2,722 research outputs found
Auxiliary master equation for nonequilibrium dual-fermion approach
We introduce auxiliary quantum master equation - dual fermion approach
(QME-DF) and argue that it presents a convenient way to describe steady-states
of correlated impurity systems. The combined scheme yields an expansion around
a reference much closer to the true nonequilibrium state than in the original
dual fermion formulation. In steady-state situations, the scheme is numerically
cheaper and allows to avoid long time propagation of previous considerations.
Anderson impurity is used as a test model. The QME-DF simulations are compared
with numerically exact tdDMRG results.Comment: 8 pages, 4 figure
Stochastic Programming with Probability
In this work we study optimization problems subject to a failure constraint.
This constraint is expressed in terms of a condition that causes failure,
representing a physical or technical breakdown. We formulate the problem in
terms of a probability constraint, where the level of "confidence" is a
modelling parameter and has the interpretation that the probability of failure
should not exceed that level. Application of the stochastic Arrow-Hurwicz
algorithm poses two difficulties: one is structural and arises from the lack of
convexity of the probability constraint, and the other is the estimation of the
gradient of the probability constraint. We develop two gradient estimators with
decreasing bias via a convolution method and a finite difference technique,
respectively, and we provide a full analysis of convergence of the algorithms.
Convergence results are used to tune the parameters of the numerical algorithms
in order to achieve best convergence rates, and numerical results are included
via an example of application in finance
Duality and separation theorems in idempotent semimodules
We consider subsemimodules and convex subsets of semimodules over semirings
with an idempotent addition. We introduce a nonlinear projection on
subsemimodules: the projection of a point is the maximal approximation from
below of the point in the subsemimodule. We use this projection to separate a
point from a convex set. We also show that the projection minimizes the
analogue of Hilbert's projective metric. We develop more generally a theory of
dual pairs for idempotent semimodules. We obtain as a corollary duality results
between the row and column spaces of matrices with entries in idempotent
semirings. We illustrate the results by showing polyhedra and half-spaces over
the max-plus semiring.Comment: 24 pages, 5 Postscript figures, revised (v2
Negative Differential Spin Conductance by Population Switching
An examination of the properties of many-electron conduction through
spin-degenerate systems can lead to situations where increasing the bias
voltage applied to the system is predicted to decrease the current flowing
through it, for the electrons of a particular spin. While this does not
necessarily constitute negative differential conductance (NDC) per se, it is an
example of negative differential conductance per spin (NDSC) which to our
knowledge is discussed here for the first time. Within a many-body master
equation approach which accounts for charging effects in the Coulomb Blockade
regime, we show how this might occur.Comment: 6 page, 2 figure
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Numerically exact full counting statistics of the energy current in the Kondo regime
We use the inchworm Quantum Monte Carlo method to investigate the full
counting statistics of particle and energy currents in a strongly correlated
quantum dot. Our method is used to extract the heat fluctuations and entropy
production of a quantum thermoelectric device, as well as cumulants of the
particle and energy currents. The energy--particle current cross correlations
reveal information on the preparation of the system and the interplay of
thermal and electric currents. We furthermore demonstrate the signature of a
crossover from Coulomb blockade to Kondo physics in the energy current
fluctuations, and show how the conventional master equation approach to full
counting statistics systematically fails to capture this crossover
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