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Titos Matsakos

Publications and source records attributed to Titos Matsakos.

14 recordsLinked to original sources
arXiv2025

A quantum unstructured search algorithm for discrete optimisation: the use case of portfolio optimisation

We propose a quantum unstructured search algorithm to find the extrema or roots of discrete functions, $f(\mathbf{x})$, such as the objective functions in combinatorial and other discrete optimisation problems. The first step of the Quantum Search for Extrema and Roots Algorithm (QSERA) is to translate conditions of the form $f(\mathbf{x}_*) \simeq f_*$, where $f_*$ is the extremum or zero, to an unstructured search problem for $\mathbf{x}_*$. This is achieved by mapping $f(\mathbf{x})$ to a function $u(z)$ to create a quantum oracle, such that $u(z_*) = 1$ and $u(z \neq z_*) = 0$. The next step is to employ Grover's algorithm to find $z_*$, which offers a quadratic speed-up over classical algorithms. The number of operations needed to map $f(\mathbf{x})$ to $u(z)$ determines the accuracy of the result and the circuit depth. We describe the implementation of QSERA by assembling a quantum circuit for portfolio optimisation, which can be formulated as a combinatorial problem. QSERA can handle objective functions with higher order terms than the commonly-used Quadratic Unconstrained Binary Optimisation (QUBO) framework. Moreover, while QSERA requires some a priori knowledge of the extrema of $f(\mathbf{x})$, it can still find approximate solutions even if the conditions are not exactly satisfied.

quant-ph↗
arXiv2024

Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors

Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation -- i.e. simulation of the risk factor evolution over time to generate probability distributions -- into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.

quant-ph↗
arXiv2023

Covariant formulation of refracted gravity

We propose a covariant formulation of refracted gravity (RG), a classical theory of gravity based on the introduction of gravitational permittivity (GP), a monotonic function of the local mass density, in the standard Poisson equation. GP mimics dark matter (DM) phenomenology. The covariant formulation of RG (CRG) that we propose belongs to the class of scalar-tensor theories, where the scalar field $φ$ has a self-interaction potential $V(φ)=-Ξφ$, with $Ξ$ a normalization constant. We show that $φ$ is twice the GP in the weak-field limit. Far from a spherical source of density $ρ_s(r)$, the transition between the Newtonian and the RG regime appears below the acceleration scale $a_Ξ=(2Ξ-8πGρ/φ)^{1/2}$, with $ρ=ρ_s+ρ_{bg}$, $ρ_{bg}$ being an isotropic and homogeneous background. In the limit $2Ξ\gg 8πGρ/φ$, we obtain $a_Ξ\sim 10^{-10}$~m~s$^{-2}$. This is comparable to the acceleration $a_0$ originally introduced in MOND. From CRG, we also derived the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar field that mimics DM also drives the accelerated expansion of the Universe. From the stress-energy tensor of $φ$, we derived the equation of state of a redshift-dependent effective dark energy (DE) $w_{DE}=p_{DE}/ρ_{DE}$. Current observational constraints on $w_{DE}$ and distance modulus data of SNIa suggest that $Ξ$ has a comparable value to the cosmological constant $Λ$ in the standard model. CRG, therefore, suggests a natural explanation of the known relation $a_0\sim Λ^{1/2}$ and appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, highlighting a possible deep connection between phenomena currently attributed to DM and DE separately.

astro-ph.CO↗
arXiv2022

The dynamics of three nearby E0 galaxies in refracted gravity

We tested whether refracted gravity, a theory of modified gravity that describes the dynamics of galaxies without the aid of dark matter, can model the dynamics of the three massive elliptical galaxies, NGC 1407, NGC 4486, and NGC 5846, out to $\sim$$10R_{\rm e}$, where the baryonic mass component fades out and dark matter is required in Newtonian gravity. We probed these outer regions with the kinematics of the globular clusters provided by the SLUGGS survey. Refracted gravity mimics dark matter with the gravitational permittivity, a monotonic function of the local mass density depending on three parameters, $ε_0$, $ρ_{\rm c}$, and $Q$, which are expected to be universal. Refracted gravity satisfactorily reproduces the velocity dispersion profiles of the stars and red and blue globular clusters, with stellar mass-to-light ratios in agreement with stellar population synthesis models, and orbital anisotropy parameters consistent with previous results obtained in Newtonian gravity with dark matter. The sets of the three parameters of the gravitational permittivity found for each galaxy are consistent with each other within $\sim$2$σ$. We compare the mean $\{ε_0,Q,\log_{10}\left[ρ_{\rm c}\left(\mathrm{g}\, \mathrm{cm}^{-3}\right)\right]\} = \{0.089^{+0.038}_{-0.035}, 0.47^{+0.29}_{-0.21}, -24.25^{+0.28}_{-0.20}\}$ found here with the means of the parameters required to model the rotation curves and vertical velocity dispersion profiles of 30 disk galaxies from the DiskMass Survey (DMS): $ρ_{\rm c}$ and $Q$ agree within 1$σ$ with the DMS values, whereas $ε_0$ agrees within 3$σ$. This agreement suggests that ellipticals and disk galaxies allow for common values of the parameters of the permittivity and supports the universality of the permittivity function.

astro-ph.GA↗
arXiv2021

Dynamics of DiskMass Survey galaxies in refracted gravity

We test if Refracted Gravity (RG) can describe the dynamics of disk galaxies without resorting to dark matter. RG is a classical theory of gravity where the standard Poisson equation is modified by the gravitational permittivity, $ε$, a universal monotonic function of the local mass density. We use the rotation curves and the vertical velocity dispersions of 30 galaxies in the DiskMass Survey (DMS) to determine $ε$. RG describes the kinematic profiles with mass-to-light ratios consistent with SPS models, and disk thicknesses in agreement with observations, once observational biases are considered. Our results rely on setting the three free parameters of $ε$ for each galaxy. However, we show that the differences of these parameters from galaxy to galaxy could be ascribed to statistical fluctuations. We adopt an approximate method to find a single set of parameters that may properly describe the kinematics of the entire sample and suggest the universality of $ε$. Finally, we show that the RG models of the individual rotation curves can only partly describe the radial acceleration relation (RAR). Evidently, the RG models underestimate the observed accelerations of 0.1-0.3 dex at low Newtonian accelerations. Another problem is the strong correlation, at much more than 5$σ$, between the residuals of the RAR models and three radially-dependent properties of galaxies, whereas the DMS data show a considerably less significant correlation, at more than 4$σ$, for only two of them. These correlations might originate the non-null intrinsic scatter of the RG models, at odds with the observed intrinsic scatter of galaxy samples different from DMS, which is consistent with 0. Further studies are required to assess if these discrepancies in the RAR originate from the DMS sample, which might not be ideal for deriving the RAR, or if they are genuine failures of RG.

astro-ph.GA↗
arXiv2017

On the origin of dynamically isolated hot Earths

A distinct population of planetary systems that contain dynamically isolated, Earth-size planets with orbital periods $P_\mathrm{orb}\sim 1\,$day was recently identified in an analysis of data from the Kepler planet candidate catalog. We argue that these objects could represent the remnant rocky cores of giant planets that arrived at the stellar vicinity on high-eccentricity orbits and were rapidly stripped of their gaseous envelopes after crossing their respective Roche limits (RLs) $a_\mathrm{R,p}$. In this picture, objects with $P_\mathrm{orb}\gtrsim1\,$day are mostly "early" cores that originated in planets with an initial periastron distance $a_\mathrm{per,0}\le a_\mathrm{R,p}$; they had high initial eccentricities but their orbits underwent fast tidal circularization after the cores were exposed. Objects with $P_\mathrm{orb}\lesssim 1\,$day are, by contrast, mostly "late" cores that originated in planets with $a_\mathrm{per,0}>a_\mathrm{R,p}$; these planets underwent orbital circularization to a radius $>a_\mathrm{per,0}$ but eventually reached $a_\mathrm{R,p}$ through tidal orbital decay. This picture naturally accounts for the spatial distribution of hot Earths and for the similarity of their inferred occurrence rate to that of hot Jupiters, and it fits well with the interpretation of the so-called sub-Jovian desert in the orbital-period--planetary-mass plane in terms of high-eccentricity planet migration to the vicinity of the RL.

astro-ph.EP↗
arXiv2017

A test of the high-eccentricity migration scenario for close-in planets

In the high-eccentricity migration (HEM) scenario, close-in planets reach the vicinity of the central star on high-eccentricity orbits that become circularized---with a concomitant decrease in the semimajor axis---through a tidal interaction with the star. Giant planets that arrive with periastron distances that are smaller than the Roche limit $a_\mathrm{R}$ lose their gaseous envelopes, resulting in an inner edge to the surviving planets' distribution. The observational evidence for this effect, while extensive, is nonetheless somewhat ambiguous because of the effect of tidal orbital decay. Here we consider another key prediction of the HEM scenario---the existence of a spatial eccentricity gradient near the location where the circularization time becomes comparable to the planet's age for typical parameters. Previous studies already found evidence for this gradient and demonstrated that its properties are consistent with the circularization process being dominated by tidal dissipation in the planet (encapsulated by the tidal quality factor $Q^\prime_\mathrm{p}$). Our work extends these treatments by constructing explicit model distributions for comparison with the data and by carrying out backward-in-time integrations using observed system parameters. We show that circularization generally occurs outside the distribution's inner edge (which defines the boundary of the so-called sub-Jovian desert) and that typically $Q^\prime_\mathrm{p}\approx10^6$ in the circularization zone (to within a factor of 3). We also find tentative evidence for an eccentricity gradient in lower-mass planets, indicating that formation through HEM may be relevant down to Neptune scales.

astro-ph.EP↗
arXiv2016

The gravitational interaction between planets on inclined orbits and protoplanetary disks as the origin of primordial spin--orbit misalignments

Many of the observed spin--orbit alignment properties of exoplanets can be explained in the context of the primordial disk misalignment model, in which an initially aligned protoplanetary disk is torqued by a distant stellar companion on a misaligned orbit, resulting in a precessional motion that can lead to large-amplitude oscillations of the spin--orbit angle. We consider a variant of this model in which the companion is a giant planet with an orbital radius of a few au. Guided by the results of published numerical simulations, we model the dynamical evolution of this system by dividing the disk into inner and outer parts---separated at the location of the planet---that behave as distinct, rigid disks. We show that the planet misaligns the inner disk even as the orientation of the outer disk remains unchanged. In addition to the oscillations induced by the precessional motion, whose amplitude is larger the smaller the initial inner-disk-to-planet mass ratio, the spin--orbit angle also exhibits a secular growth in this case---driven by ongoing mass depletion from the disk---that becomes significant when the inner disk's angular momentum drops below that of the planet. Altogether, these two effects can produce significant misalignment angles for the inner disk, including retrograde configurations. We discuss these results within the framework of the Stranded Hot Jupiter scenario and consider their implications, including to the interpretation of the alignment properties of debris disks.

astro-ph.EP↗
arXiv2016

A wind-driving disc model for the mm-wavelength polarization structure of HL Tau

The recent advent of spatially resolved mm- and cm-wavelength polarimetry in protostellar accretion discs could help clarify the role of magnetic fields in the angular momentum transport in these systems. The best case to date is that of HL~Tau, where the inability to produce a good fit to the 1.25-mm data with a combination of vertical and azimuthal magnetic field components was interpreted as implying that centrifugally driven winds (CDWs) are probably not a significant transport mechanism on the $\sim 10^2\,$au scale probed by the observations. Using synthetic polarization maps of heuristic single-field-component discs and of a post-processed simulation of a wind-driving disc, we demonstrate that a much better fit to the data can be obtained if the radial field component, a hallmark of the CDW mechanism, dominates in the polarized emission region. A similar inference was previously made in modelling the far-infrared polarization map of the pc-scale dust ring in the Galactic centre. To reconcile this interpretation with theoretical models of protostellar discs, which indicate that the wind is launched from a comparatively high elevation above the mid-plane, we propose that most of the polarized emission originates -- with a high ($\ga 10$\%) intrinsic degree of polarization -- in small ($\la 0.1\,$mm) grains that remain suspended above the mid-plane, and that the bulk of the mm-wavelength emission is produced -- with low intrinsic polarization -- by larger grains that have settled to the mid-plane.

astro-ph.SR↗
arXiv2016

Dynamics of galaxies and clusters in \textit{refracted gravity}

We investigate the proof of concept and the implications of \textit{refracted gravity}, a novel modified gravity aimed to solve the discrepancy between the luminous and the dynamical mass of cosmic structures without resorting to dark matter. Inspired by the behavior of electric fields in matter, refracted gravity introduces a gravitational permittivity that depends on the local mass density and modifies the standard Poisson equation. The resulting gravitational field can become more intense than the Newtonian field and can mimic the presence of dark matter. We show that the refracted gravitational field correctly describes (1) the rotation curves and the Tully-Fisher relation of disk galaxies; and (2) the observed temperature profile of the X-ray gas of galaxy clusters. According to these promising results, we conclude that refracted gravity deserves further investigation.

astro-ph.GA↗
arXiv2016

On the origin of the sub-Jovian desert in the orbital-period--planetary-mass plane

Transit and radial velocity observations indicate a dearth of sub-Jupiter--mass planets on short-period orbits, outlined roughly by two oppositely sloped lines in the period--mass plane. We interpret this feature in terms of high-eccentricity migration of planets that arrive in the vicinity of the Roche limit, where their orbits are tidally circularized, long after the dispersal of their natal disk. We demonstrate that the two distinct segments of the boundary are a direct consequence of the different slopes of the empirical mass--radius relation for small and large planets, and show that this relation also fixes the mass coordinate of the intersection point. The period coordinate of this point, as well as the detailed shape of the lower boundary, can be reproduced with a plausible choice of a key parameter in the underlying migration model. The detailed shape of the upper boundary, on the other hand, is determined by the post-circularization tidal exchange of angular momentum with the star and can be reproduced with a stellar tidal quality factor $Q^\prime_*\sim10^6$.

astro-ph.EP↗
arXiv2015

A hot Jupiter for breakfast? --- Early stellar ingestion of planets may be common

Models of planet formation and evolution predict that giant planets form efficiently in protoplanetary disks, that most of these migrate rapidly to the disk's inner edge, and that, if the arriving planet's mass is $\lesssim$ Jupiter's mass, it could remain stranded near that radius. We argue that such planets would be ingested by tidal interaction with the host star on a timescale $\lesssim1\,$Gyr, and that, in the case of a solar-type host, this would cause the stellar spin to approach the direction of the ingested planet's orbital axis even if the two were initially highly misaligned. Primordially misaligned stars whose effective temperatures are $\gtrsim6250\,$K cannot be realigned in this way because, in contrast with solar-type hosts, their angular momenta are typically higher than the orbital angular momentum of the ingested planet as a result of inefficient magnetic braking and of a comparatively large moment of inertia. Hot Jupiters located farther out from the star can contribute to this process, but their effect is weaker because the tidal interaction strength decreases rapidly with increasing semimajor axis. We demonstrate that, if $\sim50\%$ of planetary systems harbored a stranded hot Jupiter, this scenario can in principle account for (1) the good alignment exhibited by planets around cool stars irrespective of the planet's mass or orbital period, (2) the prevalence of misaligned planets around hot stars, (3) the apparent upper bound on the mass of hot Jupiters on retrograde orbits, and (4) the inverse correlation between stellar spin periods and hot-Jupiter masses.

astro-ph.EP↗
arXiv2015

Classification of magnetized star--planet interactions: bow shocks, tails, and inspiraling flows

Close-in exoplanets interact with their host stars gravitationally as well as via their magnetized plasma outflows. The rich dynamics that arises may result in distinct observable features. Our objective is to study and classify the morphology of the different types of interaction that can take place between a giant close-in planet (a Hot Jupiter) and its host star, based on the physical parameters that characterize the system. We perform 3D magnetohydrodynamic numerical simulations to model the star--planet interaction, incorporating a star, a Hot Jupiter, and realistic stellar and planetary outflows. We explore a wide range of parameters and analyze the flow structures and magnetic topologies that develop. Our study suggests the classification of star--planet interactions into four general types, based on the relative magnitudes of three characteristic length scales that quantify the effects of the planetary magnetic field, the planetary outflow, and the stellar gravitational field in the interaction region. We describe the dynamics of these interactions and the flow structures that they give rise to, which include bow shocks, cometary-type tails, and inspiraling accretion streams. We point out the distinguishing features of each of the classified cases and discuss some of their observationally relevant properties. The magnetized interactions of star--planet systems can be categorized, and their general morphologies predicted, based on a set of basic stellar, planetary, and orbital parameters.

astro-ph.EP↗
arXiv2008

Stability and structure of analytical MHD jet formation models with a finite outer disk radius

(Abridged) Finite radius accretion disks are a strong candidate for launching astrophysical jets from their inner parts and disk-winds are considered as the basic component of such magnetically collimated outflows. The only available analytical MHD solutions for describing disk-driven jets are those characterized by the symmetry of radial self-similarity. Radially self-similar MHD models, in general, have two geometrical shortcomings, a singularity at the jet axis and the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis and impose a physical boundary at finite radial distance. We focus here on studying the effects of imposing an outer radius of the underlying accreting disk (and thus also of the outflow) on the topology, structure and variability of a radially self-similar analytical MHD solution. The initial condition consists of a hybrid of an unchanged and a scaled-down analytical solution, one for the jet and the other for its environment. In all studied cases, we find at the end steady two-component solutions.

astro-ph↗