arXiv subjects

David Gaspard

Publications and source records attributed to David Gaspard.

12 recordsLinked to original sources

arXiv2026

Directionality emergence and localization in a quantum random Lorentz gas

The propagation of a spherical wave through a two-dimensional random Lorentz gas composed of small fixed scatterers is studied. Inspired by the Mott problem (how an initially isotropic quantum wave can give rise to a single particle-like track), we investigate, on a schematic model, whether such a directional behavior can emerge purely from the multiscattering process, without any explicit measurement or decoherence mechanism. Using the Foldy-Lax formalism, we derive the far-field angular behavior of the wavefunction, and introduce a directionality vector to quantify its anisotropy and identify its preferred direction. Numerical simulations reveal the existence of a strongly directional regime within a specific wavenumber range, which emerges from multiscattering with more than $100$ scatterers and which can be related to Anderson localization.

quant-ph↗

arXiv2024

Transmission eigenvalue distribution in disordered media from radiant field theory

We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a $2\times 2$ matrix radiance, reminiscent of the radiative transfer equation but capable of capturing coherent interference effects. This framework goes beyond the limitations of the Dorokhov-Mello-Pereyra-Kumar theory by accounting for both quasiballistic and diffusive regimes. It also handles open geometries inaccessible to standard wave-equation solvers such as infinite slabs. Analytical and numerical solutions are provided for these geometries, highlighting in particular the impact of the waveguide shape and the grazing modes on the transmission eigenvalue distribution in the quasiballistic regime. By removing the macroscopic assumptions of random matrix models, this microscopic theory enables the calculation of transmission statistics in regimes previously out of reach. It also provides a foundation for exploring more complex observables and physical effects relevant to wavefront shaping in realistic disordered systems.

math-ph↗

arXiv2024

Radiant Field Theory: A Transport Approach to Shaped Wave Transmission through Disordered Media

We present a field-theoretic framework to characterize the distribution of transmission eigenvalues for coherent wave propagation through disordered media. The central outcome is a transport equation for a matrix-valued radiance, analogous to the classical radiative transport equation but capable of capturing coherent effects encoded in the transmission matrix. Unlike the Dorokhov-Mello-Pereyra-Kumar (DMPK) theory, our approach does not rely on the isotropy hypothesis, which presumes uniform angular scattering by material slices. As a result, it remains valid beyond the diffusive regime, accurately describing the transmission eigenvalue distribution in the quasiballistic regime as well. Moreover, the framework is more versatile than the DMPK theory, enabling straightforward incorporation of experimental realities such as absorption and incomplete channel control. These factors are frequently encountered in wave experiments on complex media but have lacked an ab initio theoretical treatment until now. We validate our predictions through numerical simulations based on the microscopic wave equation, confirming the accuracy and broad applicability of the theory.

math-ph↗

arXiv2023

Effective-medium approach to the resonance distribution of wave scattering in a random point field

In a previous paper [Phys. Rev. A 105, 042205 (2022)], the distribution of resonance poles in the complex plane of the wavenumber $k$ associated to the multiple scattering of a quantum particle in a random point field was numerically discovered. This distribution presented two distinctive structures: a set of peaks at small $k$ when the wavelength is larger than the interscatterer distance, and a band almost parallel to the real axis at larger $k$. In this paper, a theoretical study based on wave transport theory is proposed to explain the origin of these structures and to predict their distribution in the complex $k$ plane. First, it is shown that the peaks at small $k$ can be understood using the effective wave equation for the average wavefunction over the disorder. Then, that the band at large $k$ can be described by the Bethe-Salpeter equation for the square modulus of the wavefunction. This study is supported by careful comparisons with numerical simulations.

quant-ph↗

arXiv2023

Transverse quantum decoherence of a fast particle in a gas

The decoherence of a fast quantum particle in a gas is studied by applying the Kramers-Moyal expansion to the quantum master equation for the reduced density matrix of the particle. This expansion leads to a general form of the Caldeira-Leggett master equation accounting for the angular variation of the differential cross section. The equation describes the decoherence in both the longitudinal and transverse directions with respect to the particle motion. It is shown that, when the differential cross section is concentrated in the forward direction, transverse decoherence dominates. The coherence region off the diagonal of the density matrix is characterized by coherence lengths, which can be deduced, for Gaussian states, from the momentum covariance matrix according to a Heisenberg-type uncertainty relation. Finally, the longitudinal-to-transverse ratio of the coherence lengths is estimated for an alpha particle of a few MeVs. This ratio indicates that the coherence region looks like an ellipsoid elongated in the direction of motion.

quant-ph↗

arXiv2022

Quantum master equations for a fast particle in a gas

The propagation of a fast particle in a low-density gas at thermal equilibrium is studied in the context of quantum mechanics. A quantum master equation in the Redfield form governing the reduced density matrix of the particle is derived explicitly from first principles. Under some approximations, this equation reduces to the linear Boltzmann equation. The issue of the positivity of the time evolution is also discussed by means of a Lindblad form. The Born and Markov assumptions underlying these equations, as well as other approximations regarding the bath correlation function, are discussed in details. Furthermore, all these master equations are shown to be equivalent with each other if the density matrix of the particle is diagonal in the momentum basis, or if the collision rate is independent of the particle momentum.

quant-ph↗

arXiv2022

Multiple scattering model of the quantum random Lorentz gas

A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point scatterers is derived in detail, and expressed in terms of the scattering length. The fundamental properties of the model, such as the cross section and the scattering matrix, are calculated. In addition, the model is shown to verify the optical theorem and thus probability conservation. Finally, the differential and total cross sections are numerically computed in two situations whether the Lorentz gas is smaller or larger than the mean free path. A distinct Airy diffraction peak is obtained for a large enough number of scatterers. This observation is related to the extinction paradox.

quant-ph↗

arXiv2022

Resonance distribution in the quantum random Lorentz gas

The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wavenumber without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a non-resonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case.

quant-ph↗

arXiv2019

Complex-energy analysis of proton-proton fusion

An analysis of the astrophysical $S$ factor of the proton-proton weak capture ($\mathrm{p}+\mathrm{p}\rightarrow {}^2\mathrm{H}+\mathrm{e}^++ν_{\mathrm{e}}$) is performed on a large energy range covering solar-core and early Universe temperatures. The measurement of $S$ being physically unachievable, its value relies on the theoretical calculation of the matrix element $Λ$. Surprisingly, $Λ$ reaches a maximum near $0.13~\mathrm{MeV}$ that has been unexplained until now. A model-independent parametrization of $Λ$ valid up to about $5~\mathrm{MeV}$ is established on the basis of recent effective-range functions. It provides an insight into the relationship between the maximum of $Λ$ and the proton-proton resonance pole at $(-140-467\,\mathrm{i})~\mathrm{keV}$ from analytic continuation. In addition, this parametrization leads to an accurate evaluation of the derivatives of $Λ$, and hence of $S$, in the limit of zero energy.

nucl-th↗

arXiv2018

Connection formulas between Coulomb wave functions

The mathematical relations between the regular Coulomb function $F_{η\ell}(ρ)$ and the irregular Coulomb functions $H^\pm_{η\ell}(ρ)$ and $G_{η\ell}(ρ)$ are obtained in the complex plane of the variables $η$ and $ρ$ for integer or half-integer values of $\ell$. These relations, referred to as "connection formulas", form the basis of the theory of Coulomb wave functions, and play an important role in many fields of physics, especially in the quantum theory of charged particle scattering. As a first step, the symmetry properties of the regular function $F_{η\ell}(ρ)$ are studied, in particular under the transformation $\ell\mapsto-\ell-1$, by means of the modified Coulomb function $Φ_{η\ell}(ρ)$, which is entire in the dimensionless energy $η^{-2}$ and the angular momentum $\ell$. Then, it is shown that, for integer or half-integer $\ell$, the irregular functions $H^\pm_{η\ell}(ρ)$ and $G_{η\ell}(ρ)$ can be expressed in terms of the derivatives of $Φ_{η,\ell}(ρ)$ and $Φ_{η,-\ell-1}(ρ)$ with respect to $\ell$. As a consequence, the connection formulas directly lead to the description of the singular structures of $H^\pm_{η\ell}(ρ)$ and $G_{η\ell}(ρ)$ at complex energies in their whole Riemann surface. The analysis of the functions is supplemented by novel graphical representations in the complex plane of $η^{-1}$.

math-ph↗

arXiv2018

Decoherence and determinism in a one-dimensional cloud-chamber model

The hypothesis by Sparenberg et al. (2013) that the particular linear tracks appearing in the measurement of a spherically-emitting radioactive source in a cloud chamber are determined by the (random) positions of atoms or molecules inside the chamber is further explored in the framework of a recently established one-dimensional model by Carlone et al. (2015). In this model, meshes of localized spins 1/2 play the role of the cloud-chamber atoms and the spherical wave is replaced by a linear superposition of two wave packets moving from the origin to the left and to the right, evolving deterministically according to the Schrödinger equation. We first revisit these results using a time-dependent approach, where the wave packets impinge on a symmetric two-sided detector. We discuss the evolution of the wave function in the configuration space and stress the interest of a non-symmetric detector in a quantum-measurement perspective. Next we use a time-independent approach to study the scattering of a plane wave on a single-sided detector. Preliminary results are obtained, analytically for the single-spin case and numerically for up to 8 spins. They show that the spin-excitation probabilities are sometimes very sensitive to the parameters of the model, which corroborates the idea that the measurement result could be determined by the atom positions. The possible origin of decoherence and entropy increase in future models is finally discussed.

quant-ph↗

arXiv2018

Effective-range function methods for charged particle collisions

Different versions of the effective-range function method for charged particle collisions are studied and compared. In addition, a novel derivation of the standard effective-range function is presented from the analysis of Coulomb wave functions in the complex plane of the energy. The recently proposed effective-range function denoted as $Δ_\ell$ [Phys. Rev. C 96, 034601 (2017)] and an earlier variant [Hamilton et al., Nucl. Phys. B 60, 443 (1973)] are related to the standard function. The potential interest of $Δ_\ell$ for the study of low-energy cross sections and weakly bound states is discussed in the framework of the proton-proton ${}^1S_0$ collision. The resonant state of the proton-proton collision is successfully computed from the extrapolation of $Δ_\ell$ instead of the standard function. It is shown that interpolating $Δ_\ell$ can lead to useful extrapolation to negative energies, provided scattering data are known below one nuclear Rydberg energy (12.5 keV for the proton-proton system). This property is due to the connection between $Δ_\ell$ and the effective-range function by Hamilton et al. that is discussed in detail. Nevertheless, such extrapolations to negative energies should be used with caution because $Δ_\ell$ is not analytic at zero energy. The expected analytic properties of the main functions are verified in the complex energy plane by graphical color-based representations.

nucl-th↗