Spontaneous damping

Thus, the condition V 2 = /1 1I2 for suppression of spontaneous emission from the antisymmetric state is valid for identical as well as nonidentical atoms, whereas the coherent interaction between the superpositions appears only for nonidentical atoms with different transition frequencies and/or spontaneous damping rates. 

In solid form, Mg is difficult to ignite because heat is conducted rapidly away from the source of ignition it must be heated above its mp before it will bum. However, in finely divided form it may be ignited by a spark dr the flame of a, match. Mg fires do not flare up violently unless there is moisture present. Therefore it must be kept away from w, moisture, etc. It m y. be ignited by a spark, match flame, or even spontaneously when the Mg is finely divided and damp, particularly with w-oil emulsion. Also, Mg reacts with moisture, acids, etc to evolve H2 which is a highly dangerous fire arid explosion hazard (Ref 23)... 

In damp air, materials with standard reduction potentials less than 0.88 V oxidize spontaneously. Atmospheric O2 easily oxidizes iron and aluminum, the most important structural metals ... 

White phosphorus has an autoignition temperature only shghtly above ambient, dispersed it will soon heat itself to that by the slow oxidation responsible for its glow. Red is not spontaneously combustible, however if it does catch fire white will be produced, so that the fire, once extinguished, may spontaneously re-ignite. Both can produce phosphine, among other products, by slow reaction with water. Sealed containers of damp phosphorus (white is often stored under water) may pressurise with highly toxic, pyrophoric, gas mixtures [1]. 

It is noted that all systems in turmoil tend to subside spontaneously to simple states, independent of previous history. It happens when the effects of previously applied external influences damp out and the systems evolve toward states in which their properties are determined by intrinsic factors only. They are called equilibrium states. Experience shows that all equilibrium states are macroscopically completely defined by the internal energy U, the volume V, and the mole numbers Nj of all chemical components. 

Everyone knows damp clothes become dry when hung outside on the washing line. Any residual water is lost by evaporation from the cloth. In fact, moisture evaporates even if the damp clothes hang limp in the absence of a breeze. The water spontaneously leaves the fabric to effect the physicochemical process H20(i) —> H20(g). 

In parallel with the studies described above, which concern perfectly deterministic equations of evolution, it appeared necessary to complete the theory by studying the spontaneous fluctuations. Near equilibrium, any deviation is rapidly damped but near a bifurcation point, a fluctuation may may lead the system across the barrier. The fluctuation is then stabilized, or even amplified this is the origin of the phenomenon which Prigogine liked calling creation of order through fluctuations. More specifically, one witnesses in this way a step toward self-organization. 

Under physiological conditions, phosphate esters of Ser and Thr residues are stable and only show a low rate of spontaneous hydrolysis. Thus, the cell requires its own tools for regulated cleavage of phosphate residues, to terminate and damp signals mediated by protein phosphorylation. This role is performed by specific protein phosphatases. 

Find the equation for its average density matrix and show that for t-> oo both levels are equally occupied. Thus the temperature tends to infinity, owing to the fact that no damping by spontaneous emission is included in (2.20). 

Entropy production during chemical change has been interpreted [7] as the result of resistance, experienced by electrons, accelerated in the vacuum. The concept is illustrated by the initiation of chemical interaction in a sample of identical atoms subject to uniform compression. Reaction commences when the atoms, compacted into a symmetrical array, are further activated into the valence state as each atom releases an electron. The quantum potentials of individual atoms coalesce spontaneously into a common potential field of non-local intramolecular interaction. The redistribution of valence electrons from an atomic to a metallic stationary state lowers the potential energy, apparently without loss. However, the release of excess energy, amounting to Au = fivai — fimet per atom, into the environment, requires the acceleration of electronic charge from a state of rest, and is subject to radiation damping [99],... 

Nozzle resonances technology.3 While forming a jet from a nozzle, this jet has a spontaneous tendency to break into droplets. By applying a vibration at a specific frequency (Figure 4b), uniform droplets are formed with a size approximately double the jet diameter. Several liters per hours can be reached for larger size droplets of 1 mm, but decreases proportionally to the droplet diameter. On the other hand, resonance is damped if the solution viscosity is too high. 

---