Operational dynamical modeling of spin 1/2 relativistic particles

Cabrera, Renán; Campos, Andre G.; Rabitz, Herschel; Bondar, Denys I.

doi:10.1140/epjst/e2018-800075-7

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The Cif As a Classical Limit2

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Cited by 5 publications

(3 citation statements)

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“…That is, both spinors must have opposite velocities. Hence, for a negative energy spinor, the following substitutions must be made in (42) [23]…”

Section: Free Particlesmentioning

confidence: 99%

Construction of Dirac spinors for electron vortex beams in background electromagnetic fields

Campos,

Hatsagortsyan,

Keitel

2020

Preprint

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“…That is, both spinors must have opposite velocities. Hence, for a negative energy spinor, the following substitutions must be made in (42) [23]…”

Section: Free Particlesmentioning

confidence: 99%

Construction of Dirac spinors for electron vortex beams in background electromagnetic fields

Campos,

Hatsagortsyan,

Keitel

2020

Preprint

Self Cite

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“…Taking the classical limit of this (and indeed any) system is by no means straightforward (see, e.g., [74]), particularly given the stochastic term correlations also involve the factor of which formally must be limited to zero. As we shall see in the next section, difficulties arise from this which require the CIF to resolve.…”

Section: The Cif As a Classical Limitmentioning

confidence: 99%

“…This becomes exact in the → 0 limit. Note that this approach implicitly adopts the definition of the classical limit as that in which observable operators commute [74]. Integration of the first term in the effective action by parts yields:…”

Section: B Alternative Sle Classical Limitmentioning

confidence: 99%

How to Win Friends and Influence Functionals: Deducing Stochasticity From Deterministic Dynamics

McCaul¹,

Bondar²

2019

Preprint

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The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. Using the Koopman von-Neumann formulation of classical mechanics, we present here the Classical Influence Functional (CIF) -a method to bridge the gap between deterministic and stochastic dynamics, and unify the formalisms describing these disparate behaviours. Using this new technique, we demonstrate how irreversible behaviour arises generically from the reduced microscopic dynamics of a system-environment amalgam. The classical influence functional is then used to rigorously derive a generalised Langevin equation from a microscopic Hamiltonian. In this method stochastic terms are not identified heuristically, but instead arise from an exact mapping only available in the path-integral formalism of classical mechanics. As a consequence of the CIF, we are also able to show that the proper classical limit of stochastic quantum dynamics corresponds to this Langevin equation, providing a further unifying link to quantum theories. These derivations highlight the utility of CIFs, and its potential as a tool in both fundamental and applied research.

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