Double wells, scalar fields and quantum phase transitions in ions traps

Since Hund's work on the ammonia molecule, the double well potential has formed a key paradigm in physics. Its importance is further underlined by the central role it plays in the Landau theory of phase transitions. Recently, the study of entanglement properties of many-body systems has added a new angle to the study of quantum phase transitions of discrete and continuous degrees of freedom, i.e., spin and harmonic chains. Here we show that control of the radial degree of freedom of trapped ion chains allows for the simulation of linear and non-linear Klein-Gordon fields on a lattice, in which the parameters of the lattice, the non-linearity and mass can be controlled at will. The system may be driven through a phase transition creating a double well potential between different configurations of the ion crystal. The dynamics of the system are controllable, local properties are measurable and tunnelling in the double well potential would be observable.Comment: 6 pages, 5 figure

Gravitational Wave Decay: Implications for cosmological scalar-tensor theories

The recent discovery that gravitational waves and light travel with the same speed, with an error below $10^{-15}$, has greatly constrained the parameter space of infrared modifications of gravity. In this thesis we study the phenomenology of gravitational-wave propagation in modifications of gravity relevant for dark energy with an additional scalar degree of freedom. Of particular interest are Horndeski and Beyond Horndeski models surviving after the event GW170817. Here the dark energy field is responsible for the spontaneous breaking of Lorentz invariance on cosmological scales. This implies that gravitons $gamma$ can experience new dispersion phenomena and in particular they can decay into dark energy fluctuations $pi$. First, we study the perturbative decay channels $gamma ightarrow pipi$ and $gamma ightarrowgammapi$ in Beyond Horndeski models. The first process is found to be large and thus incompatible with recent gravitational-wave observations. This provides a very stringent constraint for the particular coefficient $m{4}{2}$ of the Effective Field Theory of Dark Energy or, in the covariant language, on quartic Beyond Horndeski operators. We then study how the same coupling affects at loop level the propagation of gravitons. It is found that the new contribution modifies the dispersion relation in a way that is incompatible with current observations, giving bounds of the same magnitude as the decay. Next, we improve our analysis of the decay by taking into account the large occupation number of gravitons and dark energy fluctuations in realistic situations. When the operators $m_3^3$ (cubic Horndeski) and $m{4}{2}$ are present, we show that the gravitational wave acts as a classical background for $pi$ and affects its dynamics, with $pi$ growing exponentially. In the regime of small gravitational-wave amplitude, we compute analytically the produced $pi$ and the change in the gravitational wave. For the operator $m_3^3$, $pi$ self-interactions are of the same order as the resonance and affect the growth in a way that cannot be described analytically. For the operator $m{4}{2}$, in some regimes self-interactions remain under control and our analysis improves the bounds from the perturbative decay, ruling out quartic Beyond Horndeski operators from having any relevance for cosmological applications. Finally, we show that in the regime of large amplitude for the gravitational wave $pi$ becomes unstable. If $m_3^3$ takes values relevant for cosmological applications, we conclude that dark energy fluctuations feature ghost and gradient instabilities in presence of gravitational waves of typical binary systems. Taking into account the populations of binary systems, we find that the instability is triggered in the whole Universe. The fate of the instability and the subsequent time-evolution of the system depends on the UV completion, so that the theory may end up in a state very different from the original one. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter

Beyond Perturbation Theory in Cosmology

Over many years, our current understanding of the Universe has been extremely relied on perturbation theory (PT) both theoretically and experimentally. There are, however, many situations in cosmology in which the analysis beyond PT is required. In this thesis we study three examples: the resonant decay of gravitational waves (GWs), the dark energy (DE) instabilities induced by GWs, and the tail of the primordial field distribution function. The first two cases are within the context of the Effective Field Theory (EFT) of DE, whereas the last one is within inflation. We first review the construction of the EFT of DE, which is the most general Lagrangian for the scalar and tensor perturbations around the flat FLRW metric. Specifically, this EFT can be mapped to the covariant theories, known as Horndeski and Beyond Horndeski theories. We then study the implications on the dark energy theories coming from the fact that GWs travel with the speed $c_T = 1$ at LIGO/Virgo frequencies. After that, we consider the perturbative decay of GWs into DE fluctuations ($gamma ightarrow pipi$) due to the $ilde{m}_4^2$ operator. This process is kinematically allowed by the spontaneous breaking of Lorentz invariance. Therefore, having no perturbative decay of gravitons together with $c_T = 1$ at LIGO/Virgo, rules out all quartic and quintic beyond Horndeski theories. As the first non-perturbative regime in this thesis, we study the decay of GWs into DE fluctuations $pi$, taking into account the large occupation numbers of gravitons. When the $m_3^3$ (cubic Horndeski) and $ilde{m}_4^2$ (beyond Horndeski) operators are present, the GW acts as a classical background for $pi$ and modifies its dynamics. In particular, $pi$ fluctuations are described by a Mathieu equation and feature instability bands that grow exponentially. In the regime of small GW amplitude which corresponds to narrow resonance, we calculate analytically the produced $pi$, its energy and the change of the GW signal. Eventually, the resonance is affected by $pi$ self-interactions in a way that we cannot describe analytically. The fact that $pi$ self-couplings coming from the $m_3^3$ operator become quickly comparable with the resonant term affects the growth of $pi$ so that the bound on $alpha_{ m B}$ remains inconclusive. However, in the case of the $ilde{m}_4^2$ operator self-interactions can be neglected at least in some regimes. Therefore, our resonant analysis improves the perturbative bounds on $alpha_{ m H}$, ruling out quartic Beyond Horndeski operators. In the second non-perturbative regime we show that $pi$ may become unstable in the presence of a GW background with sufficiently large amplitude. We find that dark-energy fluctuations feature ghost and/or gradient instabilities for GW amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for $|alpha_{ m B}| gtrsim 10^{-2}$, i.e. when the modification of gravity is sizable. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. In conclusion, the only dark-energy theories with sizable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter. In the second part of the thesis we consider physics of inflation. Inflationary perturbations are approximately Gaussian and deviations from Gaussianity are usually calculated using in-in perturbation theory. This method, however, fails for unlikely events on the tail of the probability distribution: in this regime non-Gaussianities are important and perturbation theory breaks down for $|zeta| gtrsim |f_{ m NL}|^{-1}$. We then show that this regime is amenable to a semiclassical treatment, $hbar ightarrow 0$. In this limit the wavefunction of the Universe can be calculated in saddle-point, corresponding to a resummation of all the tree-level Witten diagrams. The saddle can be found by solving numerically the classical (Euclidean) non-linear equations of motion, with prescribed boundary conditions. We apply these ideas to a model with an inflaton self-interaction $propto lambda dot{zeta}^4$. Numerical and analytical methods show that the tail of the probability distribution of $zeta$ goes as $exp(-lambda^{1/4}zeta^{3/2})$, with a clear non-perturbative dependence on the coupling. Our results are relevant for the calculation of the abundance of primordial black holes

IDENTIFICATION OF NONLINEAR BEHAVIOR IN A COMPOSITE STRUCTURE WITH CORE-CRUSHING DAMAGE

ABSTRACT Many damage detection methods that are applied to composite structures rely on nonlinear features in the dynami

The theory of parametrically amplified electron-phonon superconductivity

The ultrafast optical manipulation of ordered phases in strongly correlated materials is a topic of significant theoretical, experimental, and technological interest. Inspired by a recent experiment on light-induced superconductivity in fullerenes [Mitrano et al., Nature 530, 2016], we develop a comprehensive theory of light-induced superconductivity in driven electron-phonon systems with lattice nonlinearities. In analogy with the operation of parametric amplifiers, we show how the interplay between the external drive and lattice nonlinearities lead to significantly enhanced effective electron-phonon couplings. We provide a detailed and unbiased study of the nonequilibrium dynamics of the driven system using the real-time Green's function technique. To this end, we develop a Floquet generalization of the Migdal-Eliashberg theory and derive a numerically tractable set of quantum Floquet-Boltzmann kinetic equations for the coupled electron-phonon system. We study the role of parametric phonon generation and electronic heating in destroying the transient superconducting state. Finally, we predict the transient formation of electronic Floquet bands in time- and angle-resolved photo-emission spectroscopy experiments as a consequence of the proposed mechanism.Comment: 42 pages, 17 figure

Universal phenomenology at critical exceptional points of nonequilibrium O(N)O(N) models

In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of $O(N)$ field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of $2N-3$ Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions $d<4$ they universally either destroy a preexisting static order, or give rise to a fluctuation-induced first order transition. This is demonstrated within a non-perturbative approach based on Dyson-Schwinger equations for $N=2$, and a generalization for arbitrary $N$, which can be solved exactly in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an $xy$ magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium

Theoretical Aspects of Massive Gravity

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the vDVZ discontinuity and the Boulware-Deser ghost were uncovered. We re-derive these results in a pedagogical manner, and develop the St\"ukelberg formalism to discuss them from the modern effective field theory viewpoint. We review recent progress of the last decade, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, we review some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra-dimensions and brane worlds.Comment: 141 pages. Expanded version of an article invited for Reviews of Modern Physics. v2 corrections, updated with new development

Continuation methods for lab experiments of nonlinear vibrations

In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S-Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD-controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker-structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement-frequency plane

Interplay of Geometry and Mechanics: Disordered Spring Networks and Shape-changing Cerebella

This thesis reports work in three topics - I) isotropic strain-induced rigidity transitions in under-constrained spring networks II) uniaxial strain-induced stiffening transitions in semiflexible networks with area-conserving inclusions and III) non-linearities in the buckling without bending morphogenesis model for growing cerebella. All models are two dimensional and we employ either discrete and continuum models to study these systems.In I), motivated by the rigidity transitions in isotropically strained disordered spring networks, we study rigidity transitions in isotropically strained area-conserving random polygonal loops. We find a crossover transition in these loops. We also provide arguments towards showing convexity as a necessary condition for the transition and cyclic polygonal configurations, a sufficient condition. In II), towards modeling the uniaxial compression stiffening experiments in mEF cells and composite systems of fibrin and dextran beads, we construct area-conserving regular polygonal loops. These loops demonstrate compression stiffening. We also report the compression softening of on-lattice semiflexible polymer networks. The softening mechanism is independent of Euler-buckling instabilities. Introduction of area-conserving regular polygons as inclusions in the semiflexible network introduces non-affinities in the elastic response of the system. The non-affine bending of filaments leads to compression stiffening of the semiflexible network. In III), we find that by adding non-linearities to the buckling without bending morphogenesis model, we obtain cusped folds which visually resemble the cusped folds of the cerebellum. Introduction of non-linearities in the energy functional of the model robustly develops a quadratic non-linearity in the Euler-Lagrange equations. We study the effect of such a non-linear force for a simple harmonic oscillator like system and see that there too we obtain cusped `folds\u27. We also discuss steric confinements on the growing cerebellum and a paradigmatic demonstration of hierarchical folds in the cerebellum