Temperature and Voltage Probes Far from Equilibrium

We consider an open system of non-interacting electrons consisting of a small sample connected to several reservoirs and temperature or voltage probes. We study the non-linear system of equations that determines the probe parameters. We show that it has a unique solution, which can be computed with a fast converging iterative algorithm. We illustrate our method with two well-known models: the three-terminal system and the open Aharovov-Bohm interferometer

Ergodic Properties of the Spin - Boson System

We investigate the dynamics of a 2-level atom (or spin-1/2) coupled to a mass-less bosonic field at positive temperature. We prove that, at small coupling, the combined quantum system approaches thermal equilibrium. Moreover we establish that this approach is exponentially fast in time. We first reduce the question to a spectral problem for the Liouvillean, a self-adjoint operator naturally associated with the system. To compute this operator, we invoke Tomita-Takesaki theory. Once this is done we use complex deformation techniques to study its spectrum. The corresponding zero temperature model is also reviewed and compared.Comment: 31 pages, postscrip

Scattering Phases and Density of States for Exterior Domain

For a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian -\DO on $\Omega$ and the S-matrix on the complement $\Omega^c$. Using the restriction $A_E$ of $(-\Delta-E)^{-1}$ to the boundary of $\Omega$, we establish that $A_{E_0}^{-1/2}A_EA_{E_0}^{-1/2}-1$ is trace class when $E_0$ is negative and give bounds on the energy dependence of this difference. This allows for precise bounds on the total scattering phase, the definition of a $\zeta$-function, and a Krein spectral formula, which improve similar results found in the literature.Comment: 15 pages, Postscript, A

Entropic fluctuations in XY chains and reflectionless Jacobi matrices

We study the entropic fluctuations of a general XY spin chain where initially the left(x0) part of the chain is in thermal equilibrium at inverse temperature Tl/Tr. The temperature differential results in a non-trivial energy/entropy flux across the chain. The Evans-Searles (ES) entropic functional describes fluctuations of the flux observable with respect to the initial state while the Gallavotti-Cohen (GC) functional describes these fluctuations with respect to the steady state (NESS) the chain reaches in the large time limit. We also consider the full counting statistics (FCS) of the energy/entropy flux associated to a repeated measurement protocol, the variational entropic functional (VAR) that arises as the quantization of the variational characterization of the classical Evans-Searles functional and a natural class of entropic functionals that interpolate between FCS and VAR. We compute these functionals in closed form in terms of the scattering data of the Jacobi matrix h canonically associated to the XY chain. We show that all these functionals are identical if and only if h is reflectionless (we call this phenomenon entropic identity). If h is not reflectionless, then the ES and GC functionals remain equal but differ from the FCS, VAR and interpolating functionals. Furthermore, in the non-reflectionless case, the ES/GC functional does not vanish at 1 (i.e., the Kawasaki identity fails) and does not have the celebrated ES/GC symmetry. The FCS, VAR and interpolating functionals always have this symmetry. In the cases where h is a Schr\"odinger operator, the entropic identity leads to some unexpected open problems in the spectral theory of one-dimensional discrete Schr\"odinger operators

Inferring telescope polarization properties through spectral lines without linear polarization

We present a technique to determine the polarization properties of a telescope through observations of spectral lines that have no intrinsic linear polarization signals. For such spectral lines, any observed linear polarization must be induced by the telescope optics. We apply the technique to observations taken with the SPINOR at the DST and demonstrate that we can retrieve the characteristic polarization properties of the DST at three wavelengths of 459, 526, and 615 nm. We determine the amount of crosstalk between the intensity Stokes I and the linear and circular polarization states Stokes Q, U, and V, and between Stokes V and Stokes Q and U. We fit a set of parameters that describe the polarization properties of the DST to the observed crosstalk values. The values for the ratio of reflectivities X and the retardance tau match those derived with the telescope calibration unit within the error bars. Residual crosstalk after applying a correction for the telescope polarization stays at a level of 3-10%. We find that it is possible to derive the parameters that describe the polarization properties of a telescope from observations of spectral lines without intrinsic linear polarization signal. Such spectral lines have a dense coverage (about 50 nm separation) in the visible part of the spectrum (400-615 nm), but none were found at longer wavelengths. Using spectral lines without intrinsic linear polarization is a promising tool for the polarimetric calibration of current or future solar telescopes such as DKIST.Comment: 22 pages, 24 figures, accepted for publication in A&

Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Supersonic beams of hydrogen atoms, prepared selectively in Rydberg-Stark states of principal quantum number $n$ in the range between 25 and 35, have been deflected by 90$^\circ$, decelerated and loaded into off-axis electric traps at initial densities of $\approx 10^6$ atoms/cm$^{-3}$ and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 K and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as $n^{-4}$ and corresponding closely to the natural lifetimes of the initially prepared Rydberg-Stark states. The decay rate was found to continually decrease over time and to reach an almost $n$-independent rate of more than (1 ms)$^{-1}$ after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. TheComment: 36 pages, 18 figure