Functional integral approach to semi-relativistic Pauli–Fierz models

Hiroshima, Fumio

doi:10.1016/j.aim.2014.02.015

Cited by 14 publications

(14 citation statements)

References 37 publications

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“…An exhaustive presentation of the earlier results can be found in [27]. This book also contains detailed discussions of Feynman-Kac formulas in semi-relativistic QED (see also the recent article [21]), as well as results and references on path integral representations for related models with paths running through the infinite-dimensional state space of the radiation field. Remark 1.4 (1) For the standard model of NRQED without spin, the first identity in (1.13) is due to [15].…”

Section: Feynman-kac Formulas and Applications To Spectral Theorymentioning

confidence: 99%

Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields

Güneysu

Matte

Møller

2016

Probab. Theory Relat. Fields

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We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant systems. In particular, we prove the existence of a stochastic flow satisfying the strong Markov property and the Feller property. To this end we employ an explicit solution ansatz. In the matrix-valued case, i.e., if the electron spin is taken into account, it is given by a series of operator-valued time-ordered integrals, whose integrands are factorized into annihilation, preservation, creation, and scalar parts. The Feynman-Kac formula implied by these results is new in the matrix-valued case. Furthermore, we discuss stochastic differential equations and Feynman-Kac representations for an operator-valued integral kernel of the semi-group. As a byproduct we obtain analogous results for Nelson's model.

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Section: Feynman-kac Formulas and Applications To Spectral Theorymentioning

confidence: 99%

Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields

Güneysu

Matte

Møller

2016

Probab. Theory Relat. Fields

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“…This is unfortunately not applicable for arbitrary values of α. By functional integration however it is proven in [Hir14] that H is essentially self-adjoint on D for M > 0, which is due to show that e −tH D ⊂ D. Then the main purpose of this paper is to show the self-adjointness of H on D for arbitrary values of coupling constants (in this paper α is absorbed in the prefactor of ϕ), and not only for V ∈ V rel but also for V ∈ V conf . This can be achieved by proving the nontrivial bound (2.2) mentioned below, which bound implies the closedness of H⌈ D .…”

Section: Resultsmentioning

confidence: 99%

“…Essential self-adjointness of H is shown in [Hir14,Theorem 4.5] by a path measure approach under some conditions. We furthermore show its self-adjointness under weaker conditions in this paper.…”

Section: Fundamental Factsmentioning

confidence: 99%

Self-adjointness of the semi-relativistic Pauli–Fierz Hamiltonian

Hidaka

Hiroshima

2015

Rev. Math. Phys.

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The spinless semi-relativistic Pauli-Fierz Hamiltonianin quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, H f the free hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential selfadjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semirelativistic Pauli-Fierz model with a fixed total momentum P ∈ R d :is also proven for arbitrary P .

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“…We will next combine all these ingredients into one general framework, which will be a generalized form the Pauli-Fierz Hamiltonian [64]. For completeness, we note that semi-relativistic extensions of the Pauli-Fierz Hamiltonian exist [70][71][72], but as starting point we stay within the non-relativistic limit for the matter subsystem. This limit is already enough for a vast set of applications.…”

Section: A Relativistic Wave Equationsmentioning

confidence: 99%

Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and nano-optical applications

Jestädt

Ruggenthaler

Oliveira

et al. 2019

Advances in Physics

152

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We present the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli-Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit for the effective nuclei the formalism reduces to coupled Ehrenfest-Maxwell-Pauli-Kohn-Sham equations. We present an implementation of the approach in the real-space real-time code Octopus. For the implementation we use the Riemann-Silberstein formulation of classical electrodynamics and rewrite Maxwell's equations in Schrödinger form. This allows us to use existing time-evolution algorithms developed for quantum-mechanical systems also for Maxwell's equations. We introduce a predictorcorrector scheme and show how to couple the Riemann-Silberstein time-evolution of the electromagnetic fields self-consistently to the time-evolution of the electrons and nuclei. Furthermore, the Riemann-Silberstein approach allows to seamlessly combine macroscopic dielectric media with a microscopic coupling to matter currents. For an efficient absorption of outgoing electromagnetic waves, we present a perfectly matched layer for the Riemann-Silberstein vector. We introduce the concept of electromagnetic detectors, which allow to measure outgoing radiation in the far field and provide a direct way to record various spectroscopies. We present a multi-scale approach in space and time which allows to deal with the different length-scales of light and matter for a multitude of applications. We apply the approach to laser-induced plasmon excitation in a nanoplasmonic dimer system. We find that the self-consistent coupling of light and matter leads to significant local field effects which can not be captured with the conventional light-matter forward coupling. For our nanoplasmonic example we show that the self-consistent foward-backward coupling leads to changes in observables which are larger than the difference between local density and gradient corrected approximations for the exchange correlation functional. In addition, in our example we observe harmonic generation which appears only beyond the dipole approximation and can be directly observed in the outgoing electromagnetic waves on the simulation grid. The self-consistent coupling of the electromagnetic fields to the ion motion reveals significant energy transfer from the electromagnetic fields to matter on the scale of a few tens of femtoseconds. Overall, our approach is ideally suited for applications in nano-optics, nano-plasmonics, (photo) electrocatalysis, light-matter coupling in 2D materials, cases where laser pulses carry orbital angular momentum, or light-tailored chemical reactions in optical cavities to name but ...

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Functional integral approach to semi-relativistic Pauli–Fierz models

Cited by 14 publications

References 37 publications

Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields

Stochastic differential equations for models of non-relativistic matter interacting with quantized radiation fields

Self-adjointness of the semi-relativistic Pauli–Fierz Hamiltonian

Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and nano-optical applications

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