Many-body vacuum polarization

The procedures for many-body perturbation calculations (MBPT) for atomic and molecular systems are nowadays very well developed, and the dominating electrostatic as well as magnetic perturbations can be taken to essentially all orders of perturbation theory (see, for instance, [1]). Less pronounced, but in many cases still quite significant, are the quantum electrodynamical (QED) perturbations—retardation, virtual pairs, electron self-energy, vacuum polarization and vertex correction. Sophisticated procedures for their evaluation have also been developed, but for practical reasons such calculations are prohibitive beyond second order (two-photon exchange). Pure QED effects beyond that level can be expected to be very small, but the combination of QED and electrostatic perturbations (electron correlation) can be significant. However, none of the previously existing methods for MBPT or QED calculations is suited for this type of calculation. 

Polarization interactions for atoms and small molecules or functional groups are much weaker than the other interactions listed above. For example, in vacuum the attractive energy between two methyl groups is only about 0.15 kcal/mol (0.6 kJ/mol) at a separation of 0.4 nm. However, polarization interactions are additive, so that for large bodies with many individual polarization interactions (e.g., a protein binding a large substrate molecule) the overall contribution may be 10 to 20 kcal/mol (40-80 kJ/mol). Furthermore, these interactions will be present for both nonpolar and polar (even ionic) groups. 

There are many types of noise. Every physical body not at absolute zero temperature emits electromagnetic energy at all frequencies, by virtue of the thermal energy the body possesses. This type of radiation is called thermal noise radiation. Johnson noise is a result of random motion of electrons within a resistor semiconductor noise occurs in transistors shot noise occurs in both transmitter and receiver vacuum tubes as a result of random fluctuations in electron flow. These fluctuations are controlled by a random mechanism and, thus, in time are random processes described by the Gaussian distribution. The signal is random in phase and polarization, and usually are broad in frequency bandwidth. The average noise power is given by... 

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