arXiv subjects
Publications and source records attributed to George V. Vlasov.
In a paper appearing in this issue of Physical Review D, Burmistrov raises some critical comments on the thermodynamics of a cold tachyon Fermi gas [E. Trojan and G. V. Vlasov, Phys. Rev. D 83, 124013 (2011)]. However, apart from any possible theoretical speculation, there are the basic physical principles to test the theory.
Superconducting cosmic string may admit shock-like discontinuities of the current when the latter is spacelike ("magnetic" regime), while no shock at timelike current ("electric" regime) was discovered in numerical simulations. We find that the necessary and enough conditions for existence of stable shocks and show that the shock can be unstable in the presence of infinitesimal extrinsic perturbations of the string worldsheet. The shocks in the "magnetic" regime are not vulnerable to this instability but the shocks in the "electric" regime do not survive.
Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term χ. The hypersurface of discontinuity propagates at finite velocity determined by finite increment Δχ=χ_+ -χ_-. The current increases χ_+>χ_- in stable shocks but transition between spacelike (χ>0) and timelike (χ<0) currents is impossible.
We consider an ideal Fermi gas of tachyonic thermal excitations as a continuous medium and establish when it satisfies the causality condition. At high temperature the sound speed is always subluminal $c_s<1$, but there is no stable form of tachyon matter below the critical temperature $T_c<0.23m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but $P$ can exceed $E$, and $P=2.36E$ when $T\rightarrow T_c$.
The 'absolute stiff' matter ($P=E$) can be a Fermi or Bose gas of particles with the energy spectrum $ε_p \sim p^q$ in $q$-dimensional space, particularly $ε_p =p^3/m^2$ in 3-dimensional space. We obtain its pressure, particle number density and heat capacity at finite temperature. The behavior of 'absolute stiff' medium is determined by characteristic temperature $T_c=6π^2n/(γm^2)$. At low temperature the heat capacity obeys the linear law $C_V\sim T$ for both fermionic and bosonic matter, the pressure of 'absolute stiff' fermions $P\sim n^2+O(T^2)$, while the 'absolute stiff' Bose gas never reveals Bose-Einstein condensation.
A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are not fully independent. The interaction between particles is reflected only in the equation of state of each component, but it deals nothing with the coupling between the fluid components and does not influence the hydrodynamic motion. A general form of two-fluid decomposition is formulated for arbitrary interacting system.
We consider a substance with equation of state $P=wE$ at constant $w$ and find that it is an ideal gas of quasi-particles with the energy spectrum $ε_p\sim p^{wq}$ that can constitute either regular matter (when $w>0$) or exotic matter (when $w<0$) in a $q$-dimensional space. Particularly, an ideal gas of fermions or bosons with the energy spectrum $ε_p=m^4/p^3$ in 3-dimensional space will have the pressure $P=-E$. Exotic material, associated with the dark energy at $E+P<0$, is also included in analysis. We determine the properties of regular and exotic ideal Fermi gas at zero temperature and derive a low-temperature expansion of its thermodynamical functions at finite temperature. The Fermi level of exotic matter is shifted below the Fermi energy at zero temperature, while the Fermi level of regular matter is always above it. The heat capacity of any fermionic substance is always linear dependent on temperature, but exotic matter has negative entropy and negative heat capacity.
We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value $n_T$ and the Fermi momentum $k_F<\sqrt{\frac 32}m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but the situation $P>E$ is not forbidden. Existence of shock waves in tachyon gas is also discussed. At low density $n_T<n<3.45n_T$ the tachyon matter remains stable but no shock wave do survive.