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Effective field theory descriptions of surface waves on flowing fluids have tended to assume that the flow is irrotational, but this assumption is often impractical due to boundary layer friction and flow recirculation. Here we develop an effective field theory of surface waves in an incompressible, inviscid flow that includes vorticity due to shear. Our model consists of a two-layer flow: an upper layer with no vorticity and a lower layer with constant vorticity. We consider linear, long-wavelength perturbations on top of such a flow, and find that these can be described by two coupled scalar fields admitting three elementary excitations, one more than the usual two found in irrotational flows. We compute the scattering coefficients pertaining to modes falling into an analogue black hole. Our approach provides a more realistic framework for simulating gravitational wave phenomena possibly with an internal structure mimicking quantum gravity effects in laboratory settings.

Accelerating/decelerating trans-critical flows (waterfalls/cataracts) are analogous to space-times of black holes/white fountains since the pioneering work of Sch{\"u}tzhold \& Unruh in 2002. A single number is usually employed to classify trans-criticality namely the local depth Froude number which is the ratio between the local current speed and the local celerity of long gravity waves analogous to the light celerity. When the former reaches one, water waves are no more able to propagate upstream: the hydraulic black hole is a river of no return for them. At a higher level of understanding, two global dimensionless numbers, the upstream Froude number F r up and the obstruction ratio r up (the height of a bottom obstacle, the underlying geometry inducing the effective space-time, divided by the upstream water depth) are essential to distinguish subcritical, trans-critical and supercritical zones in the -F r up versus r up -hydraulic and nondispersive diagram. The relationship between both global parameters for transcritical flows turns out to be a peculiar limit of the behaviour of boats navigating in confined media like canals or locks with a generalized obstruction factor based on the ratio between the boat section and the canal section. Here, we revisit the classification of flows over obstacles in open water channel taking into account both effects of dispersion and scale, two neglected topics so far. For the first time, we give a complete classification of flows in an open water channel based on sub-pixel detection method measurements of the free surface supported by numerical simulations. We generalized the obstruction factor by a filling factor taking into account the maximum height of the water channel, a crucial parameter that was overlooked so far. Our ultimate purpose is to understand how to reproduce in the laboratory analogues of curved space-times from the dynamical point of view.

We consider a market of risky financial assets where the participants are an informed trader, a mass of uniformed traders and noisy liquidity providers. We prove the existence of a market-clearing equilibrium when the insider internalizes her power to impact prices. In the price-impact equilibrium the insider strategically reveals a noisier (compared to when the insider takes prices as given) signal, and prices are less reactive to the publicly available information. In contrast to the related literature, we show that in the price-impact equilibrium, the insider's ex-ante welfare monotonically increases in the signal precision. This clarifies when a trader with market power is motivated to both obtain and refine her private information. Furthermore, even though the uniformed traders act as price-takers, the effect of price impact is ex-ante welfare improving for them. By contrast, internalization of price impact may reduce insider ex-ante welfare. This happens provided the insider is sufficiently risk averse and the uninformed traders are sufficiently risk tolerant., Comment: 56 pages, 3 figures

In Quantum Electrodynamics, vacuum becomes a nonlinear optical medium: its optical index should be modified in the presence of intense external electromagnetic fields. The DeLLight project (Deflection of Light by Light) aims to observe this effect using intense focused femtosecond laser pulses delivered by LASERIX. The principle is to measure with a Sagnac interferometer the deflection of a low-intensity focused pulse (probe) crossing the vacuum index gradient induced by a high-intensity pulse (pump). A Sagnac interferometer working with femtosecond laser pulses has been developed for the DeLLight project. Compared to previous prototypes, the interferometer now includes the focusing of the probe beam in the interaction area. In this article, we measure and characterize the critical experimental parameters limiting the sensitivity of the interferometer, namely the extinction factor, the spatial resolution, and the waist at focus of the probe pulse. We discuss future improvements., Comment: 14 pages, 12 figures, Submitted to Phys. Rev. A. Version v3 corresponds to the published version in Phys Rev A

The aim of the DeLLight (Deflection of Light by Light) experiment is to observe for the first time the optical nonlinearity in vacuum, as predicted by Quantum Electrodynamics, by measuring the refraction of a low-intensity focused laser pulse (probe) when crossing the effective vacuum index gradient induced by a high-intensity focused laser pulse (pump). The deflection signal is amplified by using a Sagnac interferometer. Here, we report the first measurement performed with the DeLLight pilot interferometer, of the deflection of light by light in air, with a low-intensity pump. We show that the deflection signal measured by the interferometer is amplified, and is in agreement with the expected signal induced by the optical Kerr effect in air. Moreover, we verify that the signal varies as expected as a function of the pump intensity, the temporal delay between the pump and the probe, and their relative polarisation. These results represent a proof of concept of the DeLLight experimental method based on interferometric amplification., Comment: 14 pages, 10 figures, submitted to Phys. Rev. A

Transcritical flows in free surface hydrodynamics emulate black hole horizons and their timereversed versions known as white fountains. Both analogue horizons have been shown to emit Hawking radiation, the amplification of waves via scattering at the horizon. Here we report on an experimental validation of the hydrodynamic laws that govern transcritical flows, for the first time in a free surface water channel using an analogue space-time geometry controlled by a bottom obstacle. A prospective study, both experimental and numerical, with a second obstacle downstream of a first one is presented to test in the near-future the analogous black hole laser instability, namely the super-amplification of Hawking radiation by successive bounces on a pair of black and white horizons within cavities which allow the presence of negative energy modes necessary for the amplification process. Candidate hydrodynamic regimes are discussed thanks to a phase diagram based on the scaled relative heights of both obstacles and the ratio of flow to wave speed in the upstream region., Comment: 19 pages, 19 figures

We study a continuous time economy where throughout time, insiders receive private signals regarding the risky assets' terminal payoff. We prove existence of a partial communication equilibrium where, at each private signal time, the public receives a signal of the same form as the associated insider, but of lower quality. This causes a jump in both the public information flow and equilibrium asset price. The resultant markets, while complete between each jump time, are incomplete over each jump. After establishing equilibrium for a finite number of private signal times, we consider the limit as the private signals become more and more frequent. Under appropriate scaling we prove convergence of the public filtration to the natural filtration generated by both the fundamental factor process $X$ and a continuous time process $J$ taking the form $J_t = X_1 + Y_t$ where $X_1$ is the terminal payoff and $Y$ an independent Gaussian process. This coincides with the filtration considered in 'Additional Utility of Insiders with Imperfect Dynamical Information' (Corcuera, et al. Finance & Stochastics 2004). However, while therein the filtration was exogenously assumed to be that of an insider who observes a private signal flow, here it arises endogenously as the public filtration when there are a large number of insiders receiving signals throughout time., Comment: 47 pages, 2 figures

We present a model that builds ``dark matter"-like halo density profiles from free-falling zero-point vacuum fluctuations. It does not require a modification of Newton's laws, nor the existence of as-yet-undiscovered dark matter particles. The 3D halos predicted by our model are fully constrained by the baryonic mass distribution, and are generally far from spherical. The model introduces a new fundamental constant of vacuum, T, having the dimensions of time. We deduce the associated formalism from some basic assumptions, and adjust the model successfully on several spiral galaxy rotation data while comparing our results to the existing analyses. We believe our approach opens up a new paradigm that is worth further exploration, and that would benefit from checks relating to other phenomena attributed to dark matter at all time and distance scales. Following such a program would allow the present model to evolve, and if successful it would make vacuum fluctuations responsible for the typical manifestations of dark matter., Comment: 15 pages, 13 figures

We study a continuous time economy where agents have asymmetric information. The informed agent (``$I$''), at time zero, receives a private signal about the risky assets' terminal payoff $\Psi(X_T)$, while the uninformed agent (``$U$'') has no private signal. $\Psi$ is an arbitrary payoff function, and $X$ follows a time-homogeneous diffusion. Crucially, we allow $U$ to have von Neumann-Morgenstern preferences with a general utility function on $(0,\infty)$ satisfying the standard conditions. This extends previous constructions of equilibria with asymmetric information used when all agents have exponential utilities and enables us to study the impact of $U$'s initial share endowment on equilibrium. To allow for $U$ to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time $0$, $U$ receives a less-informative signal than $I$. In the single asset case, this signal is recoverable by viewing the equilibrium price process over an arbitrarily short period of time, and hence the PCE is a dynamic noisy rational expectations equilibrium. Lastly, when $U$ has power (constant relative risk aversion) utility, we identify the equilibrium price in the small and large risk aversion limits., Comment: 45 pages, 3 figures

In a 1D Bose gas, there is no non-trivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such 3-wave mixing processes (Beliaev and Landau damping) account for their decay via interactions with thermal fluctuations. Within an appropriate time window where the Fermi Golden Rule is expected to apply, the occupation number of the initially occupied mode decays exponentially and the rate takes a simple analytic form. The result is shown to compare favorably with simulations based on the Truncated Wigner Approximation. It is also shown that the same processes slow down the exponential growth of phonons induced by a parametric oscillation., Comment: 12 pages, 6 figures; Appendices: 16 pages, 8 figures; Version accepted for publication in Physical Review B

We report on observations made on a run of transcritical flows over an obstacle in a narrow channel. Downstream from the obstacle, the flows decelerate from supercritical to subcritical, typically with an undulation on the subcritical side (known in hydrodynamics as an undular hydraulic jump). In the Analogue Gravity context, this transition corresponds to a white-hole horizon. Free surface deformations are analyzed, mainly via the two-point correlation function which shows the presence of a checkerboard pattern in the vicinity of the undulation. In non-gated flows where the white-hole horizon occurs far downstream from the obstacle, this checkerboard pattern is shown to be due to low-frequency fluctuations associated with slow longitudinal movement of the undulation. It can thus be considered as an artifact due to a time-varying background. In gated flows, however, the undulation is typically "attached" to the obstacle, and the fluctuations associated with its movement are strongly suppressed. In this case, the observed correlation pattern is likely due to a stochastic ensemble of surface waves, scattering on a background that is essentially stationary.

First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice to reduce simulation costs. Usually, this is a severe approximation. However, for steady-state collisionless, electrostatic (Vlasov-Poisson) systems, the solution with reduced mass ratio can be scaled to the solution for the real mass ratio, with no approximation. This 'scaled mass' method, which works with already-existing PIC codes, can reduce the computation time for a large class of electrostatic PIC simulations by the square root of the mass ratio. The particle distributions of the resulting steady state must be trivially rescaled to yield the true distributions, but the self-consistent electrostatic field is independent of the mass ratio. This method is equivalent to 'numerical timestepping,' an approach that evolves electron and ion populations with different timesteps. Numerical timestepping can be viewed as a special case of the speed-limited PIC (SLPIC) method, which is not restricted to steady-state phenomena. Although the scaled-mass approach is simplest, numerical timestepping and SLPIC more easily generalize to include other effects, such as collisions. The equivalence of these new approaches is demonstrated by applying them to simulate a cylindrical Langmuir probe in electron-argon plasma, speeding up simulation by two orders of magnitude. Methods such as SLPIC can therefore play an invaluable role in interpreting probe measurements by including geometric effects, collisions, secondary emission, and non-Maxwellian distributions., Comment: 22 pages, 3 figures

Quantum electrodynamics predicts that the vacuum must behave as a nonlinear optical medium: the speed of light should be modified when the vacuum is stressed by intense electromagnetic fields. This optical phenomenon has not yet been observed. The DeLLight (Deflection of Light by Light) experiment aims to observe the optically-induced index change of vacuum, a nonlinear effect which has never been explored. The experiment is installed in the LASERIX facility at IJCLab, which delivers ultra-short intense laser pulses (2.5 J per pulse, each of 30 fs duration, with a 10 Hz repetition rate). The proposal is to measure the refraction of a probe laser pulse when crossing a transverse vacuum index gradient, produced by a very intense pump pulse. The refraction induces a transverse shift in the intensity profile of the probe, whose signal is amplified by a Sagnac interferometer. In this article, we describe the experimental method and setup, and present the complete theoretical calculations for the expected signal. With a minimum waist at focus of $5 \,\mu$m (corresponding to a maximum intensity of $\sim 3 \times 10^{20}$ W/cm$^2$), and with the nonlinear vacuum index derived from QED, the expected refraction angle is 0.13 prad. First results of the interferometer prototype are presented. It is shown that an extinction factor $\mathcal{F} = 0.4 \times 10^{-5}$ (corresponding to a signal amplification factor of 250) and a spatial resolution $\sigma_y = 10$ nm are achievable. The expected signal is then about 15 pm, and could be observed at a 5-sigma confidence level with about one month of collected data., Comment: 23 pages, 14 figures Version accepted for publication in Phys. Rev. A

We analyze recently proposed mortgage contracts that aim to eliminate selective borrower default when the loan balance exceeds the house price (the ``underwater'' effect). We show contracts that automatically reduce the outstanding balance in the event of house price decline remove the default incentive, but may induce prepayment in low price states. However, low state prepayments vanish if the benefit from home ownership is sufficiently high. We also show that capital gain sharing features, such as prepayment penalties in high house price states, are ineffective as they virtually eliminate prepayment. For observed foreclosure costs, we find that contracts with automatic balance adjustments become preferable to the traditional fixed-rate contracts at mortgage rate spreads between 20-50 basis points. We obtain these results for perpetual versions of the contracts using American options pricing methodology, in a continuous-time model with diffusive home prices. The contracts' values and optimal decision rules are associated with free boundary problems, which admit semi-explicit solutions.

From an effective field theory of electromagnetism in vacuum including all lowest-order nonlinear terms consistent with Lorentz invariance and locality of photon/photon interactions, we derive an effective medium description of strong background fields as regards their influence on a weak probe. We mainly consider as background a pump beam with well-defined wave vector and polarization. This leads us to define a nonlinear index of vacuum which, in the Euler-Heisenberg model derived from QED, has an optimal value of $1.555 \times 10^{-33} \, {\rm cm}^{2}/{\rm W}$ for a linearly polarized pump as seen by a counter-propagating, orthogonally polarized probe. We further generalize the model to include coupling to an axion field. In the limit where the axion mass is much smaller than the typical photon energy, this yields dispersive corrections, and the axionic signature is found to be greatly enhanced for a circularly polarized pump as compared to a linearly polarized one. The formalism here presented points to a simplification of the DeLLight experiment [X. Sarazin et al., Eur. Phys. J. D 70, 13 (2016)] aiming to measure the deflection of a probe by a tightly focused laser pulse., Comment: 20 pages, 2 figures. Accepted for publication in Phys. Rev. A

We study in detail the scattering of light on a soliton propagating in a waveguide which has been proposed as an experimental system in which one could observe the analogue Hawking effect. When not applying the rotating wave approximation, we show that the linearized wave equation governing perturbations has the same structure as that governing phonon propagation in an atomic Bose condensate. By taking into account the full dispersion relation, we then show that the scattering coefficients encoding the production of photon pairs are amplified by a resonance effect related to the modulation instability occurring in the presence of a continuous wave. When using a realistic example of a silicon nitride waveguide on a silica substrate, we find that a soliton of duration 10 fs would spontaneously emit about one photon pair for every cm it travels, which makes the effect readily observable. This result is confirmed by numerically solving the equation encoding the Kerr nonlinearity and governing the evolution of the full field (soliton plus perturbations). We discuss the link with previous works devoted to the analogue Hawking effect where the pair creation rates were about six orders of magnitude smaller., Comment: 27 pages, 13 figures

We report on what is to our knowledge the first scattering experiment of surface waves on an accelerating transcritical flow, which in the Analogue Gravity context is described by an effective spacetime with a black-hole horizon. This spacetime has been probed by an incident co-current wave, which partially scatters into an outgoing counter-current wave on each side of the horizon. The measured scattering amplitudes are compatible with the predictions of the hydrodynamical theory, where the kinematical description in terms of the effective metric is exact., Comment: 15 pages, 13 figures

This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, non-linear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers., Comment: 1 figure

We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the system. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking, as is the similarity of techniques used to study them., Comment: 28 pages, 15 figures; significantly modified and enlarged version, accepted in Phys. Rev. D

We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ are known, and where additionally the assets are stable in that their occupancy time measures converge to a law with density $p$. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets. We seek to identify the robust optimal growth rate, as well as a trading strategy which achieves this rate in all models. Under minimal assumptions upon $(E,c,p)$, we identify the robust growth rate with the Donsker-Varadhan rate function from occupancy time Large Deviations theory. We also prove existence of, and explicitly identify, the optimal trading strategy. We then apply our results in the case of drift uncertainty for ranked relative market capitalizations. Assuming regularity under symmetrization for the covariance and limiting density of the ranked capitalizations, we explicitly identify the robust optimal trading strategy in this setting., Comment: 34 pages

Periodic spatial variations of some parameter arise in analogue gravity experiments aimed at detecting the analogue version of the Hawking effect in a white hole flow. Having the same spatial periodicity as low-frequency dispersive modes, they can induce resonances which significantly modify the scattering coefficients. This has been shown numerically in a previous work [X. Busch et al., Phys. Rev. D 90, 105005 (2014)], but the precise dependence of the low-frequency effective temperature on the amplitude and length of the undulation remains elusive. In this article, using the Korteweg-de Vries equation, we explicitly compute this dependence in the small-amplitude limit and find three regimes of "short", "intermediate" and "long" undulations showing different scaling laws. In the latter, the effective temperature is completely determined by the properties of the undulation, independently of the surface gravity of the analogue white hole flow. These results are extended to a more realistic hydrodynamical model in an appendix., Comment: 34 pages, 11 figures, version 2 close to that published in Physical Review D