7,984 research outputs found
Full Counting Statistics in the Resonant-Level Model
We derive the large deviation function, which provides the large-time full
counting statistics for the charge transfer, in the non-equilibrium steady
state of the resonant-level model. The general form of this function in free
fermion models, in terms of transmission coefficients, was proposed by Levitov
and Lesovik in 1993 using a particular measurement set-up involving an
interacting spin. It was later suggested to hold as well for a proper quantum
mechanical measurement of the transferred charge. We give a precise proof of
both statements in the resonant-level model. We first give a full description
of the model and its steady state. That is, we explain how the decoupled system
prepared with a charge differential evolves, with the impurity coupling,
towards the Hershfield non-equilibrium density matrix, in the sense of averages
of finitely-supported operators. We describe how this holds both for the usual
resonant-level model with a point-like impurity, and for a regularised model
with an impurity spread on a finite region, shedding light on subtleties
associated to the point-like impurity. We then prove Levitov-Lesovik formula by
recasting the problem into calculating averages of finitely-supported
operators.Comment: 31 pages, 1 figur
Conformal field theory out of equilibrium: a review
We provide a pedagogical review of the main ideas and results in
non-equilibrium conformal field theory and connected subjects. These concern
the understanding of quantum transport and its statistics at and near critical
points. Starting with phenomenological considerations, we explain the general
framework, illustrated by the example of the Heisenberg quantum chain. We then
introduce the main concepts underlying conformal field theory (CFT), the
emergence of critical ballistic transport, and the CFT scattering construction
of non-equilibrium steady states. Using this we review the theory for energy
transport in homogeneous one-dimensional critical systems, including the
complete description of its large deviations and the resulting (extended)
fluctuation relations. We generalize some of these ideas to one-dimensional
critical charge transport and to the presence of defects, as well as beyond
one-dimensional criticality. We describe non-equilibrium transport in
free-particle models, where connections are made with generalized Gibbs
ensembles, and in higher-dimensional and non-integrable quantum field theories,
where the use of the powerful hydrodynamic ideas for non-equilibrium steady
states is explained. We finish with a list of open questions. The review does
not assume any advanced prior knowledge of conformal field theory,
large-deviation theory or hydrodynamics.Comment: 50 pages + 10 pages of references, 5 figures. v2: minor
modifications. Review article for special issue of JSTAT on nonequilibrium
dynamics in integrable quantum system
A hydrodynamic approach to non-equilibrium conformal field theories
We develop a hydrodynamic approach to non-equilibrium conformal field theory.
We study non-equilibrium steady states in the context of one-dimensional
conformal field theory perturbed by the irrelevant operator. By
direct quantum computation, we show, to first order in the coupling, that a
relativistic hydrodynamic emerges, which is a simple modification of
one-dimensional conformal fluids. We show that it describes the steady state
and its approach, and we provide the main characteristics of the steady state,
which lies between two shock waves. The velocities of these shocks are modified
by the perturbation and equal the sound velocities of the asymptotic baths.
Pushing further this approach, we are led to conjecture that the approach to
the steady state is generically controlled by the power law , and
that the widths of the shocks increase with time according to .Comment: 24 page
Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
We consider non-equilibrium quantum steady states in conformal field theory
(CFT) on star-graph configurations, with a particular, simple connection
condition at the vertex of the graph. These steady states occur after a large
time as a result of initially thermalizing the legs of the graph at different
temperatures, and carry energy flows. Using purely Virasoro algebraic
calculations we evaluate the exact long-time cumulant generating function for
these flows. We show that this function satisfies a generalization of the usual
non-equilibrium fluctuation relations. This extends the results by two of the
authors (J. Phys. A 45: 362001, 2012; arXiv:1302.3125) to the cases of more
than two legs. It also provides an alternative derivation centered on Virasoro
algebra operators rather than local fields, hence an alternative regularization
scheme, thus confirming the validity and universality of the long-time cumulant
generating function. Our derivation shows how the usual Virasoro algebra leads,
in large volumes, to a continuous-index Virasoro algebra for which we develop
diagramatic principles, which may be of interest in other non-equilibrium
contexts as well. Finally, our results shed light on the Poisson process
interpretation of the long-time energy transfer in CFT.Comment: 26 pages, 2 figure
Optimal periodic dividend strategies for spectrally positive L\'evy risk processes with fixed transaction costs
We consider the general class of spectrally positive L\'evy risk processes,
which are appropriate for businesses with continuous expenses and lump sum
gains whose timing and sizes are stochastic. Motivated by the fact that
dividends cannot be paid at any time in real life, we study
dividend strategies whereby dividend decisions are made according to a separate
arrival process.
In this paper, we investigate the impact of fixed transaction costs on the
optimal periodic dividend strategy, and show that a periodic
strategy is optimal when decision times arrive according to an independent
Poisson process. Such a strategy leads to lump sum dividends that bring the
surplus back to as long as it is no less than at a dividend
decision time. The expected present value of dividends (net of transaction
costs) is provided explicitly with the help of scale functions. Results are
illustrated.Comment: Accepted for publication in Insurance: Mathematics and Economic
Convenient Multiple Directions of Stratification
This paper investigates the use of multiple directions of stratification as a
variance reduction technique for Monte Carlo simulations of path-dependent
options driven by Gaussian vectors. The precision of the method depends on the
choice of the directions of stratification and the allocation rule within each
strata. Several choices have been proposed but, even if they provide variance
reduction, their implementation is computationally intensive and not applicable
to realistic payoffs, in particular not to Asian options with barrier.
Moreover, all these previously published methods employ orthogonal directions
for multiple stratification. In this work we investigate the use of algorithms
producing convenient directions, generally non-orthogonal, combining a lower
computational cost with a comparable variance reduction. In addition, we study
the accuracy of optimal allocation in terms of variance reduction compared to
the Latin Hypercube Sampling. We consider the directions obtained by the Linear
Transformation and the Principal Component Analysis. We introduce a new
procedure based on the Linear Approximation of the explained variance of the
payoff using the law of total variance. In addition, we exhibit a novel
algorithm that permits to correctly generate normal vectors stratified along
non-orthogonal directions. Finally, we illustrate the efficiency of these
algorithms in the computation of the price of different path-dependent options
with and without barriers in the Black-Scholes and in the Cox-Ingersoll-Ross
markets.Comment: 21 pages, 11 table
Nitrogen isotopic fractionation during abiotic synthesis of organic solid particles
The formation of organic compounds is generally assumed to result from
abiotic processes in the Solar System, with the exception of biogenic organics
on Earth. Nitrogen-bearing organics are of particular interest, notably for
prebiotic perspectives but also for overall comprehension of organic formation
in the young solar system and in planetary atmospheres. We have investigated
abiotic synthesis of organics upon plasma discharge, with special attention to
N isotope fractionation. Organic aerosols were synthesized from N2-CH4 and
N2-CO gaseous mixtures using low-pressure plasma discharge experiments, aimed
at simulating chemistry occurring in Titan s atmosphere and in the protosolar
nebula, respectively. Nitrogen is efficiently incorporated into the synthesized
solids, independently of the oxidation degree, of the N2 content of the
starting gas mixture, and of the nitrogen speciation in the aerosols. The
aerosols are depleted in 15N by 15-25 permil relative to the initial N2 gas,
whatever the experimental setup is. Such an isotopic fractionation is
attributed to mass-dependent kinetic effect(s). Nitrogen isotope fractionation
upon electric discharge cannot account for the large N isotope variations
observed among solar system objects and reservoirs. Extreme N isotope
signatures in the solar system are more likely the result of self-shielding
during N2 photodissociation, exotic effect during photodissociation of N2
and/or low temperature ion-molecule isotope exchange. Kinetic N isotope
fractionation may play a significant role in the Titan s atmosphere. We also
suggest that the low delta15N values of Archaean organic matter are partly the
result of abiotic synthesis of organics that occurred at that time
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