670 research outputs found
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 with connected complement and
piecewise smooth boundary, we consider the Dirichlet Laplacian -\DO on
and the S-matrix on the complement . Using the restriction
of to the boundary of , we establish that
is trace class when 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
-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&
What is absolutely continuous spectrum?
This note is an expanded version of the author's contribution to the
Proceedings of the ICMP Santiago, 2015, and is based on a talk given by the
second author at the same Congress. It concerns a research program devoted to
the characterization of the absolutely continuous spectrum of a self-adjoint
operator H in terms of the transport properties of a suitable class of open
quantum systems canonically associated to H
A note on the Landauer principle in quantum statistical mechanics
The Landauer principle asserts that the energy cost of erasure of one bit of
information by the action of a thermal reservoir in equilibrium at temperature
T is never less than . We discuss Landauer's principle for quantum
statistical models describing a finite level quantum system S coupled to an
infinitely extended thermal reservoir R. Using Araki's perturbation theory of
KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural
ergodicity assumption on the joint system S+R, that Landauer's bound saturates
for adiabatically switched interactions. The recent work of Reeb and Wolf on
the subject is discussed and compared
Coherent excitation of a single atom to a Rydberg state
We present the coherent excitation of a single Rubidium atom to the Rydberg
state (58d3/2) using a two-photon transition. The experimental setup is
described in detail, as well as experimental techniques and procedures. The
coherence of the excitation is revealed by observing Rabi oscillations between
ground and Rydberg states of the atom. We analyze the observed oscillations in
detail and compare them to numerical simulations which include imperfections of
our experimental system. Strategies for future improvements on the coherent
manipulation of a single atom in our settings are given
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