Quantum unitary dynamics in cosmological spacetimes

We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.Comment: 18 page

Uniqueness of the Fock quantization of the Gowdy T3T^3 model

After its reduction by a gauge-fixing procedure, the family of linearly polarized Gowdy $T^3$ cosmologies admit a scalar field description whose evolution is governed by a Klein-Gordon type equation in a flat background in 1+1 dimensions with the spatial topology of $S^1$, though in the presence of a time-dependent potential. The model is still subject to a homogeneous constraint, which generates $S^1$-translations. Recently, a Fock quantization of this scalar field was introduced and shown to be unique under the requirements of unitarity of the dynamics and invariance under the gauge group of $S^1$-translations. In this work, we extend and complete this uniqueness result by considering other possible scalar field descriptions, resulting from reasonable field reparameterizations of the induced metric of the reduced model. In the reduced phase space, these alternate descriptions can be obtained by means of a time-dependent scaling of the field, the inverse scaling of its canonical momentum, and the possible addition of a time-dependent, linear contribution of the field to this momentum. Demanding again unitarity of the field dynamics and invariance under the gauge group, we prove that the alternate canonical pairs of fieldlike variables admit a Fock representation if and only if the scaling of the field is constant in time. In this case, there exists essentially a unique Fock representation, provided by the quantization constructed by Corichi, Cortez, and Mena Marugan. In particular, our analysis shows that the scalar field description proposed by Pierri does not admit a Fock quantization with the above unitarity and invariance properties.Comment: 14 page

Quantum Gowdy T3T^3 model: A uniqueness result

Modulo a homogeneous degree of freedom and a global constraint, the linearly polarised Gowdy $T^3$ cosmologies are equivalent to a free scalar field propagating in a fixed nonstationary background. Recently, a new field parameterisation was proposed for the metric of the Gowdy spacetimes such that the associated scalar field evolves in a flat background in 1+1 dimensions with the spatial topology of $S^1$, although subject to a time dependent potential. Introducing a suitable Fock quantisation for this scalar field, a quantum theory was constructed for the Gowdy model in which the dynamics is implemented as a unitary transformation. A question that was left open is whether one might adopt a different, nonequivalent Fock representation by selecting a distinct complex structure. The present work proves that the chosen Fock quantisation is in fact unique (up to unitary equivalence) if one demands unitary implementation of the dynamics and invariance under the group of constant $S^1$ translations. These translations are precisely those generated by the global constraint that remains on the Gowdy model. It is also shown that the proof of uniqueness in the choice of complex structure can be applied to more general field dynamics than that corresponding to the Gowdy cosmologies.Comment: 28 pages, minor changes, version accepted for publication in Classical and Quantum Gravit

Generation of Fourier transform limited heralded single photons

In this paper we study the spectral (temporal) properties of heralded single photon wavepackets, triggered by the detection of an idler photon in the process of parametric downconversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier- transform limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfilment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wavepackets.Comment: 10 pages, 3 figure, PHYSICAL REVIEW A 75, 02381

Massless scalar field in de Sitter spacetime: unitary quantum time evolution

We prove that, under the standard conformal scaling, a massless field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. This result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum.Comment: 23 pages. Typos corrected, matches published versio

Enhanced ordering reduces electric susceptibility of liquids confined to graphene slit pores.

The behaviours of a range of polar and non-polar organic liquids (acetone, ethanol, methanol, N-methyl-2-pyrrolidone (NMP), carbon tetrachloride and water) confined to 2D graphene nanochannels with thicknesses in the range of 4.5 Å to 40 Å were studied using classical molecular dynamics and hybrid density functional theory. All liquids were found to organise spontaneously into ordered layers parallel to the confining surfaces, with those containing polar molecules having their electric dipoles aligned parallel to such surfaces. In particular, monolayers of NMP showed remarkable in-plane ordering and low molecular mobility, suggesting the existence of a previously unknown 2D solid-like phase. Calculations for polar liquids showed dramatically reduced static permittivities normal to the confining surfaces; these changes are expected to improve electron tunnelling across the liquid films, modifying the DC electrical properties of immersed assemblies of carbon nanomaterials.Mexican Council for Science and Technology (CONACyT)This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/srep2740

The electro-structural behaviour of yarn-like carbon nanotube fibres immersed in organic liquids.

Yarn-like carbon nanotube (CNT) fibres are a hierarchically-structured material with a variety of promising applications such as high performance composites, sensors and actuators, smart textiles, and energy storage and transmission. However, in order to fully realize these possibilities, a more detailed understanding of their interactions with the environment is required. In this work, we describe a simplified representation of the hierarchical structure of the fibres from which several mathematical models are constructed to explain electro-structural interactions of fibres with organic liquids. A balance between the elastic and surface energies of the CNT bundle network in different media allows the determination of the maximum lengths that open junctions can sustain before collapsing to minimize the surface energy. This characteristic length correlates well with the increase of fibre resistance upon immersion in organic liquids. We also study the effect of charge accumulation in open interbundle junctions and derive expressions to describe experimental data on the non-ohmic electrical behaviour of fibres immersed in polar liquids. Our analyses suggest that the non-ohmic behaviour is caused by progressively shorter junctions collapsing as the voltage is increased. Since our models are not based on any property unique to carbon nanotubes, they should also be useful to describe other hierarchical structures