obtained for DTN in the framework of the BEC of magnons.

![\[fig1\] (a) Classical representation of a solid. $a$ is the average distance between the particles. (b) In the wavelike representation the position of the particles is given by the thermal $de$ $Broglie$ wavelength $\lambda$. Decreasing the temperatures, the wave-packet becomes correlated for $\lambda$ $\approx$ a. For particles in the same quantum state, such as bosons at very low temperatures, the system is represented by a single macroscopic wave-function.](figure1.eps){width="7cm"}

II. BOSE-EINSTEIN CONDENSATION
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According to the Heisenberg uncertainly principle the position of a particle is smeared out over a distance given by the thermal $de$ $Broglie$ wavelength $\lambda = h/(2\pi mk_{B}T)^{1/2}$ , where $\ k_{B}$ is the Boltzmann constant, $m$ is the particle mass, and $T$ is the system temperature [@5; @11]. At room temperature $\lambda$ is typically one hundred thousand times smaller than the average spacing between the particles, $a$. This means that the matter waves of the individual particles are uncorrelated, and the system can therefore be described by classical Boltzmann statistics. As the system is cooled, eventually the distance between two particles becomes the same as the $de$ $Broglie$ wavelength, $a$ $\approx$ $\lambda$ [@1; @11]. The packet-functions 