particular orientation. This result opens the possibility of using quantum-well superlattice structures to enhance the performance of thermoelectric coolers.

Orientation dependence of grain-boundary critical currents in YBa2Cu3O7- delta bicrystals

Abstract: The critical current densities across grain boundaries have been measured as a function of misorientation angle in the basal plane of bicrystals of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ For small misorientation angles, the ratio of the grain-boundary critical current density to the bulk critical current density is roughly proportional to the inverse of the misorientation angle; for large angles, this ratio saturates to a value of about $\frac{1}{50}$ These results imply that achieving a high degree of texture both normal to and within the basal plane is important for the obtaining of very high critical currents in pure polycrystalline samples

Neutrino decay and spontaneous violation of lepton number

Abstract: The orders of magnitude of decay rates for relatively light neutrinos are studied in the framework of the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) gauge group. The assumption is made that a hierarchy parameter $\ensuremath{\epsilon}(\ensuremath{\approx}(\mathrm{muon}\mathrm{mass})\textdiv{}[\mathrm{some}\mathrm{new}\mathrm{mass}\mathrm{scale}(\mathrm{possibly}\mathrm{much}\mathrm{smaller}\mathrm{than}\mathrm{the}\mathrm{grand}\mathrm{unification}\mathrm{scale})])$ plays a meaningful role in the full theory. For orientation it is first noted that the traditional $\ensuremath{ u}\ensuremath{\gamma}$ decay channel as well as the $3\ensuremath{ u}$ decay channel give neutrino lifetimes which for "typical" parameters are substantially longer than the age of the universe. Then we examine in detail some recent proposals which are claimed to result in greatly speeded-up decays into $\ensuremath{ u}$+Majoron, where the Majoron is a true Goldstone boson associated with spontaneous breakdown of lepton number. In a theory in which the usual Higgs doublet is augmented by a complex singlet (1-2 model) it is noted that the decay width into $\ensuremath{ u}$+Majoron actually vanishes to order ${\ensuremath{\epsilon}}^{5}$. In a theory where the doublet is augmented by a complex triplet (2-3 model) this decay is shown to vanish exactly, neglecting radiative corrections. A more general Majoron theory (1-2-3 model) is constructed and shown to also yield a vanishing tree-level decay rate for $\ensuremath{ u}$+Majoron decay to order ${\ensuremath{\epsilon}}^{5}$. Finally, the tree amplitudes in the 1-2 and 1-2-3 models are shown to give decay widths for $\ensuremath{ u}$+Majoron of order ${\ensuremath{\epsilon}}^{9}$ which correspond to lifetimes much greater than the age of the universe.

Anisotropic ferromagnetism in substituted zinc oxide.

Abstract: Room-temperature ferromagnetism is observed in (110) oriented ZnO films made from targets containing 5 at. % of Sc, Ti, V, Fe, Co, or Ni, but not Cr, Mn, or Cu ions. There are large moments, $2.6{\ensuremath{\mu}}_{B}$ and $0.5{\ensuremath{\mu}}_{B}/\mathrm{\text{dopant atom}}$ for Co- and Ti-containing oxides, respectively. There is also a moment of $0.3{\ensuremath{\mu}}_{B}/\mathrm{S}\mathrm{c}$. Magnetization is very anisotropic, with variations of up to a factor of 3 depending on the orientation of the applied field relative to the substrate. Results are interpreted in terms of a spin-split donor impurity-band model, which can account for ferromagnetism in insulating or conducting high-$k$ oxides with concentrations of magnetic ions that lie far below the percolation threshold. Magnetic moments are associated with two-electron defects in the films as well as unpaired electrons of the $3d$ ions.