Structure and consequences of vortex-core states in p-wave superfluids

It is now well established that in two-dimensional chiral p-wave paired superfluids, the vortices carry zero-energy modes which obey non-abelian exchange statistics and can potentially be used for topological quantum computation. In such superfluids there may also exist other excitations below the bulk gap inside the cores of vortices. We study the properties of these subgap states, and argue that their presence affects the topological protection of the zero modes. In conventional superconductors where the chemical potential is of the order of the Fermi energy of a non-interacting Fermi gas, there is a large number of subgap states and the mini-gap towards the lowest of these states is a small fraction of the Fermi energy. It is therefore difficult to cool the system to below the mini-gap and at experimentally available temperatures, transitions between the subgap states, including the zero modes, will occur and can alter the quantum states of the zero-modes. We show that compound qubits involving the zero-modes and the parity of the occupation number of the subgap states on each vortex are still well defined. However, practical schemes taking into account all subgap states would nonetheless be difficult to achieve. We propose to avoid this difficulty by working in the regime of small chemical potential mu, near the transition to a strongly paired phase, where the number of subgap states is reduced. We develop the theory to describe this regime of strong pairing interactions and we show how the subgap states are ultimately absorbed into the bulk gap. Since the bulk gap vanishes as mu -> 0 there is an optimum value mu_c which maximises the combined gap. We propose cold atomic gases as candidate systems where the regime of strong interactions can be explored, and explicitly evaluate mu_c in a Feshbach resonant K-40 gas.Comment: 19 pages, 10 figures; v2: main text as published version, additional detail included as appendice

Simple Quantum Systems in Spacetimes with Closed Timelike Curves

Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with hard spheres and the exact solution of a totally discrete model are unitary.Comment: 15 pages, CALT-68-180

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Increased dissolved terrestrial input to the coastal ocean during the last deglaciation

Here we present the first downcore results for a new paleoproxy, the Mn/Ca ratio of foraminiferal calcite, applied to sediment accumulated in the extreme Eastern Tropical North Pacific (ETNP) over the last 30,000 years. The Mn/Ca results are compared to oxygen isotopes and sea surface temperature calculated from Mg/Ca. We determined metal ratios using flow-through time-resolved analysis to minimize the effects of secondary mineralization. The foraminiferal species used for this study calcify at different depths. Core top ratios of these variant species change in proportion to the concentration of dissolved manganese in the water column at the depth of calcification. Since terrestrial input and oxidation reduction reactions control the levels of dissolved Mn in the oceans today, it therefore should be possible to use the Mn/Ca ratios of foraminifera as a proxy for these processes in the past. Mn/Ca of a mixed-layer species (G. ruber) suggest that dissolved terrestrial input to the surface waters of the ETNP during the last glacial maximum was lower than today but began to increase with initial sea level rise and reached a maximum at 15 ka B.P. before coming down to present-day levels at the end of sea level rise in the mid-Holocene (7–5 ka). Ratios of a deeper calcifying species (N. dutertrei) mimic those of G. ruber over this same time period, consistent with shoaling of the 18°C thermocline. Mn/Ca of a benthic species (U. peregrina) does not show a maximum at 15 ka, suggesting that Mn was efficiently remineralized in the water column during deglaciation. Assuming that the period from the last glacial until the mid-Holocene was a time of increased productivity, as elevated Mn might imply, the oxygen minimum zone (OMZ) was at least as well developed during deglaciation as it is today. Expansion of the OMZ may have contributed to the Mn/Ca trends we observe through time

The averaged null energy condition for general quantum field theories in two dimensions

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur

No Time Machine Construction in Open 2+1 Gravity with Timelike Total Energy Momentum

It is shown that in 2+1 dimensional gravity an open spacetime with timelike sources and total energy momentum cannot have a stable compactly generated Cauchy horizon. This constitutes a proof of a version of Kabat's conjecture and shows, in particular, that not only a Gott pair cannot be formed from processes such as the decay of a single cosmic string as has been shown by Carroll et al., but that, in a precise sense, a time machine cannot be constructed at all.Comment: 7 pages. Several changes and 3 figures added. To appear in Phys. Rev.

Quantum interest in two dimensions

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR

Restrictions on Negative Energy Density in Flat Spacetime

In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.Comment: 17 pages, including two figures, uses epsf, minor revisions in the Introduction, conclusions unchange

van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes

The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page

Geochemical proxies of North American freshwater routing during the Younger Dryas cold event

Author Posting. © The Authors, 2006. This is the author's version of the work. It is posted here by permission of National Academy of Sciences for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences 104 (2007): 6556-6561, doi:10.1073/pnas.0611313104.The Younger Dryas cold interval represents a time when much of the Northern Hemisphere cooled from ~12.9 to 11.5 kiloyears before present. The cause of this event, which has long been viewed as the canonical example of abrupt climate change, was initially attributed to the routing of freshwater to the St. Lawrence River with an attendant reduction in Atlantic meridional overturning circulation. However, this mechanism has recently been questioned because current proxies and dating techniques have been unable to confirm that eastward routing with an increase in freshwater flux occurred during the Younger Dryas. Here we use new geochemical proxies (ΔMg/Ca, U/Ca & 87Sr/86Sr) measured in planktonic foraminifera at the mouth of the St. Lawrence Estuary as tracers of freshwater sources to further evaluate this question. Our proxies, combined with planktonic δ18Oseawater and δ13C, confirm that routing of runoff from western Canada to the St. Lawrence River occurred at the start of the Younger Dryas, with an attendant increase in freshwater flux of 0.06 ± 0.02 Sverdrup (1 Sverdrup (Sv) = 106 m3 s-1). This base discharge increase is sufficient to have reduced Atlantic meridional overturning circulation and caused the Younger Dryas cold interval. In addition, our data indicate subsequent fluctuations in the freshwater flux to the St. Lawrence River of ~0.06 to 0.12 Sv, thus explaining the variability in the overturning circulation and climate during the Younger Dryas.This research was funded by the NSF Paleoclimate Program (P.U.C.) and the NSF (G.P.K.)