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arXiv:1603.03379

Radiation reaction on a Brownian scalar electron in high-intensity fields

Keita Seto

Published Mar 10, 2016• 0 citations
arXivHTMLPDF

Abstract

Radiation reaction against a relativistic electron is of critical importance since the experiment to check this "quantumness" becomes possible soon with an extremely high-intensity laser beam. However, there is a fundamental mathematical quest to apply any laser profiles to laser focusing and superposition beyond the Furry picture of its usual method by a plane wave. To give the apparent meaning of $q(χ)$ the quantumness factor with respect to a radiation process is absent. Thus for resolving the above questions, we propose stochastic quantization of the classical radiation reaction model for any laser field profiles, via the construction of the relativistic Brownian kinematics with the dynamics of a scalar electron and the Maxwell equation with a current by a Brownian quanta. This is the first proposal of the coupling system between a relativistic Brownian quanta and fields in Nelson's stochastic quantization. Therefore, we can derive the radiation field by its Maxwell equation, too. This provides us the fact that $q(χ)$ produced by QED is regarded as $\mathscr{P}(\varOmega_τ^{\mathrm{ave}})$ of an existence probability such that a scalar electron stay on its average trajectory.

DOI
10.48550/arxiv.1603.03379

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Radiation reaction against a relativistic electron is of critical importance since the experiment to check this "quantumness" becomes possible soon with an extremely high-intensity laser beam. However, there is a fundamental mathematical quest to apply any laser profiles to laser focusing and superposition beyond the Furry picture of its usual method by a plane wave. To give the apparent meaning of q(χ)q(χ)q(χ) the quantumness factor with respect to a radiation process is absent. Thus for resolving the above questions, we propose stochastic quantization of the classical radiation reaction model for any laser field profiles, via the construction of the relativistic Brownian kinematics with the dynamics of a scalar electron and the Maxwell equation with a current by a Brownian quanta. This is the first proposal of the coupling system between a relativistic Brownian quanta and fields in Nelson's stochastic quantization. Therefore, we can derive the radiation field by its Maxwell equation, too. This provides us the fact that q(χ)q(χ)q(χ) produced by QED is regarded as P(Ωτave)\mathscr{P}(\varOmega_τ^{\mathrm{ave}})P(Ωτave​) of an existence probability such that a scalar electron stay on its average trajectory.
Tracking the real trajectory of a quantum particle is one of the interpretation problem and it is expressed by the Brownian (stochastic) motion suggested by E. Nelson. Especially the dynamics of a radiating electron, namely, radiation reaction which requires us to track its trajectory becomes important in the high-intensity physics by PW-class lasers at present. It has been normally treated by the Furry picture in non-linear QED, but it is difficult to draw the real trajectory of a quantum particle. For the improvement of this, I propose the representation of a stochastic particle interacting with fields and show the way to describe radiation reaction on its Brownian motion.
Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation from a stochastic particle hasn't been proposed yet. For the improvement of this, I propose the extension of Nelson's quantum dynamics, for describing a relativistic scalar electron with its radiation equivalent to the Klein-Gordon particle and field system.
An effective model for describing the relativistic quantum dynamics of a radiating electron is developed via a relativistic generalization of the Lindblad master equation. By incorporating both radiation reaction and vacuum fluctuations into the Dirac equation within an open quantum system framework, our approach captures the Zitterbewegung of the electron, ensuing noncommutativity of its effective spatial coordinates, and provides the quantum analogue of the Landau-Lifshitz (LL) classical equation of motion with radiation reaction. We develop the corresponding phase-space representation via the relativistic Wigner function and derive the semiclassical limit through a Foldy-Wouthuysen transformation. The latter elucidates the signature of quantum vacuum fluctuations in the LL equation, and shows its relationship with the corrected Sokolov equation. Our results offer a robust framework for investigating quantum radiation reaction effects in ultrastrong laser fields.
Abstract Near-future experiments with Petawatt class lasers are expected to produce a high flux of gamma-ray photons and electron–positron pairs through strong field quantum electrodynamical processes. Simulations of the expected regime of laser–matter interaction are computationally intensive due to the disparity of the spatial and temporal scales, and because quantum and classical descriptions need to be accounted for simultaneously (classical for collective effects and quantum for nearly instantaneous events of hard photon emission and pair creation). We study the stochastic cooling of an electron beam in a strong, constant, uniform magnetic field, both its particle distribution functions and their energy momenta. We start by obtaining approximate closed-form analytical solutions to the relevant observables. Then, we apply the quantum-hybrid variational quantum imaginary time evolution to the Fokker–Planck equation describing this process and compare it against theory and results from particle-in-cell simulations and classical partial differential equation solvers, showing good agreement. This work will be useful as a first step towards quantum simulation of plasma physics scenarios where diffusion processes are important, particularly in strong electromagnetic fields.
Recently GUER~A and LOFF~]~D0 (:) have constructed a stochastice elctromagnetic field by applying the stochastic quantization method of Nelson (2) to the classical electromagnetic field. According to their results the (( space part ~) of the Euclidean electromagnetic field F~j (with i, ] = 1, 2, 3) can be regarded as the ground-state stochastic electromagnetic field defined in the real physical time, in complete analogy with the case of the scalar massive boson field (3). In this note we shall comment on a basic assumption contained in the paper of Guerra and Loffredo. The main feature in their construction is that the magnetic field B(~, t) is assumed to be promoted to a random ~iarkov process by the stochastic quantization procedure. The electric field E(~, t) is then split into a couple of functions /~( ~, t) expressible in terms of B(~, t). By considering the classical Maxwell field in terms of normal canonical co-ordinates and employing the stochastic differential equation of Ito type, they obtained the ground-state stochastic magnetic field with zero mean and covarianee given by
where m is the particle mass at rest, c is the speed of light, p is the particle momentum and U is a potential. The root in Eq. (1) complicates substantially the way of quantizing the relativistic motion. In the literature there are two important solutions of this problem: the Klein-Gordon and Dirac equations. Their complex mathematical structures and some problems with definition of the probability density make it difficult to extend these equations for description of relativistic quantum Brownian motion. Moreover, it is not clear if the non-relativistic energy ˆ t E i   and momentum p i   operators, used in quantizing of Eq. (1), are valid in the relativistic quantum mechanics as well. The present paper proposes an alternative approach via a relativistic Wigner-Klein-Kramers equation. The quantum Brownian motion is described by the Madelung quantum hydrodynamics [4] coupled to the Breit-Fermi Hamiltonian. According to the relativistic dynamics the stochastic Langevin equation for a classical relativistic particle moving in a classical non-relativistic environment acquires the form