arXiv subjects

Daniele Tommasini

Publications and source records attributed to Daniele Tommasini.

At least 19 recordsLinked to original sources

arXiv2025

Traveling Bubbles and Vortex Pairs within Symmetric 2D Quantum Droplets

We disclose a class of stable nonlinear traveling waves moving at specific constant velocities within symmetric two-dimensional quantum droplets. We present a comprehensive analysis of these traveling bubbles and identify three qualitatively distinct regions within the one-parameter family of solutions, classified by velocity: (i) well-separated phase singularities at low velocity, (ii) singularities within the same density dip at intermediate velocity, and (iii) rarefaction pulses without singularities at higher (subsonic) velocities. Then, we generalize the discussion to unstable cases, incorporating higher order vortex-antivortex pairs and arrays of vortices that move cohesively with a common velocity within the fluid. In all cases, we provide analytic approximations that aid the understanding of the results in different regimes.

nlin.PS↗

arXiv2021

Comment on "An efficient code to solve the Kepler equation. Elliptic case"

In a recent MNRAS article, Raposo-Pulido and Pelaez (RPP) designed a scheme for obtaining very close seeds for solving the elliptic Kepler Equation with the classical and the modified Newton-Rapshon methods. This implied an important reduction in the number of iterations needed to reach a given accuracy. However, RPP also made strong claims about the errors of their method that are incorrect. In particular, they claim that their accuracy can always reach the level $\sim5\varepsilon$, where $\varepsilon$ is the machine epsilon (e.g. $\varepsilon=2.2\times10^{-16} $ in double precision), and that this result is attained for all values of the eccentricity $e<1$ and the mean anomaly $M\in[0,π]$, including for $e$ and $M$ that are arbitrarily close to $1$ and $0$, respectively. However, we demonstrate both numerically and analytically that any implementation of the classical or modified Newton-Raphson methods for Kepler's equation, including those described by RPP, have a limiting accuracy of the order $\sim\varepsilon/\sqrt{2(1-e)}$. Therefore the errors of these implementations diverge in the limit $e\to1$, and differ dramatically from the incorrect results given by RPP. Despite these shortcomings, the RPP method can provide a very efficient option for reaching such limiting accuracy. We also provide a limit that is valid for the accuracy of any algorithm for solving Kepler equation, including schemes like bisection that do not use derivatives. Moreover, similar results are also demonstrated for the hyperbolic Kepler Equation. The methods described in this work can provide guidelines for designing more accurate solutions of the elliptic and hyperbolic Kepler equations.

astro-ph.IM↗

arXiv2021

Bivariate Infinite Series Solution of Kepler's Equations

A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on an iterative procedure for the analytical computation of all the higher-order partial derivatives of the eccentric anomaly with respect to the eccentricity $e$ and mean anomaly $M$ in a given base point $(e_c,M_c)$ of the $(e,M)$ plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of $(e_c,M_c)$, and their convergence is studied numerically. In particular, the polynomials that are obtained by truncating the infinite series up to the fifth degree reach high levels of accuracy in significantly large regions of the parameter space $(e,M)$. Besides their theoretical interest, these series can be used for designing 2-D spline numerical algorithms for efficiently solving Kepler's equations for all values of the eccentricity and mean anomaly.

astro-ph.IM↗

arXiv2018

Fast Switch and Spline Scheme for Accurate Inversion of Nonlinear Functions: The New First Choice Solution to Kepler's Equation

Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline interpolation, which can be applied to monotonic functions under very general conditions. To optimize the algorithm, we designed a specific ultra-fast spline routine. We also derive analytically the theoretical errors of the method and test it on examples that are of interest in physics. In particular, we compute the real branch of Lambert's $W(y)$ function, which is defined as the inverse of $x \exp(x)$, and we solve Kepler's equation. In all cases, our predictions for the theoretical errors are in excellent agreement with our numerical results, and are smaller than what could be expected from the general error analysis of spline interpolation by many orders of magnitude, namely by an astonishing $3\times 10^{-22}$ factor for the computation of $W$ in the range $W(y)\in [0,10]$, and by a factor $2\times 10^{-4}$ for Kepler's problem. In our tests, this scheme is much faster than Newton-Raphson method, by a factor in the range $10^{-4}$ to $10^{-3}$ for the execution time in the examples, when the values of the inverse function over an entire interval or for a large number of points are requested. For Kepler's equation and tolerance $10^{-6}$ rad, the algorithm outperforms Newton's method for all values of the number of points $N\ge 2$.

physics.comp-ph↗

arXiv2015

Modulational instability windows in the nonlinear Schrödinger equation involving higher-order Kerr responses

We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schrödinger equation involving local, arbitrary nonlinear responses to the applied field. In particular, our theory accounts for the recently proposed higher-order Kerr nonlinearities, providing very simple analytical criteria for the identification of multiple regimes of stability and instability of plane-wave solutions in such systems. Moreover, we discuss a new parametric regime in the higher-order Kerr response which allows for the observation of several, alternating stability-instability windows defining a yet unexplored instability landscape.

nlin.PS↗

arXiv2014

Self-induced mode mixing of ultraintense lasers in vacuum

We study the effects of the quantum vacuum on the propagation of a Gaussian laser beam in vacuum. By means of a double perturbative expansion in paraxiality and quantum vacuum terms, we provide analytical expressions for the self-induced transverse mode mixing, rotation of polarization, and third harmonic generarion. We discuss the possibility of searching for the self-induced, spatially dependent phase shift of a multipetawatt laser pulse, which may allow the testing of quantum electrodynamics and new physics models, such as Born-Infeld theory and models involving new minicharged or axion-like particles, in parametric regions that have not yet been explored in laboratory experiments.

physics.optics↗

arXiv2014

Optimized photonic gauge of extreme high vacuum with Petawatt lasers

One of the latest proposed applications of ultra-intense laser pulses is their possible use to gauge extreme high vacuum by measuring the photon radiation resulting from nonlinear Thomson scattering within a vacuum tube. Here, we provide a complete analysis of the process, computing the expected rates and spectra, both for linear and circular polarizations of the laser pulses, taking into account the effect of the time envelope in a slowly varying envelope approximation. We also design a realistic experimental configuration allowing for the implementation of the idea and compute the corresponding geometric efficiencies. Finally, we develop an optimization procedure for this photonic gauge of extreme high vacuum at high repetition rate Petawatt and multi-Petawatt laser facilities, such as VEGA, JuSPARC and ELI.

physics.optics↗

arXiv2012

Measuring Extreme Vacuum Pressure with Ultra-Intense Lasers

We show that extreme vacuum pressures can be measured with current technology by detecting the photons produced by the relativistic Thomson scattering of ultra-intense laser light by the electrons of the medium. We compute the amount of radiation scattered at different frequencies and angles and design strategies for the efficient measurement of pressure. In particular, we show that a single day experiment at a high repetition rate Petawatt laser facility such as VEGA, that will be operating in 2014 in Salamanca, will be sensitive, in principle, to pressures p as low as 10^{-16} Pa, and will be able to provide highly reliable measurements for p>10^{-14} Pa.

physics.optics↗

arXiv2012

Ultrasolitons: multistability and subcritical power threshold from higher-order Kerr terms

We show that an optical system involving competing higher-order Kerr nonlinearities can support the existence of ultrasolitons, namely extremely localized modes that only appear above a certain threshold for the central intensity. Such new solitary waves can be produced for powers below the usual collapse threshold, but they can also coexist with ordinary, lower-intensity solitons. We derive analytical conditions for the occurrence of multistability and analyze the dynamics of the different kinds of fundamental eigenmodes that can be excited in these nonlinear systems. We also discuss the possible transitions between solitary waves belonging to different nonlinear regimes through the mechanism of soliton switching.

nlin.PS↗

arXiv2010

Fermionic light in common optical media

Recent experiments have proved that the response to short laser pulses of common optical media, such as air or Oxygen, can be described by focusing Kerr and higher order nonlinearities of alternating signs. Such media support the propagation of steady solitary waves. We argue by both numerical and analytical computations that the low power fundamental bright solitons satisfy an equation of state which is similar to that of a degenerate gas of fermions at zero temperature. Considering in particular the propagation in both $O_2$ and air, we also find that the high power solutions behave like droplets of ordinary liquids. We then show how a grid of the fermionic light bubbles can be generated and forced to merge in a liquid droplet. This leads us to propose a set of experiments aimed at the production of both the fermionic and liquid phases of light, and at the demonstration of the transition from the former to the latter.

nlin.PS↗

arXiv2010

Filamentation processes and dynamical excitation of light condensates in optical media with competing nonlinearities

We analyze both theoretically and by means of numerical simulations the phenomena of filamentation and dynamical formation of self-guided nonlinear waves in media featuring competing cubic and quintic nonlinearities. We provide a theoretical description of recent experiments in terms of a linear stability analysis supported with simulations, showing the possibility of experimental observation of the modulational instability suppression of intense light pulses travelling across such nonlinear media. We also show a novel mechanism of indirect excitation of {\em light condensates} by means of coalescence processes of nonlinear coherent structures produced by managed filamentation of high power laser beams.

nlin.PS↗

arXiv2010

Light by light diffraction in vacuum

We show that a laser beam can be diffracted by a more concentrated light pulse due to quantum vacuum effects. We compute analytically the intensity pattern in a realistic experimental configuration, and discuss how it can be used to measure for the first time the parameters describing photon-photon scattering in vacuum. In particular, we show that the Quantum Electrodynamics prediction can be detected in a single-shot experiment at future 100 petawatt lasers such as ELI or HIPER. On the other hand, if carried out at one of the present high power facilities, such as OMEGA EP, this proposal can lead either to the discovery of non-standard physics, or to substantially improve the current PVLAS limits on the photon-photon cross section at optical wavelengths. This new example of manipulation of light by light is simpler to realize and more sensitive than existing, alternative proposals, and can also be used to test Born-Infeld theory or to search for axion-like or minicharged particles.

hep-ph↗

arXiv2009

Precision tests of QED and non-standard models by searching photon-photon scattering in vacuum with high power lasers

We study how to search for photon-photon scattering in vacuum at present petawatt laser facilities such as HERCULES, and test Quantum Electrodynamics and non-standard models like Born-Infeld theory or scenarios involving minicharged particles or axion-like bosons. First, we compute the phase shift that is produced when an ultra-intense laser beam crosses a low power beam, in the case of arbitrary polarisations. This result is then used in order to design a complete test of all the parameters appearing in the low energy effective photonic Lagrangian. In fact, we propose a set of experiments that can be performed at HERCULES, eventually allowing either to detect photon-photon scattering as due to new physics, or to set new limits on the relevant parameters, improving by several orders of magnitude the current constraints obtained recently by PVLAS collaboration. We also describe a multi-cross optical mechanism that can further enhance the sensitivity, enabling HERCULES to detect photon-photon scattering even at a rate as small as that predicted by QED. Finally, we discuss how these results can be improved at future exawatt facilities such as ELI, thus providing a new class of precision tests of the Standard Model and beyond.

hep-ph↗

arXiv2009

Dripping, pressure and surface tension of self-trapped laser beams

We show that a laser beam which propagates through an optical medium with Kerr (focusing) and higher order (defocusing) nonlinearities displays pressure and surface-tension properties yielding capillarity and dripping effects totally analogous to usual liquid droplets. The system is reinterpreted in terms of a thermodynamic grand potential, allowing for the computation of the pressure and surface tension beyond the usual hydrodynamical approach based on Madelung transformation and the analogy with the Euler equation. We then show both analytically and numerically that the stationary soliton states of such a light system satisfy the Young-Laplace equation, and that the dynamical evolution through a capillary is described by the same law that governs the growth of droplets in an ordinary liquid system.

nlin.PS↗

arXiv2008

Nonlinear Propagation of Crossing Electromagnetic Waves in Vacuum due to Photon-Photon Scattering

We review the theory for photon-photon scattering in vacuum, and some of the proposals for its experimental search, including the results of our recent works on the subject. We then describe a very simple and sensitive proposal of an experiment and discuss how it can be used at the present (HERCULES) and the future (ELI) ultrahigh power laser facilities either to find the first evidence of photon-photon scattering in vacuum, or to significantly improve the current experimental limits.

physics.optics↗

arXiv2008

Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place both in atomic systems like Bose-Einstein Condensates in alkalii gases with two and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in absence of any quantum effect and can be formulated in the frame of a mean field theory, in terms of the minimization of a thermodynamic potential. We also show numerically that the effect of linear gain and three-body recombination also provides a rich dynamics with the emergence of self-organization behaviour.

nlin.PS↗

arXiv2008

Detecting photon-photon scattering in vacuum at exawatt lasers

In a recent paper, we have shown that the QED nonlinear corrections imply a phase correction to the linear evolution of crossing electromagnetic waves in vacuum. Here, we provide a more complete analysis, including a full numerical solution of the QED nonlinear wave equations for short-distance propagation in a symmetric configuration. The excellent agreement of such a solution with the result that we obtain using our perturbatively-motivated Variational Approach is then used to justify an analytical approximation that can be applied in a more general case. This allows us to find the most promising configuration for the search of photon-photon scattering in optics experiments. In particular, we show that our previous requirement of phase coherence between the two crossing beams can be released. We then propose a very simple experiment that can be performed at future exawatt laser facilities, such as ELI, by bombarding a low power laser beam with the exawatt bump.

physics.optics↗

arXiv2007

Nonlinear phase shift from photon-photon scattering in vacuum

We show that QED nonlinear effects imply a phase correction to the linear evolution of electromagnetic waves in vacuum. We provide explicit solutions of the modified Maxwell's equations for the propagation of a superposition of two plane waves, and calculate analytically and numerically the corresponding phase shift. This provides a new framework for the search of all-optical signatures of photon-photon scattering in vacuum. In particular, we propose an experiment for measuring the phase shift in projected high-power laser facilities.

physics.optics↗