arXiv subjects

Scott Robertson

Publications and source records attributed to Scott Robertson.

At least 19 recordsLinked to original sources

arXiv2026

Black hole analogues in two-dimensional flows with constant shear

We investigate the gravitational analogy for shallow water waves propagating on a unidirectional background flow with constant shear. Generalizing the standard irrotational treatment, we demonstrate that a transverse background vorticity is perfectly compatible with the existence of an effective curved spacetime for longitudinal surface waves. We extract the modified acoustic metric and show that the conformal factor, which governs wave scattering, becomes strongly dependent on the vorticity. Consequently, we find that the presence of background shear significantly suppresses the scattering of modes over an inhomogeneous bathymetry, while mildly modifying the analogue surface gravity at the transcritical horizon. These results highlight the nontrivial role of rotational dynamics in analogue gravity experiments.

gr-qc↗

arXiv2025

Parametric pair production of collective excitations in a Bose-Einstein condensate

By exciting the transverse breathing mode of an elongated Bose-Einstein condensate, we parametrically produce longitudinal collective excitations in a pairwise manner. This process also referred to as Faraday wave generation, can be seen as an analog to cosmological particle production. Building upon single particle detection, we investigate the early time dynamics of the exponential growth and compare our observations with a Bogoliubov description. The growth rate we observe experimentally is in very good agreement with theoretical predictions, demonstrating the validity of the Bogoliubov description and thereby confirming the smallness of quasiparticle interactions in such an elongated gas. We also discuss the presence of oscillations in the atom number, which are due to pair correlations and to the rate at which interactions are switched off.

cond-mat.quant-gas↗

arXiv2025

Observation of entanglement in a cold atom analog of cosmological preheating

We observe entanglement between collective excitations of a Bose-Einstein condensate in a configuration analogous to particle production during the preheating phase of the early universe. In our setup, the oscillation of the inflaton field is mimicked by the transverse breathing mode of a cigar-shaped condensate, which parametrically excites longitudinal quasiparticles with opposite momenta. After a short modulation period, we observe entanglement of these pairs which reveals the role played by vacuum fluctuations in seeding the parametric growth, confirming the quantum origin of the excitations. As the system continues to evolve, we observe a decrease in correlations and a disappearance of non-classical features. These point towards future experimental probes of the late-time nonlinear regime where further analogies can be drawn with reheating, i.e. the thermalization of the post-inflationary Universe.

cond-mat.quant-gas↗

arXiv2025

PasteTrace: A Single Source Plagiarism Detection Tool For Introductory Programming Courses

Introductory Computer Science classes are important for laying the foundation for advanced programming courses. However, students without prior programming experience may find these courses challenging, leading to difficulties in understanding concepts and engaging in academic dishonesty such as plagiarism. While there exists plagiarism detection techniques and tools, not all of them are suitable for academic settings, especially in introductory programming courses. This paper introduces PasteTrace, a novel open-source plagiarism detection tool designed specifically for introductory programming courses. Unlike traditional methods, PasteTrace operates within an Integrated Development Environment that tracks the student's coding activities in real-time for evidence of plagiarism. Our evaluation of PasteTrace in two introductory programming courses demonstrates the tool's ability to provide insights into student behavior and detect various forms of plagiarism, outperforming an existing well-established tool. A video demonstration of PasteTrace and its source code, and case study data are made available at https://doi.org/10.6084/m9.figshare.27115852

cs.CY↗

arXiv2025

Optimal Investment in Equity and Credit Default Swaps in the Presence of Default

We consider an equity market subject to risk from both unhedgeable shocks and default. The novelty of our work is that to partially offset default risk, investors may dynamically trade in a credit default swap (CDS) market. Assuming investment opportunities are driven by functions of an underlying diffusive factor process, we identify the certainty equivalent for a constant absolute risk aversion investor with a semi-linear partial differential equation (PDE) which has quadratic growth in both the function and gradient coefficients. For general model specifications, we prove existence of a solution to the PDE which is also the certainty equivalent. We show the optimal policy in the CDS market covers not only equity losses upon default (as one would expect), but also losses due to restricted future trading opportunities. We use our results to price default dependent claims though the principal of utility indifference, and we show that provided the underlying equity market is complete absent the possibility of default, the equity-CDS market is complete accounting for default. Lastly, through a numerical application, we show the optimal CDS policies are essentially static (and hence easily implementable) and that investing in CDS dramatically increases investor indirect utility.

q-fin.MF↗

arXiv2024

Dissipative parametric resonance in a modulated 1D Bose gas

We synthesize results of previous works to give a coherent and self-consistent account of parametric resonance in a modulated quasi-1D Bose gas in the presence of a dissipative mechanism. The resonant behaviour is shown to be largely in line with the predictions of a phenomenological model published in 2014, while the associated dissipation rate is consistent with that derived in 2022 from three-wave mixing processes between the produced phonons and thermal fluctuations.

cond-mat.quant-gas↗

arXiv2024

Vortical scattering channel in an aquatic space-time

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.

gr-qc↗

arXiv2024

On the art of designing effective space-times with free surface flows in Analogue Gravity

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.

gr-qc↗

arXiv2024

Strategic Informed Trading and the Value of Private Information

We consider a market of risky financial assets whose participants are an informed trader, a representative uninformed trader, and noisy liquidity providers. We prove the existence of a market-clearing equilibrium when the insider internalizes her power to impact prices, but the uninformed trader takes prices as given. Compared to the associated competitive economy, in equilibrium the insider strategically reveals a noisier signal, and prices are less reactive to publicly available information. Additionally, and in direct contrast to the related literature, in equilibrium the insider's indirect utility monotonically increases in the signal precision. Therefore, the insider is motivated not only to obtain, but also to refine, her signal. Lastly, we show that compared to the competitive economy, the insider's internalization of price impact is utility improving for the uninformed trader, but somewhat surprisingly may be utility decreasing for the insider herself. This utility reduction occurs provided the insider is sufficiently risk averse compared to the uninformed trader, and provided the signal is of sufficiently low quality.

q-fin.TR↗

arXiv2024

Performance of a Sagnac interferometer to observe vacuum optical nonlinearity

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.

physics.optics↗

arXiv2024

Interferometric measurement of the deflection of light by light in air

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.

physics.optics↗

arXiv2023

How to create analogue black hole or white fountain horizons and LASER cavities in experimental free surface hydrodynamics?

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.

physics.flu-dyn↗

arXiv2023

Equilibrium with Heterogeneous Information Flows

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.

q-fin.PR↗

arXiv2023

Gravitational effects of free-falling quantum vacuum

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.

gr-qc↗

arXiv2022

Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility

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.

q-fin.MF↗

arXiv2022

Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping

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.

cond-mat.quant-gas↗

arXiv2021

Correlations on weakly time-dependent transcritical white-hole flows

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.

gr-qc↗

arXiv2021

Accelerated Steady-State Electrostatic Particle-in-Cell Simulation of Langmuir Probes

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.

physics.plasm-ph↗