Matter waves expansion

The high sensitivity of this method is related to the fact that we observe a matter-wave interference between the excitation and the condensate, i.e., a heterodyne measurement. Expansion in the inhomogeneous Bogoliubov projection basis confirm this picture [Tozzo 2004] We estimate that this improved sensitivity should give us access to the singly quantized excitation regime. 

It is a simple matter to find the far field from these currents as a function of the continuous radiation direction r - We show a typical example in Fig. 4.4, bottom. However, rather than plotting it as a function of radiation angle, it is plotted as a function of rex, see Fig. 4.4 middle. This makes it more compatible with our choice of variable for the incident wave and the plane wave expansion in general. We obtain mainbeams at = Sx and we also note that the visible... 

Bohr magnetons. A measurement of the expansion energies of the molecular cloud gave energies of a few nK, which is evidence of a macroscopic molecular matter wave. 

A second example of an explosion remnant is the fine lacework of the Cygnus loop, located 2500 light-years from Earth. In supersonic expansion, the gas produces shock waves that excite and ionise interstellar matter, causing it to glow. 

During collapse, which lasts only a split second, the temperature goes up to 10 billion K, as it was in the infant Universe when it was barely 1 second old. The density exceeds that of an atomic nucleus (10 g cm ). Compressed like a spring, the matter then bounces back, for compression went just a little too far. This abrupt return to expansion gives rise to a shock wave that moves back out through the star. 

Whereas the mathematics of the Mie theory is straightforward, if somewhat cumbersome, the physics of the interaction of an electromagnetic wave with a sphere is extremely complicated. It is a relatively easy matter to write the infinite series expansions of the electromagnetic fields at all points of space. It is an even easier matter these days to produce great reams of output from Mie computations. A more difficult task, however, is to visualize the fields, to... 

A mathematical analysis of pressure waves created by thermoelastic expansion of brain matter showed that the sound pressure required for human subjects to barely perceive microwave pulses is about the same as the known minimum audible sound pressure for bone conduction (1 3,27). The frequency of sound provides another line of evidence. It was shown that the fundamental frequency of sound is given by... 

Sound waves are intrinsically different from electromagnetic waves. Thus, while the latter (radio waves infrared, visible or ultraviolet light X-rays gamma rays) can travel in vacuum, sound waves must be contained in some form of matter as they involve expansion and compression cycles travelling through a medium. Compression cycles push molecules together, whereas expansion cycles pull them apart. 

With the perturbed wave functions and energies in hand, it is a straightforward matter to calculate oscillator strengths via Equation (61). The coefficients / , (i = 0, 1, 2,..., 15), in the expansion of /is-2p are listed in Table 10. In this case, however, we are limited to the order of the perturbation, viz. 15 in the present calculation (this limit can easily be changed by increasing the dimensions of the arrays in the computer programs used). 

The presence of the second term, however, creates complications. The full convolution form of the equation must be kept, even at long times furthermore, the kernel for the convolution involves (bilinearly) the correlation function itself, for all kc k 0. Thus, we may no longer deal with a single wave vector to find the behavior of (Ak(t)A k) for a particular k it is necessary to know the correlation function for all k kc. This point could grieviously complicate the making of a small wave vector expansion of the laws of motion, since no matter how small we make k, we still have to deal with the whole range of k. We shall take the point of view, however, that kc is small enough that k can be considered small, and thus we shall perform k expansions just as we performed k expansions. 

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