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We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively-charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modeled by a four-component distribution function in the two-dimensional phase space $(x,v)$, obeying a Vlasov-Poisson set of equations. The ions are modeled by a Landau-Lifshitz equation for their spin density, which contains ion-ion and electron-ion magnetic exchange terms. We perform a linear response study of the coupled Vlasov-Poisson-Landau-Lifshitz (VPLL) equations for the case of a Maxwell-Boltzmann equilibrium, focussing in particular on the spin dispersion relation. Condition of stability or instability for the spin modes are identified, which depend essentially on the electron spin polarization rate $\eta$ and the electron-ion magnetic coupling constant $K$. We also develop an Eulerian grid-based computational code for the fully nonlinear VPLL equations, based on the geometric Hamiltonian method first developed in [N. Crouseilles et al. Journal of Plasma Physics, 89(2):905890215, 2023]. This technique allows us to achieve great accuracy for the conserved quantities, such as the modulus of the ion spin vector and the total energy. Numerical tests in the linear regime are in accordance with the estimations of the linear response theory. For two-stream equilibria, we study the interplay of instabilities occurring in both the charge and the spin sectors. The set of parameters used in the simulations, with densities close to those of solids ($\approx 10^{29} \rm m^{-3}$) and temperatures of the order of 10 eV, may be relevant to the warm dense matter regime appearing in some inertial fusion experiments.

We present a new technique for efficiently transitioning a quantum system from an initial to a final stationary state in less time than is required by an adiabatic (quasi-static) process. Our approach makes use of Nelson's stochastic quantization, which represents the quantum system as a classical Brownian process. Thanks to this mathematical analogy, known protocols for classical overdamped systems can be translated into quantum protocols. In particular, one can use classical methods to find optimal quantum protocols that minimize both the time duration and some other cost function to be freely specified. We have applied this method to the time-dependent harmonic oscillator and tested it on two different cost functions: (i) the cumulative energy of the system over time and (ii) the dynamical phase of the wavefunction. In the latter case, it is possible to construct protocols that are "adiabatically optimal", i.e., they minimize their distance from an adiabatic process for a given duration.

We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature regime, where thermal fluctuations are modeled by a random magnetic field whose variance is proportional to the temperature. By rescaling the temperature proportionally to the computational cell size $\Delta x$ ($T \to T\,\Delta x/a_{\text{eff}}$, where $a_{\text{eff}}$ is the lattice constant) [M. B. Hahn, J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures $T_{\text{C}}$ that are in line with the experimental values for cobalt, iron and nickel. For finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie temperature varies with the smallest size $d$ of the system. We show that the difference between the computed finite-size $T_{\text{C}}$ and the bulk $T_{\text{C}}$ follows a power-law of the type: $(\xi_0/d)^\lambda$, where $\xi_0$ is the correlation length at zero temperature, and $\lambda$ is a critical exponent. We obtain values of $\xi_0$ in the nanometer range, also in accordance with other simulations and experiments. The computed critical exponent is close to $\lambda=2$ for all considered materials and geometries. This is the expected result for a mean-field approach, but slightly larger than the values observed experimentally., Comment: 28 pages

A diffusive process that is reset to its origin at random times, so-called stochastic resetting (SR), is an ubiquitous expedient in many natural systems . Yet, beyond its ability to improve the efficiency of target searching, SR is a true non-equilibrium thermodynamic process that brings forward new and challenging questions . Here, we show how the recent developments of experimental information thermodynamics renew the way to address SR and can lead, beyond a new understanding, to better control on the non-equilibrium nature of SR. This thermodynamically controlled SR is experimentally implemented within a time-dependent optical trapping potential. We show in particular that SR converts heat into work from a single bath continuously and without feedback. This implements a Maxwell's demon that constantly erases information. In our experiments, the erasure takes the form of a protocol that allows to evaluate the true energetic cost of SR. We show that using an appropriate measure of the available information, this cost can be reduced to a reversible minimum while being bounded by the Landauer limit. We finally reveal that the individual trajectories generated by the demon all break ergodicity and thus demonstrate the non-ergodic nature of the demon's modus operandi. Our results offer new approaches to processes, such as SR, where the informational framework provides key experimental tools for their non-equilibrium thermodynamic control., Comment: 19 pages, 14 figures

Nelson's stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wave function. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson's stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double slit and harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed \emph{before} the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson's theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production.

We consider the interaction dynamics of a classical oscillator and a quantum two-level system for different pure-dephasing Hamiltonians of the type $\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehat\sigma_z$. This type of systems represents a severe challenge for popular hybrid quantum-classical descriptions. For example, in the case of the common Ehrenfest model, the classical density evolution is shown to decouple entirely from the pure-dephasing quantum dynamics. We focus on a recently proposed hybrid wave equation that is based on Koopman's wavefunction description of classical mechanics. This model retains quantum-classical correlations whenever a coupling potential is present. Here, several benchmark problems are considered and the results are compared with those arising from fully quantum dynamics. A good agreement is found for a series of study cases involving harmonic oscillators with linear and quadratic coupling, as well as time-varying coupling parameters. In all these cases the classical evolution coincides exactly with the oscillator dynamics resulting from the fully quantum description. In the special case of time-independent coupling involving a classical oscillator with varying frequency, the quantum Bloch rotation exhibits peculiar features that escape from the hybrid description. In addition, nonlinear corrections to the harmonic Hamiltonian lead to an overall growth of decoherence at long times, which is absent in the fully quantum treatment., Comment: 24 pages, 10 figures. Contribution to the Special Collection "Koopman methods in classical and quantum-classical mechanics" in the Journal of Physics A

By controlling in real-time the variance of the radiation pressure exerted on an optically trapped microsphere, we engineer temperature protocols that shortcut thermal relaxation when transferring the microsphere from one thermal equilibrium state to an other. We identify the entropic footprint of such accelerated transfers and derive optimal temperature protocols that either minimize the production of entropy for a given transfer duration or accelerate as much as possible the transfer for a given entropic cost. Optimizing the trade-off yields time-entropy bounds that put speed limits on thermalization schemes. We further show how optimization expands the possibilities for accelerating Brownian thermalization down to its fundamental limits. Our approach paves the way for the design of optimized, finite-time thermodynamic cycles at the mesoscale. It also offers a platform for investigating fundamental connections between information geometry and finite-time processes., Comment: 4 pages, 3 figures, plus Appendix

The concept of Logical Entropy, $S_L = 1- \sum_{i=1}^n p_i^2$, where the $p_i$ are normalized probabilities, was introduced by David Ellerman in a series of recent papers. Although the mathematical formula itself is not new, Ellerman provided a sound probabilistic interpretation of $S_L$ as a measure of the distinctions of a partition on a given set. The same formula comes across as a useful definition of entropy in quantum mechanics, where it is linked to the notion of purity of a quantum state. The quadratic form of the logical entropy lends itself to a generalization of the probabilities that include negative values, an idea that goes back to Feynman and Wigner. Here, we analyze and reinterpret negative probabilities in the light of the concept of logical entropy. Several intriguing quantum-like properties of the logical entropy are derived and discussed in finite dimensional spaces. For infinite-dimensional spaces (continuum), we show that, under the sole hypothesis that the logical entropy and the total probability are preserved in time, one obtains an evolution equation for the probability density that is basically identical to the quantum evolution of the Wigner function in phase space, at least when one considers only the momentum variable. This result suggest that the logical entropy plays a profound role in establishing the peculiar rules of quantum physics.

We propose to use a correlated noise bath to drive an optically trapped Brownian particle that mimics active biological matter. Thanks to the flexibility and precision of our setup, we are able to control the different parameters that drive the stochastic motion of the particle with unprecedented accuracy, thus reaching strongly correlated regimes that are not easily accessible with real active matter. In particular, by using the correlation time (i.e., the "color") of the noise as a control parameter, we can trigger transitions between two non-equilibrium steady states with no expended work, but only a calorific cost. Remarkably, the measured heat production is directly proportional to the spectral entropy of the correlated noise, in a fashion that is reminiscent of Landauer's principle. Our procedure can be viewed as a method for harvesting information from the active fluctuations., Comment: 5 pages, 4 figures, plus Appendix

Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space methods based on Wigner functions, fluid models require the solution of a small number of equations in ordinary space, implying a lesser computational cost. They are therefore well suited to study systems composed of a very large number of particles, such as large metallic nano-objects. They can be generalized to include the spin degrees of freedom, as well as semirelativistic effects such as the spin-orbit coupling. Here, we review the basic properties, advantages and limitations of quantum fluid models, and provide some examples of their applications.

A review of the theoretical and computational aspects of plasma-wall transition is presented. The conditions for the existence of plasma sheaths in front of a solid surface are established. Various regimes are analyzed -collisionless and collisional. fluid and kinetic, with and without ionization. The partition of the plasma-wall transition into distinct regions (Debye sheath, quasineutral presheath. magnetic presheath, etc...) is also discussed. Applications to the theory of electrostatic probes are illustrated by means of a recently developed kinetic model. The influence of the probe on ion temperature measurements is studied in detail.

We propose to reinterpret Einstein's field equations as a nonlinear eigenvalue problem, where the cosmological constant $\Lambda$ plays the role of the (smallest) eigenvalue. This interpretation is fully worked out for a simple model of scalar gravity. The essential ingredient for the feasibility of this approach is that the classical field equations be nonlinear, i.e., that the gravitational field is itself a source of gravity. The cosmological consequences and implications of this approach are developed and discussed.

We show that in the Dirac-Milne universe (a matter-antimatter symmetric universe where the two components repel each other), rotation curves are generically flat beyond the characteristic distance of about 3 virial radii, and that a Tully-Fisher relation with exponent $\approx 3$ is satisfied. Using 3D simulations with a modified version of the RAMSES code, we show that the Dirac-Milne cosmology presents a Faber-Jackson relation with a very small scatter and an exponent equal to $\approx 3$ between the mass and the velocity dispersion. We also show that the mass derived from the rotation curves assuming Newtonian gravity is systematically overestimated compared to the mass really present. We also show that the Dirac-Milne universe, featuring a polarization between its matter and antimatter components, presents a behavior similar to that of MOND (Modified Newtonian Dynamics), characterized by an additional surface gravity compared to the Newtonian case. We show that in the Dirac-Milne universe, at the present epoch, the intensity of the additional gravitational field $g_{am}$ due to the presence of clouds of antimatter is of the order of a few $10^{-11}$ m/s$^2$, similar to the characteristic acceleration of MOND. We study the evolution of this additional acceleration $g_{am}$ and show that it depends on the redshift, and is therefore not a fundamental constant. Combined with its known concordance properties on SNIa luminosity distance, age, nucleosynthesis and structure formation, the Dirac-Milne cosmology may then represent an interesting alternative to the $\Lambda$CDM, MOND, and other scenarios for explaining the Dark Matter and Dark Energy conundrum.

We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped. The distribution $n(x,t)$ of the classical positions is used to reconstruct the quantum Bohm potential $V_{\rm Bohm} = -\frac{\hbar^2}{2 m} \frac{\Delta \sqrt{n}}{\sqrt{n}}$, which in turn acts on the shape of the potential wells. As a result, the classical particles experience an effective "quantum" force. This protocol is tested with numerical simulations using single- and double-well potentials, evidencing typical quantum effects such as long-lasting correlations and quantum tunneling. For harmonic confinement, the analogy is implemented experimentally using micron-sized dielectric beads optically trapped by a laser beam.

The presence of complex hierarchical gravitational structures is one of the main features of the observed universe. Here, structure formation is studied both for the standard ($\Lambda \rm CDM$) cosmological model and for the Dirac-Milne universe, a matter-antimatter symmetric universe that was {\gm recently} proposed as an alternative "coasting" cosmological scenario. One-dimensional numerical simulations reveal the analogies and differences between the two models. Although structure formation is faster in the Dirac-Milne universe, both models predict that it ends shortly before the present epoch, at cosmological redshift $z \approx 3$ for the Dirac-Milne cosmology, and at $z \approx 0.5$ for the $\Lambda \rm CDM$ universe. The present results suggest that the matter power spectrum observed by the Sloan Digital Sky Survey might be entirely due to the nonlinear evolution of matter and antimatter domains of relatively small initial dimensions, of the order of a few tens of parsecs comoving at cosmological redshift $z =1080$., Comment: To be published in Physical Review D

We characterize throughout the spectral range of an optical trap the nature of the noise at play and the ergodic properties of the corresponding Brownian motion of an overdamped trapped single microsphere, comparing experimental, analytical and simulated data. We carefully analyze noise and ergodic properties $(i)$ using the Allan variance for characterizing the noise and $(ii)$ exploiting a test of ergodicity tailored for experiments done over finite times. We derive these two observables in the low-frequency Ornstein-Uhlenbeck trapped-diffusion regime and study analytically their evolution towards the high-frequency Wiener free-diffusion regime, in a very good agreement with simulated and experimental results. This leads to reveal noise and ergodic spectral signatures associated with the distinctive features of both regimes., Comment: 13 pages, 11 figures

Graphene conductive properties have been long exploited in the field of organic photovoltaics and optoelectronics by the scientific community worldwide. We engineered and characterized a hybrid biointerface in which graphene is coupled with photosensitive polymers, and tested its ability to elicit lighttriggered neural activity modulation in primary neurons and blind retina explants. We designed such a graphene-based device by modifying a photoactive P3HT-based retinal interface, previously reported to rescue light sensitivity in blind rodents, with a CVD graphene layer replacing the conductive PEDOT:PSS layer to enhance charge separation. The new graphene-based device was characterized for its electrochemical features and for the ability to photostimulate primary neurons and blind retina explants, while preserving biocompatibility. Light-triggered responses, recorded by patch-clamp in vitro or MEA ex vivo, show a stronger light-transduction efficiency when the neurons are interfaced with the graphene-based device with respect to the PEDOT:PSS-based one. The possibility to ameliorate flexible photo-stimulating devices via the insertion of graphene, paves the way for potential biomedical applications of graphenebased neuronal interfaces in the context of retinal implants., Comment: 10 pages, 5 figures

Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed matter physics, atomic physics, and quantum chemistry. DFT establishes that a system of $N$ interacting electrons can be described uniquely by its single-particle density $n(\boldsymbol{r})$, instead of the $N$-body wave function, yielding an enormous gain in terms of computational speed and memory storage space. Here, we use time-dependent DFT to show that a classical collisionless plasma can always, in principle, be described by a set of fluid equations for the single-particle density and current. The results of DFT guarantee that an exact closure relation, fully reproducing the Vlasov dynamics, necessarily exists, although it may be complicated (nonlocal in space and time, for instance) and difficult to obtain in practice. This goes against the common wisdom in plasma physics that the Vlasov and fluid descriptions are mutually incompatible, with the latter inevitably missing some "purely kinetic" effects., Comment: To appear in the Special Issue "The many facets of the Vlasov equation", published by the Journal of Plasma Physics, from the Vlasovia 2019 conference, Strasbourg, France, July 2019

Conduction electrons in metallic nano-objects ($\rm 1\,nm = 10^{-9}\, m$) behave as mobile negative charges confined by a fixed positively-charged background, the atomic ions. In many respects, this electron gas displays typical plasma properties such as screening and Langmuir waves, with more or less pronounced quantum features depending on the size of the object. To study these dynamical effects, the mathematical artillery of condensed-matter theorists mainly relies on wave function $\psi(r,t)$ based methods, such as the celebrated Hartree-Fock equations. The theoretical plasma physicist, in contrast, lives and breaths in the six-dimensional phase space, where the electron gas is fully described by a probability distribution function $f(r,p,t)$ that evolves according to an appropriate kinetic equation. Here, we illustrate the power and flexibility of the phase-space approach to describe the electron dynamics in small nano-objects. Starting from classical and semiclassical scenarios, we progressively add further features that are relevant to solid-state plasmas: quantum, spin, and relativistic effects, as well as collisions and dissipation. As examples of applications, we study the spin-induced modifications to the linear response of a homogeneous electron gas and the nonlinear dynamics of the electrons confined in a thin metal films of nanometric dimensions.

We propose an optimization strategy to control the dynamics of a stochastic system transferred from one thermal equilibrium to another and apply it experimentally to a Brownian particle in an optical trap under compression. Based on a variational principle that treats the transfer duration and the expended work on an equal footing, our strategy leads to a family of protocols that are either optimally cheap for a given duration or optimally fast for a given energetic cost. This approach unveils a universal relation $\Delta t\,\Delta W \ge (\Delta t\,\Delta W)_{\rm opt}$ between the transfer duration and the expended work. We verify experimentally that the lower bound is reached only with the optimized protocols., Comment: 10 pages, 14 figures

We theoretically investigate the creation of a magnetic moment in gold nanoparticles by circularly polarized laser light. To this end, we describe the collective electron dynamics in gold nanoparticles using a semiclassical approach based on a quantum hydrodynamic model that incorporates the prin- cipal quantum many-body and nonlocal effects, such as the electron spill-out, the Hartree potential, and the exchange and correlation effects. We use a variational approach to investigate the breathing and the dipole dynamics induced by an external electric field. We show that gold nanoparticles can build up a static magnetic moment through the interaction with a circularly polarized laser field. We analyze that the responsible physical mechanism is a plasmonic, orbital inverse Faraday effect, which can be understood from the time-averaged electron current that contains currents rotating on the nanoparticles surface. The computed laser-induced magnetic moments are sizeable, of about 0.35 muB/atom for a laser intensity of 450 GW/cm2 at plasmon resonance.

We review the main arguments against antigravity, a different acceleration of antimatter relative to matter in a gravitational field, discussing and challenging Morrison's, Good's and Schiff's arguments. Following Price, we show that, very surprisingly, the usual expression of the Equivalence Principle is violated by General Relativity when particles of negative mass are supposed to exist, which may provide a fundamental explanation of MOND phenomenology, obviating the need for Dark Matter. Motivated by the observation of repulsive gravity under the form of Dark Energy, and by the fact that our universe looks very similar to a coasting (neither decelerating nor accelerating) universe, we study the Dirac-Milne cosmology, a symmetric matter-antimatter cosmology where antiparticles have the same gravitational properties as holes in a semiconductor. Noting the similarities with our universe (age, SN1a luminosity distance, nucleosynthesis, CMB angular scale), we focus our attention on structure formation mechanisms, finding strong similarities with our universe. Additional tests of the Dirac-Milne cosmology are briefly reviewed, and we finally note that a crucial test of the Dirac-Milne cosmology will be soon realized at CERN next to the ELENA antiproton decelerator, possibly as early as fall 2018, with the AEgIS, ALPHA-g and Gbar antihydrogen gravity experiments., Comment: Proceedings of the Low Energy Antiproton Physics Conference (LEAP), Sorbonne University, Paris, March 12th to 16th, 2018

Spin currents have been shown to play a key role in the ultrafast laser-driven demagnetization process in ferromagnetic thin films. Here, we show that an oscillating spin current can be generated in the film via the application of a femtosecond laser pulse in the visible range. In particular, we prove that the spin current is due to ballistic electrons traveling back and forth in the film. The dependence of the current intensity on the driving electric field is also investigated., Comment: SPIE Nanoscience + Engineering 2018: Spintronics XI, San Diego, 19-23 August 2018

Quantum effects play a significant role in nanometric plasmonic devices, such as small metal clusters and metallic nanoshells. For structures containing a large number of electrons, ab-initio methods such as the time-dependent density functional theory (TD-DFT) are often impractical because of severe computational constraints. Quantum hydrodynamics (QHD) offers a valuable alternative by representing the electron population as a continuous fluid medium evolving under the action of the self-consistent and external fields. Although relatively simple, QHD can incorporate quantum and nonlinear effects, nonlocal effects such as the electron spillout, as well as exchange and correlations. Here, we show an application of the QHD methods to the plasmonic breathing oscillations in metallic nanoshells. We illustrate the main advantages of this approach by comparing systematically the QHD results with those obtained with a TD-DFT code., Comment: SPIE Nanoscience + Engineering conference, Plasmonics: Design, Materials, Fabrication, Characterization, and Applications XVI, San Diego, August 19-23, 2018

We propose and illustrate a quantum hydrodynamic (QHD) model for the description of plasmonic oscillations in the $\rm C_{60}$ molecule. Although simpler than competing approaches such as time-dependent density functional theory (TDDFT), the model contains the key ingredients to characterize plasmonic modes, namely the Hartree, exchange and correlation potentials, as well as nonlocal, nonlinear and quantum effects to the lowest order. A variational technique is used to solve analytically the QHD model for the case of breathing (monopolar) plasmonic oscillations, revealing a bulk mode near the plasmon frequency. Numerical simulations of both the QHD equations and a TDDFT model confirm the existence of this mode and highlight a second collective mode at lower energy. Such monopolar modes may be measured experimentally using electron energy loss spectroscopy.

We construct a family of models with negative gravitational mass in the context of Newtonian gravity. We focus in particular on a model that reproduces the features of the so-called Dirac-Milne universe, a matter-antimatter symmetric universe that was recently proposed as an alternative cosmological scenario [A. Benoit-Levy and G. Chardin, A&A 537, A78 (2012)]. We perform one-dimensional N-body simulations of these negative-mass models for an expanding universe and study the associated formation of gravitational structures. The similarities and differences with the standard cosmological model are highlighted and discussed., Comment: Equation 14 has been corrected (NB: typo in the published PRD version)

We propose to use oscillating spin currents with slowly varying frequency (chirp) to manipulate and control the magnetization dynamics in a nanomagnet. By recasting the Landau-Lifshitz-Slonczewski equation in a quantum-like two-level formalism, we show that a chirped spin current polarized in the direction normal to the anisotropy axis can induce a stable precession of the magnetic moment at any angle (up to $90^\circ$) with respect to the anisotropy axis. The drive current can be modest ($10^6\,\rm A/cm^2$ or lower) provided the chirp rate is sufficiently slow. The induced precession is stable against thermal noise, even for small nano-objects at room temperature. Complete reversal of the magnetization can be achieved by adding a small external magnetic field antiparallel to the easy axis. Alternatively, a combination of chirped ac and dc currents with different polarization directions can also be used to trigger the reversal.

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-1/2 fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations.

An effective self-consistent model is derived and used to study the dynamics of an electron gas confined in a nonparabolic and anisotropic quantum well. This approach is based on the equations of quantum hydrodynamics, which incorporate quantum and nonlinear effects in an approximate fashion. The effective model consists of a set of six coupled differential equations (dynamical system) for the electric dipole and the size of the electron gas. Using this model we show that: (i) High harmonic generation is related to the appearance of chaos in the phase space, as attested by related Poincar\'e sections; (ii) Higher order harmonics can be excited efficiently and with relatively weak driving fields by making use of chirped electromagnetic waves.

Ultracold neutrons confined in the Earth's gravitational field display quantized energy levels that have been observed for over a decade. In recent resonance spectroscopy experiments [T. Jenke et al., Nature Phys. 7, 468 (2011)], the transition between two such gravitational quantum states was driven by the mechanical oscillation of the plates that confine the neutrons. Here we show that, by applying a sinusoidal modulation with slowly varying frequency (chirp), the neutrons can be brought to higher excited states by climbing the energy levels one by one. The proposed experiment should make it possible to observe the quantum-classical transition that occurs at high neutron energies. Furthermore, it provides a technique to realize superpositions of gravitational quantum states, to be used for precision tests of gravity at short distances.

When an unmagnetized plasma comes in contact with a material surface, the difference in mobility between the electrons and the ions creates a nonneutral layer known as the Debye sheath (DS). However, in magnetic fusion devices, the open magnetic field lines intersect the structural elements of the device with near grazing incidence angles. The magnetic field tends to align the particle flow along its own field lines, thus counteracting the mechanism that leads to the formation of the DS. Recent work using a fluid model [P. Stangeby, Nucl. Fusion {\bf 52}, 083012 (2012)] showed that the DS disappears when the incidence angle is smaller than a critical value (around $5^\circ$ for ITER-like parameters). Here, we study this transition by means of numerical simulations of a kinetic model both in the collisionless and weakly collisional regimes. We show that the main features observed in the fluid model are preserved: for grazing incidence, the space charge density near the wall is reduced, the ion flow is subsonic, and the electric field and plasma density profiles are spread out over several ion Larmor radii instead of a few Debye lengths as in the unmagnetized case. As there is no singularity at the DS entrance in the kinetic model, this phenomenon depends smoothly on the magnetic field incidence angle and no particular critical angle arises. The simulation results and the predictions of the fluid model are in good agreement, although some discrepancies subsist, mainly due to the assumptions of isothermal closure and diagonality of the pressure tensor in the fluid model.

Numerical simulations of self-gravitating systems are generally based on N-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we performed one-dimensional Vlasov simulations of a long-standing cosmological problem, namely the fractal properties of an expanding Einstein-de Sitter universe in Newtonian gravity. The N-body results were confirmed for high-density regions and extended to regions of low matter density, where the N-body approach usually fails.