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Parrondo games as a lattice gas automata
 J. STAT. PHYS
, 2001
"... Parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game. We show that this phenomenon can be modelled by probabilistic lattice gas automata. Furthermore, motivated by the recent introduction of quantum coin flipping ga ..."
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Cited by 19 (1 self)
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Parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game. We show that this phenomenon can be modelled by probabilistic lattice gas automata. Furthermore, motivated by the recent introduction of quantum coin flipping games, we show that quantum lattice gas automata provide an interesting definition for quantum Parrondo games.
The Clifford Algebra Approach to Quantum Mechanics A: The Schrödinger and Pauli Particles
"... PACS numbers: Using a method based on Clifford algebras taken over the reals, we present here a fully relativistic version of the Bohm model for the Dirac particle. This model is different from the one originally proposed by Bohm and Hiley and by Doran and Lasenby. We obtain exact expressions for th ..."
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Cited by 12 (9 self)
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PACS numbers: Using a method based on Clifford algebras taken over the reals, we present here a fully relativistic version of the Bohm model for the Dirac particle. This model is different from the one originally proposed by Bohm and Hiley and by Doran and Lasenby. We obtain exact expressions for the Bohm energymomentum density, a relativistic quantum HamiltonJacobi for the conservation of energy which includes an expression for the quantum potential and a relativistic time development equation for the spin vectors of the particle. We then show that these reduce to the corresponding nonrelativistic expressions for the Pauli particle which have already been derived by Bohm, Schiller and Tiomno and in more general form by Hiley and Callaghan. In contrast to the original presentations, there is no need to appeal to classical mechanics at any stage of the development of the formalism. All the results for the Dirac, Pauli and Schrödinger cases are shown to emerge respectively from the hierarchy of Clifford algebras C13, C30, C01 taken over the reals as Hestenes has already argued. Thus quantum mechanics is emerging from one mathematical structure with no need to appeal to an external Hilbert space with wave functions.
Dürr D.: Adiabatic Pair Creation
 in Heavy Ion and Laser Fields, arXiv:hepth/0609200v2
"... We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at la ..."
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Cited by 10 (3 self)
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We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at large negative and positive times. The rigorous treatment of
Charge Renormalization and Static Electron/Positron Pair Production for a Nonlinear Dirac model with weak interactions
 SIAM J. Math. Anal
"... Abstract. The HartreeFock approximation of Quantum Electrodynamics provides a rigorous framework for the description of relativistic electrons in external fields. This nonlinear model takes into account the infinitely many virtual electrons of Dirac’s vacuum as well as the Coulomb interactions bet ..."
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Cited by 5 (5 self)
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Abstract. The HartreeFock approximation of Quantum Electrodynamics provides a rigorous framework for the description of relativistic electrons in external fields. This nonlinear model takes into account the infinitely many virtual electrons of Dirac’s vacuum as well as the Coulomb interactions between all the particles. The state of the system is an infiniterank projection satisfying a nonlinear equation. In this paper, we construct solutions to this equation, in the regime of weak interactions (that is, small coupling constant α), and strong external fields (that is, large atomic charge Z such that αZ: = κ stays fixed). In this regime, we are able to remove the ultraviolet cutoff Λ as soon as α log Λ stays fixed. As an application of this result, we compare the critical strength κc(α) of the external potential needed to produce an additional particle in the vacuum, when α = 0 or α> 0. We prove that limα→0 κc(α)/κc(0)> 1, and we identify the limit exactly. Because of the dielectric behavior of Dirac’s vacuum, static electron/positron pair production occurs in the interacting case for a stronger field that in the noninteracting case, which is a mere consequence of charge renormalization.
Pair production in inhomogeneous fields
 Phys. Rev. D
, 2005
"... We employ the recently developed worldline numerics, which combines stringinspired field theory methods with Monte Carlo techniques, to develop an algorithm for the computation of pairproduction rates in scalar QED for inhomogeneous background fields. We test the algorithm with the classic Sauter ..."
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Cited by 4 (0 self)
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We employ the recently developed worldline numerics, which combines stringinspired field theory methods with Monte Carlo techniques, to develop an algorithm for the computation of pairproduction rates in scalar QED for inhomogeneous background fields. We test the algorithm with the classic Sauter potential, for which we compute the local production rate for the first time. Furthermore, we study the production rate for a superposition of a constant E field and a spatially oscillating field for various oscillation frequencies. Our results reveal that the approximation by a local derivative expansion already fails for frequencies small compared to the electron mass scale, whereas for strongly oscillating fields a derivative expansion for the averaged field represents an acceptable approximation. The worldline picture makes the nonlocal nature of pair production transparent and facilitates a profound understanding of this important quantum phenomenon. 1
Static electronpositron pair creation in strong fields for a nonlinear dirac model. arXiv preprint arXiv :1112.2581
, 2011
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Limits on the Applicability of Classical Electromagnetic Fields as Inferred from the Radiation Reaction
"... Can the wavelength of a classical electromagnetic field be arbitrarily small, or its electric field strength be arbitrarily large? If we require that the radiationreaction force on a charged particle in response to an applied field be smaller than the Lorentz force we find limits on the classical el ..."
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Can the wavelength of a classical electromagnetic field be arbitrarily small, or its electric field strength be arbitrarily large? If we require that the radiationreaction force on a charged particle in response to an applied field be smaller than the Lorentz force we find limits on the classical electromagnetic field that herald the need for a better theory, i.e., one in better accord with experiment. The classical limitations find ready interpretation in quantum electrodynamics. The examples of Compton scattering and the QED critical field strength are discussed. It is still open to conjecture whether the present theory of QED is valid at field strengths beyond the critical field revealed by a semiclassical argument. 1
Large orders in strongfield QED
, 2006
"... Abstract. We address the issue of largeorder expansions in strongfield QED. Our approach is based on the oneloop effective action encoded in the associated photon polarisation tensor. We concentrate on the simple case of crossed fields aiming at possible applications of highpower lasers to measu ..."
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Abstract. We address the issue of largeorder expansions in strongfield QED. Our approach is based on the oneloop effective action encoded in the associated photon polarisation tensor. We concentrate on the simple case of crossed fields aiming at possible applications of highpower lasers to measure vacuum birefringence. A simple nexttoleading order derivative expansion reveals that the indices of refraction increase with frequency. This signals normal dispersion in the smallfrequency regime where the derivative expansion makes sense. To gain information beyond that regime we determine the factorial growth of the derivative expansion coefficients evaluating the first 80 orders by means of computer algebra. From this we can infer a nonperturbative imaginary part for the indices of refraction indicating absorption (pair production) as soon as energy and intensity become (super)critical. These results compare favourably with an analytic evaluation of the polarisation tensor asymptotics. KramersKronig relations finally allow for a nonperturbative definition of the real parts as well and show that absorption goes hand in hand with anomalous dispersion for sufficiently large frequencies and fields. PACS numbers: 12.20.m, 42.50.Xa, 42.60.vLarge orders in strongfield QED 2 1.
Professeur, Universite de CergyPontoise Directeur de These: Mathieu LEWIN
, 2013
"... Universite de CergyPontoise Stabilite, dispersion et creation de paires pour certains systemes quantiques innis ..."
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Universite de CergyPontoise Stabilite, dispersion et creation de paires pour certains systemes quantiques innis
Strong field, noncommutative QED
, 2010
"... We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of consta ..."
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We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of constant backgrounds by giving a new and revealing interpretation of the photon dispersion relation. Considering scattering in background fields, we then show that the noncommutative photon is primarily responsible for generating deviations from strong field QED results. Finally, we propose a new method for constructing gauge invariant variables in noncommutative QED, and use it to analyse the physics of our null background fields.