We have calculated normalized wave function solutions to the time-dependent Dirac equation on a space-time lattice grid. Using these solutions we systematically explore phenomena that are consistent with the classical relativistic Liouville phase space approach and those that do not have a direct classical counterpart. The examples reviewed are the paradoxical Zitterbewegung, the time-resolved Klein-paradox, the dynamics of spin in an inhomogeneous magnetic field, the suppression of the spatial spreading rate and new dynamical features that occur close to relativistic resonances.We have calculated normalized wave function solutions to the time-dependent Dirac equation on a space-time lattice grid. Using these solutions we systematically explore phenomena that are consistent with the classical relativistic Liouville phase space approach and those that do not have a direct classical counterpart. The examples reviewed are the paradoxical Zitterbewegung, the time-resolved Klein-paradox, the dynamics of spin in an inhomogeneous magnetic field, the suppression of the spatial spreading rate and new dynamical features that occur close to relativistic resonances.

AIP conference proceedingsJan 1, 20001 citation

Dynamic disquantization of Dirac equation

Yuri A. Rylov

Classical model S_dc of Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. Its classical analog S_dc is described by a system of ordinary differential equations, containing the quantum constant h as a parameter. Dynamic equations for S_dc are determined by the Dirac equation uniquely. Both dynamic systems S_D and S_dc appear to be nonrelativistic. One succeeded in transforming nonrelativistic dynamic system S_dc into relativistic one S_dcr. The dynamic system S_dcr appears to be a two-particle structure (special case of a relativistic rotator). It explains freely such properties of S_D as spin and magnetic moment, which are strange for pointlike structure. The rigidity function f_r(a), describing rotational part of total mass as a function of the radius $a$ of rotator, has been calculated for S_dcr. For investigation of S_D and construction of S_dc one uses new dynamic methods: dynamic quantization and dynamic disquantization. These relativistic pure dynamic procedures do not use principles of quantum mechanics (QM). They generalize and replace conventional quantization and transition to classical approximation. Totality of these methods forms the model conception of quantum phenomena (MCQP). Technique of MCQP is more subtle and effective, than conventional methods of QM. MCQP relates to conventional QM, much as the statistical physics relates to thermodynamics.Classical model S_dc of Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. Its classical analog S_dc is described by a system of ordinary differential equations, containing the quantum constant h as a parameter. Dynamic equations for S_dc are determined by the Dirac equation uniquely. Both dynamic systems S_D and S_dc appear to be nonrelativistic. One succeeded in transforming nonrelativistic dynamic system S_dc into relativistic one S_dcr. The dynamic system S_dcr appears to be a two-particle structure (special case of a relativistic rotator). It explains freely such properties of S_D as spin and magnetic moment, which are strange for pointlike structure. The rigidity function f_r(a), describing rotational part of total mass as a function of the radius $a$ of rotator, has been calculated for S_dcr. For investigation of S_D and construction of S_dc one uses new dynamic methods: dynamic quantization and dynamic disquantization. These relativistic pure dynamic procedures do not use principles of quantum mechanics (QM). They generalize and replace conventional quantization and transition to classical approximation. Totality of these methods forms the model conception of quantum phenomena (MCQP). Technique of MCQP is more subtle and effective, than conventional methods of QM. MCQP relates to conventional QM, much as the statistical physics relates to thermodynamics.

arXiv:quant-ph/0104060Apr 11, 200113 citations

On classical and quantum relativistic dynamics

F. Reuse

Foundations of PhysicsDec 1, 197918 citations

Hamiltonian of a many-electron atom in an external magnetic field and classical electrodynamics

C. Lhuillier, J.P. Faroux

The increasing precision of experiments on the Zeeman effect of many electron atoms requires an ever increasing knowledge of relativistic and radiative effects. The generalization of the Breit equation as proposed by Hegstrom includes all these effects up to order c— 3. In the non relativistic limit the resulting Hamiltonian is quite intricate, but we show in this paper that it is possible to explain almost all of its terms within the frame of classical electrodynamics. In particular, picturing the atoms as point-like particles with intrinsic magnetic moments, we show that the physical phenomena underlying the Breit equation and its recent extension are mainly two well-known classical phenomena : i) the interaction of the magnetic moment of the constituent particles with the magnetic field they experience in their rest frame; ii) the Thomas precession of the spins of the accelerated particles.The increasing precision of experiments on the Zeeman effect of many electron atoms requires an ever increasing knowledge of relativistic and radiative effects. The generalization of the Breit equation as proposed by Hegstrom includes all these effects up to order c— 3. In the non relativistic limit the resulting Hamiltonian is quite intricate, but we show in this paper that it is possible to explain almost all of its terms within the frame of classical electrodynamics. In particular, picturing the atoms as point-like particles with intrinsic magnetic moments, we show that the physical phenomena underlying the Breit equation and its recent extension are mainly two well-known classical phenomena : i) the interaction of the magnetic moment of the constituent particles with the magnetic field they experience in their rest frame; ii) the Thomas precession of the spins of the accelerated particles.

Journal de physiqueJan 1, 19777 citations

Relativistic dynamics of resonantly driven classical and quantum systems

P. J. Peverly, Rafael Wagner, Qi-Ping Su +1 more

APSMay 1, 20010 citations

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of rotator, has been calculated for S_dcr. For investigation of S_D and construction of S_dc one uses new dynamic methods: dynamic quantization and dynamic disquantization. These relativistic pure dynamic procedures do not use principles of quantum mechanics (QM). They generalize and replace conventional quantization and transition to classical approximation. Totality of these methods forms the model conception of quantum phenomena (MCQP). Technique of MCQP is more subtle and effective, than conventional methods of QM. MCQP relates to conventional QM, much as the statistical physics relates to thermodynamics.