Complex extreme nonlinear waves: classical and quantum theory for new computing models

The historical role of nonlinear waves in developing the science of complexity, and also their physical feature of being a widespread paradigm in optics, establishes a bridge between two diverse and fundamental fields that can open an immeasurable number of new routes. In what follows, we present our most important results on nonlinear waves in classical and quantum nonlinear optics. About classical phenomenology, we lay the groundwork for establishing one uniform theory of dispersive shock waves, and for controlling complex nonlinear regimes through simple integer topological invariants. The second quantized field theory of optical propagation in nonlinear dispersive media allows us to perform numerical simulations of quantum solitons and the quantum nonlinear box problem. The complexity of light propagation in nonlinear media is here examined from all the main points of view: extreme phenomena, recurrence, control, modulation instability, and so forth. Such an analysis has a major, significant goal: answering the question can nonlinear waves do computation? For this purpose, our study towards the realization of an all-optical computer, able to do computation by implementing machine learning algorithms, is illustrated. The first all-optical realization of the Ising machine and the theoretical foundations of the random optical machine are here reported. We believe that this treatise is a fundamental study for the application of nonlinear waves to new computational techniques, disclosing new procedures to the control of extreme waves, and to the design of new quantum sources and non-classical state generators for future quantum technologies, also giving incredible insights about all-optical reservoir computing. Can nonlinear waves do computation? Our random optical machine draws the route for a positive answer to this question, substituting the randomness either with the uncertainty of quantum noise effects on light propagation or with the arbitrariness of classical, extremely nonlinear regimes, as similarly done by random projection methods and extreme learning machines

Classical Nonrelativistic Effective Field Theory and the Role of Gravitational Interactions

Coherent oscillation of axions or axion-like particles may give rise to long-lived clumps, called axion stars, because of the attractive gravitational force or its self-interaction. Such a kind of configuration has been extensively studied in the context of oscillons without the effect of gravity, and its stability can be understood by an approximate conservation of particle number in a non-relativistic effective field theory (EFT). We extend this analysis to the case with gravity to discuss the longevity of axion stars and clarify the EFT expansion scheme in terms of gradient energy and Newton's constant. Our EFT is useful to calculate the axion star configuration and its classical lifetime without any ad hoc assumption. In addition, we derive a simple stability condition against small perturbations. Finally, we discuss the consistency of other non-relativistic effective field theories proposed in the literature.Comment: 37 pages, 3 figure

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Aspects of Black Hole Physics: Scalar Sources, Holography and Gravitational Wave Emission

We investigate several aspects of black hole physics. First, we consider models of gravity minimally coupled to scalar fields. We derive a new class of asymptotically flat black holes sourced by a non-trivial asymptotically massless scalar field; we discuss their relationship with known solutions and standard no-hair theorems and their thermodynamics. We derive exact neutral and charged brane solutions sourced by a scalar field with vanishing potential, which are conformal to the Lifshitz spacetime; we discuss the symmetries and their holographic application for hyperscaling violation; we also give a quite general classification of brane solutions sourced by scalar fields useful for holographic applications. We study an inflationary model inspired by the domain wall/cosmology correspondence in which inflation is driven by a scalar with a two-exponential potential; we derive its phenomenological consequences in the slow-roll approximation and compare its predictions with the Planck 2015 data. Second, we investigate ultra-compact astrophysical objects which can act as black hole mimickers, in particular boson stars and wormholes. We discuss the existence and the stability of boson stars in higher dimensions and boson stars built with multiple scalars. We compute tidal Love numbers for various mimickers and discuss how to distinguish black holes from their possible mimickers with gravitational-wave data. We study the gravitational radiation emitted by a particle falling into an exotic compact object and show that the initial ringdown signal cannot be use distinguish between a black hole and a black hole mimicker.We investigate several aspects of black hole physics. First, we consider models of gravity minimally coupled to scalar fields. We derive a new class of asymptotically flat black holes sourced by a non-trivial asymptotically massless scalar field; we discuss their relationship with known solutions and standard no-hair theorems and their thermodynamics. We derive exact neutral and charged brane solutions sourced by a scalar field with vanishing potential, which are conformal to the Lifshitz spacetime; we discuss the symmetries and their holographic application for hyperscaling violation; we also give a quite general classification of brane solutions sourced by scalar fields useful for holographic applications. We study an inflationary model inspired by the domain wall/cosmology correspondence in which inflation is driven by a scalar with a two-exponential potential; we derive its phenomenological consequences in the slow-roll approximation and compare its predictions with the Planck 2015 data. Second, we investigate ultra-compact astrophysical objects which can act as black hole mimickers, in particular boson stars and wormholes. We discuss the existence and the stability of boson stars in higher dimensions and boson stars built with multiple scalars. We compute tidal Love numbers for various mimickers and discuss how to distinguish black holes from their possible mimickers with gravitational-wave data. We study the gravitational radiation emitted by a particle falling into an exotic compact object and show that the initial ringdown signal cannot be use distinguish between a black hole and a black hole mimicker

Soliton dynamics in the Gross–Pitaevskii equation: splitting, collisions and interferometry

Bose–Einstein condensates with attractive interactions have stable 1D solutions in the form of bright solitary-waves. These solitary waves behave, in the absence of external potentials, like macroscopic quantum particles. This opens up a wide array of applications for the testing of quantum mechanical behaviours and precision measurement. Here we investigate these applications with particular focus on the interactions of bright solitary-waves with narrow potential barriers. We first study bright solitons in the Gross–Pitaevskii equation as they are split on Gaussian and δ-function barriers, and then on Gaussian barriers in a low energy system. We present analytic and numerical results determining the general region in which a soliton may not be split on a finite width potential barrier. Furthermore, we test the sensitivity of the system to quantum fluctuations. We then study fast-moving bright solitons colliding at a narrow Gaussian potential barrier. In the limiting case of a δ-function barrier, we show analytically that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and determine whether the outgoing waves are bright solitons. We use numerical simulations to show that outside the high velocity limit nonlinear effects introduce a skew to the phase-dependence. Finally, we use these results to analyse the process of soliton interferometry. We develop analyses of both toroidal and harmonic trapping geometries for Mach–Zehnder interferometry, and then two implementations of a toroidal Sagnac inter- ferometer, also giving the analytical determination of the Sagnac phase in such systems. These results are again verified numerically. In the Mach–Zehnder case, we again probe the systems sensitivity to quantum fluctuations

Elementary and topological excitations in ultracold dipolar Bose gases

PhD ThesisQ uantum gases are an exemplar for exploring quantum phenomena; dipolar quantum gases only enriches the pool of potential experiments, exhibiting long-range and anisotropic interactions. In this thesis, we perform extensive numerical and theoretical studies of the dipolar Gross-Pitaevskii equation, exposing new intriguing phenomena of solitons and vortices in these systems. Firstly, we map out the stability diagram as a function of strength and polarisation direction of the atomic dipoles in a quasi-one-dimensional dipolar gas, identifying both roton and phonon instabilities. Then we obtain the family of dark soliton solutions supported in this system. Away from these instabilities dark solitons collide elastically. Varying the polarisation direction relative to the condensate axis enables tuning of this nonlocal interaction between repulsive and attractive; the latter case supports unusual dark soliton bound states. Remarkably, these bound states are themselves shown to behave like solitons, emerging unscathed from collisions with each other. In trapped gases the oscillation frequency of the dark soliton is strongly dependent on the atomic interactions, in stark contrast to the non-dipolar case. Considering parameter regimes allowing the existence of bright solitons we map out the existence of the soliton solutions and show three collisional regimes: free collisions, bound state formation and soliton fusion. We examine the solitons in their full three-dimensional form through a variational approach; along with regimes of instability to collapse and runaway expansion, we identify regimes of stability which are accessible to current experiments. Then, we undertake a theoretical analysis of the stability of a Thomas-Fermi density pro le for a dipolar gas in a rotating frame of reference and nd that the theoretical prediction for "anti-dipoles" is only experimentally realisable for short periods of time. We compare this theory against numerical simulations of the governing equation for these systems and nd excellent agreement. Finally, we study the elementary characteristics of turbulence in a quantum ferro uid through the context of a dipolar Bose gas condensing from a highly non-equilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarised turbulence and density corrugations. The super uid vortex lines and density uctuations adopt a columnar or strati ed con guration, with the vortices tending to form in the low density regions to minimise kinetic energy. When the interactions are dominantly dipolar, the decay rate of vortex line length is enhanced. This system poses exciting prospects for realising strati ed quantum turbulence and new levels of generating and controlling turbulence using magnetic elds.EPSR

Bright solitary waves and non-equilibrium dynamics in atomic Bose-Einstein condensates

In this thesis we investigate the static properties and non-equilibrium dynamics of bright solitary waves in atomic Bose-Einstein condensates in the zero-temperature limit, and we investigate the non-equilibrium dynamics of a driven atomic Bose-Einstein condensate at finite temperature. Bright solitary waves in atomic Bose-Einstein condensates are non-dispersive and soliton-like matter-waves which could be used in future atom-interferometry experiments. Using the mean-field, Gross-Pitaevskii description, we propose an experimental scheme to generate pairs of bright solitary waves with controlled velocity and relative phase; this scheme could form an important part of a future atom interferometer, and we demonstrate that it can also be used to test the validity of the mean-field model of bright solitary waves. We also develop a method to quantitatively assess how soliton-like static, three-dimensional bright solitary waves are; this assessment is particularly relevant for the design of future experiments. In reality, the non-zero temperatures and highly non-equilibrium dynamics occurring in a bright solitary wave interferometer are likely to necessitate a theoretical description which explicitly accounts for the non-condensate fraction. We show that a second-order, number-conserving description offers a minimal self-consistent treatment of the relevant condensate -- non-condensate interactions at low temperatures and for moderate non-condensate fractions. We develop a method to obtain a fully-dynamical numerical solution to the integro-differential equations of motion of this description, and solve these equations for a driven, quasi-one-dimensional test system. We show that rapid non-condensate growth predicted by lower-order descriptions, and associated with linear dynamical instabilities, can be damped by the self-consistent treatment of interactions included in the second-order description

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Hydrodynamics

The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics