Unique Fock quantization of scalar cosmological perturbations

We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lema\^{i}tre-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.Comment: 19 pages, minor impovementes included, typos correcte

Linear instability criteria for ideal fluid flows subject to two subclasses of perturbations

In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and those in the corresponding factor space. This classification of perturbations arises naturally from the geometric structure of hydrodynamics; our first class of perturbations is the tangent space to the co-adjoint orbit. Instability criteria for equilibrium solutions are established in the form of lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbation.Comment: 29 page

Non-Collinear Ferromagnetic Luttinger Liquids

The presence of electron-electron interactions in one dimension profoundly changes the properties of a system. The separation of charge and spin degrees of freedom is just one example. We consider what happens when a system consisting of a ferromagnetic region of non-collinearity, i.e. a domain wall, is coupled to interacting electrons in one-dimension (more specifically a Luttinger liquid). The ferromagnetism breaks spin charge separation and the presence of the domain wall introduces a spin dependent scatterer into the problem. The absence of spin charge separation and the effects of the electron correlations results in very different behaviour for the excitations in the system and for spin-transfer-torque effects in this model.Comment: 6 pages, submitted to Journal of Physics: Conference Series for JEMS 201

Observation of longitudinal and transverse self-injections in laser-plasma accelerators

Laser-plasma accelerators can produce high quality electron beams, up to giga-electronvolts in energy, from a centimeter scale device. The properties of the electron beams and the accelerator stability are largely determined by the injection stage of electrons into the accelerator. The simplest mechanism of injection is self-injection, in which the wakefield is strong enough to trap cold plasma electrons into the laser wake. The main drawback of this method is its lack of shot-to-shot stability. Here we present experimental and numerical results that demonstrate the existence of two different self-injection mechanisms. Transverse self-injection is shown to lead to low stability and poor quality electron beams, because of a strong dependence on the intensity profile of the laser pulse. In contrast, longitudinal injection, which is unambiguously observed for the first time, is shown to lead to much more stable acceleration and higher quality electron beams.Comment: 7 pages, 7 figure

Optical Transverse Injection in Laser-Plasma Acceleration

International audienceLaser-wakefield acceleration constitutes a promising technology for future electron accelerators. A crucial step in such an accelerator is the injection of electrons into the wakefield, which will largely determine the properties of the extracted beam. We present here a new paradigm of colliding-pulse injection, which allows us to generate high-quality electron bunches having both a very low emittance (0.17  mm·mrad) and a low energy spread (2%), while retaining a high charge (∼100  pC) and a short duration (3 fs). In this paradigm, the pulse collision provokes a transient expansion of the accelerating bubble, which then leads to transverse electron injection. This mechanism contrasts with previously observed optical injection mechanisms, which were essentially longitudinal. We also specify the range of parameters in which this new type of injection occurs and show that it is within reach of existing high-intensity laser facilities

Numerical growth of emittance in simulations of laser-wakefield acceleration

International audienceTransverse emittance is a crucial feature of laser-wakefield accelerators, yet accurately reproducing its value in numerical simulations remains challenging. It is shown here that, when the charge of the bunch exceeds a few tens of picocoulombs, particle-in-cell (PIC) simulations erroneously overestimate the emittance. This is mostly due the interaction of spurious Cherenkov radiation with the bunch, which leads to a steady growth of emittance during the simulation. A new computational scheme is proposed, which is free of spurious Cherenkov radiation. It can be easily implemented in existing PIC codes and leads to a substantial reduction of the emittance growth

Transverse dynamics of an intense electron bunch traveling through a pre-ionized plasma

International audienceThe propagation of a relativistic electron bunch through a plasma is an important problem in both plasma-wakefield acceleration and laser-wakefield acceleration. In those situations, the charge of the accelerated bunch is usually large enough to drive a relativistic wakefield, which then affects the transverse dynamics of the bunch itself. Yet to date, there is no fully relativistic, fully electromagnetic model that describes the generation of this wakefield and its feedback on the bunch. In this article, we derive a model which takes into account all the relevant relativistic and electromagnetic effects involved in the problem. A very good agreement is found between the model and the results of particle-in-cell simulations. The implications of high-charge effects for the transport of the bunch are discussed in detail

Metastasizing placental site trophoblastic tumor: Immunohistochemical and DNA analysis 2 case reports and a review of the literature

Placental-site trophoblastic tumor (PSTT) is a rare form of gestational trophoblastic neoplasia. The clinical behaviour of PSTT is usually benign, but sometimes it can be highly malignant with late recurrence and metastasis. We describe two cases of PSTT with pulmonary metastasis in patients aged 35 and 29 years respectively. The mitotic rate was elevated to 9 and 13 mitotic figures per 10 high-power fields respectively. Immunohistochemical staining showed a predominance of human placental lactogen (hPL) positive cells when compared with human chorionic gonadotropin (hCG) reactive cells in one case, and a reverse pattern in the other one. DNA measurement in one case showed an aneuploid tumor with a tetraploid DNA peak. The clinical behaviour of PSTT remains unpredictable, and there are no reliable means of predicting clinical outcom

Correlated two-particle scattering on finite cavities

The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the two-particle potential is chosen in separable form. The two-particle phase shift is calculated and compared to the single-particle one. The two-particle bound state behavior is discussed and the influence of the cavity on the binding properties is calculated.Comment: Derivation shortened and corrected, 14 pages 10 figure