Vacuum fluctuation

Alternatively, one can drop the E0IV factor in (11-121) and, whenever computing any matrix element, omit from consideration the contribution from disconnected vacuum fluctuation diagrams. We shall do so hereafter. 

The main source of noise of such a heterodyne detector is the photon noise that takes place at the splitting of the local oscillator. Quantum physicists see this noise as originating from vacuum fluctuation on the input arm. This gives directly the spectral density of noise at input hv/2. 

This type of process is missing from U(l) quantum field theory [6] the B(3> field produces quantum vortices [17] that interact with electrons and other charged particles. The vortices are quantized states and exist as fluctuations in the QED vacuum, fluctuations that are associated, not with an E(3) field, but with the = E(1> fields ... 

The parameter is the damping constant, and (n) is the mean number of reservoir photons. The quantum theory of damping assumes that the reservoir spectrum is flat, so the mean number of reservoir oscillators (n) = ( (O)bj(O j) = ( (1 / ) — 1) 1 in the yth mode is independent of j. Thus the reservoir oscillators form a thermal system. The case ( ) = 0 corresponds to vacuum fluctuations (zero-temperature heat bath). It is convenient to consider the quantum dynamics of the system (56)-(59) in the interaction picture. Then the master equation for the density operator p is given by... 

Fig. 5.2 shows the dependence of n on v for T = 300 K, again with both frequency (Hz) and wavenumber (cm-1) used as abscissae. It is useful to recall that at 300 K, kTIh 6 x 1012 Hz or kT/hc 200 cm-1. This point is apparent in Fig. 5.2, since n = 1 at A-1 = 200 cm-1. Since the vacuum fluctuations, which lead to spontaneous emission, are given by n = 1/2, black body radiation at frequencies greater than kT/hn, where n 1, does not lead to significant effects. For an atom in its ground state with transitions at 104 cm-1, black body induced transitions are unimportant, since n 1. However, for a Rydberg state with transitions at 10 cm-1, where n 10, the black body induced transition rates can... 

The model is oversimplified in the sense that we have not attempted to specify what effects are incorporated in u. We will, however, consider the main effects from the vacuum fluctuations as well as other possible perturbations needed to produce the degeneracy above as well as, if necessary, considering the weak energy dependence in the Hamiltonian referred to in Eq. (11). To see how the CPT theorem affects our formulation we note that our zero order problem is an irreducible representation of... 

Conventionally, the evaluation of bound-state QED corrections is made tractable by including the vacuum fluctuations in several steps. The corrections thus calculated are called radiative corrections, and their evaluation can be made by making two expansions. The first is in powers of (a/7r) and denotes the number of photon propagator loops present. The second is in the number of photon exchanges with the nucleus and is in powers of (Zot), where Z is the nuclear charge. The expression in equation 1 shows the first two terms of the (o/tt) expansion for the case of hydrogenic S-states, i.e. up to two photon loops. In this expression the second expansion has not yet been made and the (Za) dependence is still contained within the functions F and H. 

We can think of electromagnetic modes between the two bodies as the fluctuations that remain as tiny deviations from the outer turmoil. The extent of the quelling is, obviously, in proportion to the material-absorption spectra. So we can think of absorption frequencies in two ways those at which the charges naturally dance those at which charge polarization quells the vacuum fluctuations and stills the space between the surfaces.13... 

We have speculated that the vacuum fluctuation of space-time is a... 

Tryon, Edward. Is the Universe a Vacuum Fluctuation Nature 246 (1973) 396-397. Undenfriend, S, B. Witkop, B. Redfield, andH. Weissbach. Studies with Reversible Inhibitors of Monoamine Oxidase Harmaline and Related Compounds. 

The very-short-time behavior of micro-cavity quantum electrodynamics for characterizing micro-laser arrays for high speed applications, where highly nonlinear coupling of the vacuum fluctuations and the atomic polarizations exist, requires the full time-dependent quantum treatment discussed here. 

It should be mentioned that a sharp borderline between low volatility and high volatility fractions does not exist. There is a continuous change that is sensitive to temperature and vacuum fluctuations/uncertainties in a vacuum oven. Therefore, based on our observations, the amount of low volatile" fractions might be up to 15 to 20% greater than the values shown if conditions were such that the maximum amount of "low volatility tars was produced. 

Comparing Eq. (110) with Eq. (66), we find that both equations have extra terms (the e or e terms) which make the solutions oscillatory, but the physical reason for oscillations is different in both cases. In Eq. (66) different from zero e comes from the nonzero initial value of the second-harmonic mode intensity, while in Eq. (110) the nonzero value of e comes from the quantum noise. We can interpret this fact in the following way. It is the spontaneous emission of photons, or vacuum fluctuations of the second harmonic mode, that contribute to the nonzero value of the initial intensity of the second harmonic mode and lead to the periodic evolution. This means that the very small quantum fluctuations can cause macroscopic effects, such as quantum-noise-induced macroscopic revivals [38], in the nonlinear process of second-harmonic generation. 

Much more interesting and important result can be obtained from the consideration of the spatial properties of the vacuum fluctuations. The simplest example is provided by the calculation of vacuum average of the squared electric field strength [58,59]... 

One can easily see that each term in the sums in Eqs. (100) and (101) has different normalization, while in Eqs. (102) and (103) all the terms have the same normalization factor related to our choice of the constant K in (82) and (83). In addition, Eq. (103) contains an extra term proportional to (Cr ). This term comes from the vacuum fluctuations related to the mode m = 0. This causes a striking difference when one of the modes m I is in the quantum... 

In contrast to (143), this is a diagonal matrix independent of the spatial variables. Hence, in exactly the same way as with the zero-point oscillations of energy density, the vacuum fluctuations of polarization in empty space has the global nature, while those in the presence of the singular point manifest certain spatial inhomogeneity. 

It is also seen that the vacuum fluctuations of the field with m =/= m contribute to the quantum noise of polarization of the mode with given m. Similar results can be obtained for the position dependent Stokes operators obtained from (132) by canonical quantization. 

The j H(S> associated with each radiation mode is the energy associated with the familiar vacuum fluctuations, the origin of spontaneous emission and self-energy corrections. The eigenstates m(k, X)) of Hmd are number states states that more closely model the coherence and other properties of laser light will be introduced later. 

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