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 $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. 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