52 research outputs found
A note on reflectionless Jacobi matrices
The property that a Jacobi matrix is reflectionless is usually characterized
either in terms of Weyl m-functions or the vanishing of the real part of the
boundary values of the diagonal matrix elements of the resolvent. We introduce
a characterization in terms of stationary scattering theory (the vanishing of
the reflection coefficients) and prove that this characterization is equivalent
to the usual ones. We also show that the new characterization is equivalent to
the notion of being dynamically reflectionless, thus providing a short proof of
an important result of [Breuer-Ryckman-Simon]. The motivation for the new
characterization comes from recent studies of the non-equilibrium statistical
mechanics of the electronic black box model and we elaborate on this
connection. To appear in Commun. Math. Phys.Comment: 10 page
Entropic fluctuations in thermally driven harmonic networks
We consider a general network of harmonic oscillators driven out of thermal
equilibrium by coupling to several heat reservoirs at different temperatures.
The action of the reservoirs is implemented by Langevin forces. Assuming the
existence and uniqueness of the steady state of the resulting process, we
construct a canonical entropy production functional which satisfies the
Gallavotti--Cohen fluctuation theorem, i.e., a global large deviation principle
with a rate function I(s) obeying the Gallavotti--Cohen fluctuation relation
I(-s)-I(s)=s for all s. We also consider perturbations of our functional by
quadratic boundary terms and prove that they satisfy extended fluctuation
relations, i.e., a global large deviation principle with a rate function that
typically differs from I(s) outside a finite interval. This applies to various
physically relevant functionals and, in particular, to the heat dissipation
rate of the network. Our approach relies on the properties of the maximal
solution of a one-parameter family of algebraic matrix Riccati equations. It
turns out that the limiting cumulant generating functions of our functional and
its perturbations can be computed in terms of spectral data of a Hamiltonian
matrix depending on the harmonic potential of the network and the parameters of
the Langevin reservoirs. This approach is well adapted to both analytical and
numerical investigations
A note on the entropy production formula
International audienceWe give an elementary derivation of the entropy production formula of [http://hal.archives-ouvertes.fr/hal-00005457] based on Araki Perturbation Theory of KMS states. Using this derivation we show that the entropy production of any normal, stationary state is zero
Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle
We study driven finite quantum systems in contact with a thermal reservoir in
the regime in which the system changes slowly in comparison to the
equilibration time. The associated isothermal adiabatic theorem allows us to
control the full statistics of energy transfers in quasi-static processes.
Within this approach, we extend Landauer's Principle on the energetic cost of
erasure processes to the level of the full statistics and elucidate the nature
of the fluctuations breaking Landauer's bound.Comment: 24 pages, 4 figures; In the new version, Section 4 contains an
extended discussion of the violation of Landauer's boun
Energy conservation, counting statistics, and return to equilibrium
We study a microscopic Hamiltonian model describing an N-level quantum system
S coupled to an infinitely extended thermal reservoir R. Initially, the system
S is in an arbitrary state while the reservoir is in thermal equilibrium at
temperature T. Assuming that the coupled system S+R is mixing with respect to
the joint thermal equilibrium state, we study the Full Counting Statistics
(FCS) of the energy transfers S->R and R->S in the process of return to
equilibrium. The first FCS describes the increase of the energy of the system
S. It is an atomic probability measure, denoted , concentrated
on the set of energy differences ( is
the spectrum of the Hamiltonian of S, is the length of the time interval
during which the measurement of the energy transfer is performed, and
is the strength of the interaction between S and R). The second FCS,
, describes the decrease of the energy of the reservoir R and
is typically a continuous probability measure whose support is the whole real
line. We study the large time limit of these two measures
followed by the weak coupling limit and prove that the
limiting measures coincide. This result strengthens the first law of
thermodynamics for open quantum systems. The proofs are based on modular theory
of operator algebras and on a representation of by quantum
transfer operators
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