Causality problems for Fermi’s two-atom system

Hegerfeldt, Gerhard C.

doi:10.1103/physrevlett.72.596

Cited by 195 publications

(240 citation statements)

References 18 publications

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“…The existence of some (R-independent) probability for the acceptor to be excited at t < R/c, goes along with the Hegerfeldt theorem [46] stating that the initially unexcited atom (acceptor) starts to move out of the ground state immediately. As pointed out by Milonni and co-authors [49]:…”

Section: B Dynamics Of Energy Transfermentioning

confidence: 99%

Quantum Electrodynamics of Resonance Energy Transfer

Juzeliūnas¹,

Andrews²

2000

Advances in Chemical Physics

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Section: B Dynamics Of Energy Transfermentioning

confidence: 99%

Quantum Electrodynamics of Resonance Energy Transfer

Juzeliūnas¹,

Andrews²

2000

Advances in Chemical Physics

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“…[28] For every Hermitian and semi-bounded Hamiltonian H, either T r(Λ(t)ρ) = T r(Λρ(t)) = 0 ∀t ∈ R or T r(Λ(t)ρ) = T r(Λρ(t)) > 0 ∀t ∈ R except on a set of Lebesgue measure zero.…”

Section: Fundamental Theorems Of Qmmentioning

confidence: 99%

Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics

Marcucci

Conti

2016

Phys. Rev. A

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It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, as the Hamiltonian. Resonances, i.e. states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism, based on the so-called Rigged Hilbert Space (RHS). In the RHS, the states with complex energy are denoted as Gamow Vectors (GV), and they model decay processes.We study GV of the Reversed Harmonic Oscillator (RHO), and we analytically and numerically investigate the unstable evolution of wave packets. We introduce the background function to study initial data not composed only by a summation of GV and we analyse different wave packets belonging to specific function spaces. Our work furnishes support to the idea that irreversible wave propagations can be investigated using Rigged Hilbert Space Quantum Mechanics and provides insights for the experimental investigation of irreversible dynamics.

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“…Ds, 42.50.Ct One striking aspect of quantum mechanics is the existence of nonlocal correlations between spatially separated objects [1,2]. This might in principle give rise to nonlocal observable effects, although the possibility of using such correlations for transmitting superluminal signals has been investigated in many different frameworks with negative conclusions [3].…”

mentioning

confidence: 99%

“…is the free-field operator at time t, while E (1) ℓ (r C , t) and E (2) ℓ (r C , t) are the source-dependent contributions to the electric field operator. The presence of the θ functions expresses the causal behaviour of the source electromagnetic field operator.…”

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confidence: 99%

Nonlocal Properties of Dynamical Three-Body Casimir-Polder Forces

2007

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We consider the three-body Casimir-Polder interaction between three atoms during their dynamical self-dressing. We show that the time-dependent three-body Casimir-Polder interaction energy displays nonlocal features related to quantum properties of the electromagnetic field and to the nonlocality of spatial field correlations. We discuss the measurability of this intriguing phenomenon and its relation with the usual concept of stationary three-body forces.PACS numbers: 12.20. Ds, 42.50.Ct One striking aspect of quantum mechanics is the existence of nonlocal correlations between spatially separated objects [1,2]. This might in principle give rise to nonlocal observable effects, although the possibility of using such correlations for transmitting superluminal signals has been investigated in many different frameworks with negative conclusions [3]. Quantum fields display nonlocal correlations too [4] and it is therefore relevant to investigate if these correlations have observable consequences. In this letter we discuss observable manifestations of nonlocality of quantum electromagnetic fields in dynamical three-body Casimir-Polder forces between three atoms; in the present context they arise from nonlocal spatial correlations of the electric field in the vacuum state during the dynamical self-dressing of the atoms. The physical basis of our work is that Casimir-Polder (CP) long-range interatomic interactions are directly related to the electric field correlations evaluated at the positions of the atoms, both for two-and many-body components [5,6,7,8]. In the case of three atoms, in which we are mainly interested, the CP potential energy is related to the electric field correlation at the position of two atoms, dressed by the third. In the dynamical (i.e. time-dependent) case, for example during the selfdressing or the spontaneous decay of one of the three atoms, spatial field correlations have a nonlocal evolution and we investigate if this has observable consequences in the three-body Casimir-Polder interaction between the three atoms. On the other hand, three-body CasimirPolder forces can be also obtained, from different physical considerations, as the interaction of one atom with the field fluctuations generated by the other two atoms [9]. In a dynamical situation, field fluctuations are expected to propagate causally, and thus the interaction with the third atom is not expected to show nonlocal features.In this paper we compare in detail results from the two approaches outlined above, and show that apparently contradictory conclusions derive from the fact that the two approaches consider two different, albeit related, interaction energies. Also, our results suggest that what is * Electronic address: roberto.passante@fisica.unipa.it usually considered as the three-body energy, as obtained from the energy shift of the system due to the atomfield interaction, needs a careful definition from the point of view of measurement theory. We wish to point out that Casimir forces in non-equilibrium situations have rece...

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Causality problems for Fermi’s two-atom system

Cited by 195 publications

References 18 publications

Quantum Electrodynamics of Resonance Energy Transfer

Quantum Electrodynamics of Resonance Energy Transfer

Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics

Nonlocal Properties of Dynamical Three-Body Casimir-Polder Forces

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