904 research outputs found
Decoherence of Histories and Hydrodynamic Equations for a Linear Oscillator Chain
We investigate the decoherence of histories of local densities for linear
oscillators models. It is shown that histories of local number, momentum and
energy density are approximately decoherent, when coarse-grained over
sufficiently large volumes. Decoherence arises directly from the proximity of
these variables to exactly conserved quantities (which are exactly decoherent),
and not from environmentally-induced decoherence. We discuss the approach to
local equilibrium and the subsequent emergence of hydrodynamic equations for
the local densities.Comment: 37 pages, RevTe
Semipurity of tempered Deligne cohomology
In this paper we define the formal and tempered Deligne cohomology groups,
that are obtained by applying the Deligne complex functor to the complexes of
formal differential forms and tempered currents respectively. We then prove the
existence of a duality between them, a vanishing theorem for the former and a
semipurity property for the latter. The motivation of these results comes from
the study of covariant arithmetic Chow groups. The semi-purity property of
tempered Deligne cohomology implies, in particular, that several definitions of
covariant arithmetic Chow groups agree for projective arithmetic varieties
Entanglement entropy in quantum spin chains with finite range interaction
We study the entropy of entanglement of the ground state in a wide family of
one-dimensional quantum spin chains whose interaction is of finite range and
translation invariant. Such systems can be thought of as generalizations of the
XY model. The chain is divided in two parts: one containing the first
consecutive L spins; the second the remaining ones. In this setting the entropy
of entanglement is the von Neumann entropy of either part. At the core of our
computation is the explicit evaluation of the leading order term as L tends to
infinity of the determinant of a block-Toeplitz matrix whose symbol belongs to
a general class of 2 x 2 matrix functions. The asymptotics of such determinant
is computed in terms of multi-dimensional theta-functions associated to a
hyperelliptic curve of genus g >= 1, which enter into the solution of a
Riemann-Hilbert problem. Phase transitions for thes systems are characterized
by the branch points of the hyperelliptic curve approaching the unit circle. In
these circumstances the entropy diverges logarithmically. We also recover, as
particular cases, the formulae for the entropy discovered by Jin and Korepin
(2004) for the XX model and Its, Jin and Korepin (2005,2006) for the XY model.Comment: 75 pages, 10 figures. Revised version with minor correction
Towards reduction of type II theories on SU(3) structure manifolds
We revisit the reduction of type II supergravity on SU(3) structure
manifolds, conjectured to lead to gauged N=2 supergravity in 4 dimensions. The
reduction proceeds by expanding the invariant 2- and 3-forms of the SU(3)
structure as well as the gauge potentials of the type II theory in the same set
of forms, the analogues of harmonic forms in the case of Calabi-Yau reductions.
By focussing on the metric sector, we arrive at a list of constraints these
expansion forms should satisfy to yield a base point independent reduction.
Identifying these constraints is a first step towards a first-principles
reduction of type II on SU(3) structure manifolds.Comment: 20 pages; v2: condition (2.13old) on expansion forms weakened,
replaced by (2.13new), (2.14new
High-resolution error detection in the capture process of a single-electron pump
The dynamic capture of electrons in a semiconductor quantum dot (QD) by raising a potential
barrier is a crucial stage in metrological quantized charge pumping. In this work, we use a quantum
point contact (QPC) charge sensor to study errors in the electron capture process of a QD formed in
a GaAs heterostructure. Using a two-step measurement protocol to compensate for 1/f noise in the
QPC current, and repeating the protocol more than 106 times, we are able to resolve errors with
probabilities of order 106. For the studied sample, one-electron capture is affected by errors in
30 out of every million cycles, while two-electron capture was performed more than 106 times
with only one error. For errors in one-electron capture, we detect both failure to capture an electron
and capture of two electrons. Electron counting measurements are a valuable tool for investigating
non-equilibrium charge capture dynamics, and necessary for validating the metrological accuracy
of semiconductor electron pumps
Direct observation of exchange-driven spin interactions in one-dimensional system
We present experimental results of transverse electron focusing measurements performed on an ntype
GaAs based mesoscopic device consisting of one-dimensional (1D) quantum wires as injector
and detector. We show that non-adiabatic injection of 1D electrons at a conductance of e2/
h results in
a single first focusing peak, which transforms into two asymmetric sub-peaks with a gradual
increase in the injector conductance up to 2e2/
h , each sub-peak representing the population of spinstate
arising from the spatially separated spins in the injector. Further increasing the conductance
flips the spin-states in the 1D channel, thus reversing the asymmetry in the sub-peaks. On applying
a source-drain bias, the spin-gap, so obtained, can be resolved, thus providing evidence of exchange
interaction induced spin polarization in the 1D systems. V
Enhanced indistinguishability of in-plane single photons by resonance fluorescence on an integrated quantum dot
Integrated quantum light sources in photonic circuits are envisaged as the building blocks of future on-chip architectures for quantum logic operations. While semiconductor quantum dots have been proven to be the highly efficient emitters of quantum light, their interaction with the host material induces spectral decoherence, which decreases the indistinguishability of the emitted photons and limits their functionality. Here, we show that the indistinguishability of in-plane photons can be greatly enhanced by performing resonance fluorescence on a quantum dot coupled to a photonic crystal waveguide. We find that the resonant optical excitation of an exciton state induces an increase in the emitted single-photon coherence by a factor of 15. Two-photon interference experiments reveal a visibility of 0.80 ± 0.03, which is in good agreement with our theoretical model. Combined with the high in-plane light-injection efficiency of photonic crystal waveguides, our results pave the way for the use of this system for the on-chip generation and transmission of highly indistinguishable photons
The de Rham homotopy theory and differential graded category
This paper is a generalization of arXiv:0810.0808. We develop the de Rham
homotopy theory of not necessarily nilpotent spaces, using closed dg-categories
and equivariant dg-algebras. We see these two algebraic objects correspond in a
certain way. We prove an equivalence between the homotopy category of schematic
homotopy types and a homotopy category of closed dg-categories. We give a
description of homotopy invariants of spaces in terms of minimal models. The
minimal model in this context behaves much like the Sullivan's minimal model.
We also provide some examples. We prove an equivalence between fiberwise
rationalizations and closed dg-categories with subsidiary data.Comment: 47 pages. final version. The final publication is available at
http://www.springerlink.co
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
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