Field photon

It-from-bit embodies the central notion that every it - that is, every aspect of reality electrons, protons, photons, fields of force, or even the what we call space-time itself - is in the deepest sense a derivative of experimentally deduced answers to yes/no questions that is, to bits. If we allow ourselves for a moment to go back to the roots of what it is that we by convention call reality, we see that it is something that is literally defined by a particular sequence of yes/no responses elicited from either a mechanical or (our own biological) sensory apparatus in other words, reality s origin is fundamentally information-theoretic. 

Thus the current operator indeed transforms like a vector. This must be the case in order that the equation Qdu(x) = ju(x) transform properly, assuming the transformation property (11-267) for Au(x). We now inquire briefly into tike question of the uniqueness of the U(ia) operator, in particular into the question of the phase associated with the fermion field operator. Note that the phase of the photon field operator is uniquely determined (Eq. (11-267)) by the fact that An is a hermitian field which commutes with the total charge operator Q. The negaton-positon field operator on the other hand does not commute with the total charge operator, in fact... 

Consider, by contrast, a two-color experiment where the continuum is accessed by two laser fields with a well defined relative phase, a and , . A schematic illustration of the experiment envisioned is provided in Fig. 1 a, where we consider the specific case of excitation with one- and three-photon fields of... 

In this section we first (Section IV A) derive a formal expression for the channel phase, applicable to a general, isolated molecule experiment. Of particular interest are bound-free experiments where the continuum can be accessed via both a direct and a resonance-mediated process, since these scenarios give rise to rich structure of 8 ( ), and since they have been the topic of most experiments on the phase problem. In Section IVB we focus specifically on the case considered in Section III, where the two excitation pathways are one- and three-photon fields of equal total photon energy. We note the form of 8 (E) = 813(E) in this case and reformulate it in terms of physical parameters. Section IVC considers several limiting cases of 813 that allow useful insight into the physical processes that determine its energy dependence. In the concluding subsection of Section V we note briefly the modifications of the theory that are introduced in the presence of a dissipative environment. 

We follow the convention adopted by the literature on coherent control via the one- versus three-photon excitation method, where the frequency of the three-photon field is denoted coi and that of the one-photon field is denoted C03. 

The reactants in equation (72) may be a normal molecule or a photon field, e.g. R2=hv, where h is Planck s constant and v is the frequency of the photon. The complex made by the photon and the molecule may or may not activate the interconversion space for a given photodissociation process. 

Grimes DM Grimes, CA (2006) A unique electromagnetic photon field using Feynman s electron characteristics and Maxwell s equations. J Gomputational and Theoretical Nanoscience 3 649-663... 

The regimes of the parameters (191) and (193) are now subdivided with respect to overlapping of the individual photon fields ... 

If the individual wavepacket solutions of the present theory could be superimposed, this would imply that the field vectors become multivalued at every point inside the photon beam. The individual photon fields would then have to cancel each other. This implies that the axisymmetric small-scale wavepacket solution of Section VII does not apply and cannot satisfy the basic Eqs. (l)-(8) in the case of a nearly plane (one-dimensional) and broad photon-dense beam configuration. 

From this mutual cancellation of the individual photon fields an apparently paradoxical conclusion would follow, namely, that the beam energy gradually vanishes as 0 decreases beyond 0 To preserve the energy... 

Radiationless transitions are postulated to occur as the result of interactions with the phonon field. The result of this treatment, which follows closely the photon field interaction given for radiative transitions, yields an expression for the spontaneous radiationless transition rate... 

We note several very general formulations of the problem. A striking example of this is Ya.B. s 1967 paper [14 ], in which he considers the possibility of a theory in which the bare photon field is absent, while the observed electromagnetic field is created entirely by quantum fluctuations of a vacuum. This bold idea, which extends to electrodynamics an earlier idea about gravitational interaction (in part, under the influence of Ya.B. s papers on the cosmological constant), has not yet been either proved or disproved. However, both ideas have elicited lively discussion in the scientific literature. 

The two important consequences of the third-order optical nonlinearities represented by x are third-harmonic generation and intensity dependence of the refractive index. Third-harmonic generation (THG) describes the process in which an incident photon field of frequency (oj) generates, through nonlinear polarization in the medium, a coherent optical field at 3a>. Through x interaction, the refractive index of the nonlinear medium is given as n = nQ+n I where n describes intensity dependence of the refractive index ana I is the instantaneous intensity of the laser pulse. There is no symmetry restriction on the third-order processes which can occur in all media including air. 

Our derivation of Equations (2.1) and (2.2) follows very closely the presentation of Loudon (1983 ch.2). The basic concept is to describe the molecule quantum mechanically, the photon field classically, and to treat the interaction between them in first-order perturbation theory. 

Figure 19.19 Left side Variation of the photoluminescence intensity E (b) of the PEG-functionalized Au and CdTe nanoparticles depending on the temperature (a) (c) shows the calculated photon-field enhancement factor P of the CdTe nanoparticles as a function of time. Right side Schematic representation of a dynamic nanothermometer based on a nanoparticle superstructure. This superstructure consists of two types of nanoparticles (gold and CdTe) connected by polymeric spacers.118 (Reprinted with permission from J. Lee et al., Angew. Chem. Int. Ed., 2005, 44, 7439-7442. Copyright Wiley-VCH Verlag GmbH Co. KGaA.)...

There are many cases in which the molecular Hamiltonian and the interactions with the photon fields are not completely known. For many isolated polyatomic molecules or for molecules in condensed phases, for ex-... 

Here, a is the Dirac matrix, E is a certain energy parameter, and Ho is the Hamiltonian of an isolated atom whose eigenvalues are denoted by er Ho r) = er r). Equation (4) can be readily inferred (see paper of V. Yakhontov in this volume) by taking into account the relativistic atom-photon field interaction... 

In the dipole approximation, the relativistic atom-photon field interaction V(r,t) takes the form [4]... 

Consider a resonance case > = >. For the global system, there are two states 0) nB = 1) and 11)1 = 0) with equal energy note the qualitative difference for 0) nB = 1) the energy is in the field while l) nB = 0), energy localizes at the material system the photon field has not available energy (it is "empty"). 

Retain the two-state model idea for the photon field and define the operator... 

From the perspective of a photon field, the interaction information embedded in the function A(Ci,C2, yi,y2, (x,y l), (x,y 2)) would imprint at both channels. 

The second line corresponds to a nonseparable photon state, whereas the first line would correspond to a direct product state between material system base state and photon fields. It is the sum that describes an entangled state. 

The latter describes entanglement of the zero-point energy state with the "excited" state sustained by a material system the former corresponds to ground state entanglement with a photon field. 

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