  Proposed by the author Q-ball mechanism of the pseudogap state and high-Tc
superconductivity in cuprates was recently supported by micro X-ray diffraction
data in HgBa$_2$CuO$_{4+y}$. This provides a remarkable opportunity to
investigate X-ray diffraction produced by the quantum thermodynamic time
crystals, a direct embodiment of those are just the Euclidean Q-balls
considered in the aforementioned theory. Simultaneously, it is also
demonstrated that T-linear temperature dependence of electrical resistivity in
the Q-ball phase arises due to scattering of electrons on the condensed
charge/spin fluctuations inside the Q-balls. This gives a clue concerning
possible mechanism of T-linear behaviour of electrical resistivity in the
strange metal phase of high-T$_c$ cuprates. For this purpose the Green's
functions of X-ray photons and fermions scattered by the Q-balls in the
pseudogap phase of high-Tc superconductors are calculated using the Feynman
diagrammatic technique. The Bragg's peaks intensity, provided by the imaginary
part of the retarded photon Green's function, is calculated. In total, obtained
results describe X-ray and electron scattering on the finite size Q-ball of
CDW/SDW density, that oscillates with bosonic frequency $\Omega=2\pi nT$ in
Matsubara time, i.e. the quantum thermodynamic time crystal. It is found, that
theoretical results are in good correspondence with X-ray diffraction data in
HgBa$_2$CuO$_{4+y}$ reported recently. The T-linear dependence of electrical
resistivity arises due to inverse temperature dependence of the Q-ball radius
as function of temperature.
