Self-Adjointness of the Pauli-Fierz Hamiltonian for Arbitrary Values of Coupling Constants

Hiroshima, Fumio

doi:10.1007/s00023-002-8615-8

Cited by 87 publications

(87 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These quantum-optical situations also naturally restrict the available photonic modes. Such physical situations are then well described by models of nonrelativistic particles interacting with a quantized electromagnetic field, such as the Pauli-Fierz Hamiltonian (see, e.g., [74,75]) or the Nelson model [70,71]. In the lowest order of approximations we find the situation of a two-level system interacting with one photonic mode, similar to the one presented in Sec.…”

Section: Nonrelativistic Qedftsupporting

confidence: 66%

See 1 more Smart Citation

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

et al. 2014

View full text Add to dashboard Cite

In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

show abstract

Section: Nonrelativistic Qedftsupporting

confidence: 66%

“…makes the coupled Pauli-Fierz Hamiltonian self-adjoint without any further renormalization procedure [75]. Such a restriction is assumed in the following.…”

Section: Qedft For Approximate Nonrelativistic Theoriesmentioning

confidence: 99%

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

et al. 2014

View full text Add to dashboard Cite

show abstract

“…[12,46]). The stability of the system under consideration is equivalent to the statement of existence of the ground state of H SM g , i.e.…”

Section: Introductionmentioning

confidence: 99%

Ground State and Resonances in the Standard Model of the Non-Relativistic QED

Sigal

2009

J Stat Phys

View full text Add to dashboard Cite

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces. I IntroductionProblem and outline of the results. Non-relativistic quantum electro-dynamics (QED) describes the processes of emission and absorption of radiation by systems of matter, such as atoms and molecules, as well as other processes arising from interaction of the quantized electro-magnetic field with non-relativistic matter. The mathematical framework of this theory is well established. It is given in terms of the time-dependent Schrödinger equation,

show abstract

“…The second inequality is trivial if lim inf j→∞ Ψ j 2 = 0 and otherwise follows from our assumption (18). This proves that Ψ j converges strongly to zero along a subsequence, which implies that Φ m = 1.…”

Section: Theorem (Existence Of Ground State) Assume That For Some Fimentioning

confidence: 70%

“…Acknowledgment: We thank Professor Fumio Hiroshima for a useful correspondence concerning equation (53) and for sending us his preprint [18].…”

Section: Introductionmentioning

confidence: 99%

Ground states in non-relativistic quantum electrodynamics

Griesemer

Lieb

Loss³

The Stability of Matter: From Atoms to Stars

View full text Add to dashboard Cite

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state -one that minimizes the energy and satisfies the Schrödinger equation. We prove quite generally that this state exists for all values of the fine-structure constant and ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions.

show abstract

Self-Adjointness of the Pauli-Fierz Hamiltonian for Arbitrary Values of Coupling Constants

Cited by 87 publications

References 28 publications

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Ground State and Resonances in the Standard Model of the Non-Relativistic QED

Ground states in non-relativistic quantum electrodynamics

Contact Info

Product

Resources

About