57 research outputs found
Fluctuations of Quantum Currents and Unravelings of Master Equations
The very notion of a current fluctuation is problematic in the quantum
context. We study that problem in the context of nonequilibrium statistical
mechanics, both in a microscopic setup and in a Markovian model. Our answer is
based on a rigorous result that relates the weak coupling limit of fluctuations
of reservoir observables under a global unitary evolution with the statistics
of the so-called quantum trajectories. These quantum trajectories are
frequently considered in the context of quantum optics, but they remain useful
for more general nonequilibrium systems.
In contrast with the approaches found in the literature, we do not assume
that the system is continuously monitored. Instead, our starting point is a
relatively realistic unitary dynamics of the full system.Comment: 18 pages, v1-->v2, Replaced the former Appendix B by a (thematically)
different one. Mainly changes in the introductory Section 2+ added reference
'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion
Recently, several authors studied small quantum systems weakly coupled to
free boson or fermion fields at positive temperature. All the approaches we are
aware of employ complex deformations of Liouvillians or Mourre theory (the
infinitesimal version of the former). We present an approach based on polymer
expansions of statistical mechanics. Despite the fact that our approach is
elementary, our results are slightly sharper than those contained in the
literature up to now. We show that, whenever the small quantum system is known
to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad
equation) in the weak coupling limit, and the Markov approximation is
exponentially mixing, then the weakly coupled system approaches a unique
invariant state that is perturbatively close to its Markov approximation.Comment: 23 pages, v2-->v3: Revised version: The explanatory section 1.7 has
changed and Section 3.2 has been made more explici
Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics
of a dynamical Lorentz gas, by which we mean an ensemble of particles moving
through a -dimensional array of fixed soft scatterers that each possess an
internal harmonic or anharmonic degree of freedom to which moving particles
locally couple. We establish that the momentum distribution of the moving
particles approaches a Maxwell-Boltzmann distribution at a certain temperature
, provided that they are initially fast and the scatterers are in a
sufficiently energetic but otherwise arbitrary stationary state of their free
dynamics--they need not be in a state of thermal equilibrium. The temperature
to which the particles equilibrate obeys a generalized equipartition
relation, in which the associated thermal energy is equal to
an appropriately defined average of the scatterers' kinetic energy. In the
equilibrated state, particle motion is diffusive
Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
We consider a class of translation invariant models of non-relativistic QED
with net charge. Under certain natural assumptions we prove that ground states
do not exist in the Fock space
Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment
In this paper, we study inverse scattering of massless Dirac fields that
propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a
stationary approach we determine precisely the leading terms of the high-energy
asymptotic expansion of the scattering matrix that, in turn, permit us to
recover uniquely the mass of the black hole and its charge up to a sign
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
We consider massive Dirac fields evolving in the exterior region of a
5-dimensional Myers-Perry black hole and study their propagation properties.
Our main result states that the local energy of such fields decays in a weak
sense at late times. We obtain this result in two steps: first, using the
separability of the Dirac equation, we prove the absence of a pure point
spectrum for the corresponding Dirac operator; second, using a new form of the
equation adapted to the local rotations of the black hole, we show by a Mourre
theory argument that the spectrum is absolutely continuous. This leads directly
to our main result.Comment: 40 page
Derivation of some translation-invariant Lindblad equations for a quantum Brownian particle
We study the dynamics of a Brownian quantum particle hopping on an infinite
lattice with a spin degree of freedom. This particle is coupled to free boson
gases via a translation-invariant Hamiltonian which is linear in the creation
and annihilation operators of the bosons. We derive the time evolution of the
reduced density matrix of the particle in the van Hove limit in which we also
rescale the hopping rate. This corresponds to a situation in which both the
system-bath interactions and the hopping between neighboring sites are small
and they are effective on the same time scale. The reduced evolution is given
by a translation-invariant Lindblad master equation which is derived
explicitly.Comment: 28 pages, 4 figures, minor revisio
Introduction to representations of the canonical commutation and anticommutation relations
Lecture notes of a minicourse given at the Summer School on Large Coulomb
Systems - QED in Nordfjordeid, 2003, devoted to representations of the CCR and
CAR. Quasifree states, the Araki-Woods and Araki-Wyss representations, and the
lattice of von Neumenn algebras in a bosonic/fermionic Fock space are discussed
in detail
A Geometric Approach to the Landauer-Büttiker Formula
International audienceWe consider an ideal Fermi gas confined to a geometric structure consisting of a central region -- the sample -- connected to several infinitely extended ends -- the reservoirs. Under physically reasonable assumptions on the propagation properties of the one-particle dynamics within these reservoirs, we show that the state of the Fermi gas relaxes to a steady state. We compute the expected value of various current observables in this steady state and express the result in terms of scattering data, thus obtaining a geometric version of the celebrated Landauer-Büttiker formula
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