Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

Kim, Sang Pyo

doi:10.1016/j.aop.2014.08.012

Cited by 7 publications

(5 citation statements)

References 34 publications

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“…IV. Interestingly, the change of eigenspinors is analogous to the change of Landau levels of a charged scalar in a homogeneous, time-dependent magnetic field along a fixed direction, in which the rate of the vector of all Landau levels is also given by a coupling matrix [29,39]. It should be noted that the eigenspinors of an electron also change in a rotating magnetic field.…”

Section: Two-component Spinor Formulation In Rotating Electric Fieldmentioning

confidence: 99%

“…[38]). In scalar QED, the Klein-Gordon equation in a time-dependent magnetic field along a fixed direction has Landau states that continuously make transitions among different Landau states [29,39].…”

Section: Introductionmentioning

confidence: 99%

“…The rate of change of each Landau level to neighboring ones is determined by the derivative of the logarithm of the magnetic field, and the Cauchy initial value problem for the evolution of Landau states can be formulated in terms of the transition matrix of Landau levels and energies [29]. In the second quantized formulation of scalar QED, the Hamiltonian is equivalent to time-dependent oscillators with the time-dependent Landau energies, which are coupled by the coupling matrix [39]. In a similar manner, the rate of the direction change of a two-dimensional, time-dependent electric field determines the transition between eigenspinors.…”

Section: Introductionmentioning

confidence: 99%

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Spin Resonance Effect on Pair Production in Rotating Electric Fields

Kim¹

2016

Preprint

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We advance a new analytical method for the Dirac equation in two-dimensional, homogeneous, time-dependent electric fields, which expresses the Cauchy problem of the two-component spinor and its derivative as the time-ordered integral of the transition rate of the time-dependent eigenspinors and the time-dependent energy eigenvalues. The in-vacuum at later times evolves from that at the past infinity and continuously make transitions between eigenspinors and between positive and negative frequencies of the time-dependent energy eigenvalues. The production of electron and positron pairs is given by the coefficient of the negative frequency at the future infinity which evolves from the positive frequency at the past infinity. In the adiabatic case when the time scale for the rotation of eigenspinors and energy eigenvalues is much longer than the electron Compton time, we find the spin-resonance effect on the pair production, which is simply determined by the spin rotation, the pair production and the continuous transmission coefficients between the energy eigenvalues without the change of spin states.

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Section: Two-component Spinor Formulation In Rotating Electric Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spin Resonance Effect on Pair Production in Rotating Electric Fields

Kim¹

2016

Preprint

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“…Following Ref. [19], we may introduce the linear quantum invariant operators for particles and antiparticles, respectively,…”

Section: Real-time Evolutionmentioning

confidence: 99%

Geometric origin of pair production by electric field in de sitter space

Kim

2014

Gravit. Cosmol.

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The particle production in a de Sitter space provides an interesting model to understand the curvature effect on Schwinger pair production by a constant electric field or Schwinger mechanism on the de Sitter radiation. For that purpose, we employ the recently introduced complex analysis method, in which the quantum evolution in the complex time explains the pair production via the geometric transition amplitude and gives the pair-production rate as the contour integral. We compare the result by the contour integral with that of the phase-integral method.

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“…The Lorentz's pendulum with a varying length is a simple time-dependent oscillator, whose classical adiabatic invariants were investigated by Chandrasekhar [1] and Littlewood [2]. Each Fourier mode of a massive linear field in a homogeneous, time-dependent spacetime [3] or a charged scalar field in a homogeneous, time-dependent electric field is characterized by a harmonic oscillator with a time-dependent frequency [4]. The charged scalar field in a time-dependent, homogeneous magnetic field is equivalent to that of an infinite system of coupled oscillators for Landau levels [5].…”

Section: Introductionmentioning

confidence: 99%

Construction of exact Ermakov-Pinney solutions and time-dependent quantum oscillators

Kim

2016

Journal of the Korean Physical Society

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The harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schrödinger equation, which are determined by any two independent solutions to the classical equation of motion. Ermakov and Pinney have shown that a general solution to the time-dependent oscillator with an inverse cubic term can be expressed in terms of two independent solutions to the time-dependent oscillator. We explore the connection between linear quantum invariants and the Ermakov-Pinney solution for the time-dependent harmonic oscillator. We advance a novel method to construct Ermakov-Pinney solutions to a class of time-dependent oscillators and the wave functions for the time-dependent Schrödinger equation. We further show that the first and the second Pöschl-Teller potentials belong to a special class of exact time-dependent oscillators. A perturbation method is proposed for any slowly-varying time-dependent frequency.

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Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

Cited by 7 publications

References 34 publications

Spin Resonance Effect on Pair Production in Rotating Electric Fields

Spin Resonance Effect on Pair Production in Rotating Electric Fields

Geometric origin of pair production by electric field in de sitter space

Construction of exact Ermakov-Pinney solutions and time-dependent quantum oscillators

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