Ligia M.C.S. Rodrigues

λ-point transition in quantum q-gases

Abstract We show that Bose-Einstein condensation is present in highly deformed q -gases, the critical temperature being higher than for the usual ideal boson gas. The specific heat C V has a λ-point transition behaviour not exhibited by non-deformed ideal gases.

q-deformation and instability of the phonon spectrum in 4He

We present an application of a q-deformed system to phonons in 4He. We show that a discrepancy between theory and experiments concerning the stability of phonon spectrum can be overcome when we treat the gas of phonon excitations in 4He as an ideal deformed bosonic gas in a ν0 inequivalent representation. Our results are compared with data from 4He specific heat measurements for T<1K and we reproduce within 5% of accuracy the curves resulting from least-squares fits of those data.

HIGHLY DEFORMED q-OSCILLATOR SYSTEMS

We consider the large q limit of systems made of deformed Heisenberg operators. When the deformation parameter is infinite the Fock space and the statistical properties have a fermionic behaviour. We also investigate the ideal q-gas and find the virial expansion of its equation of state.

INTEGRABLE MULTIPARAMETRIC SU(N) CHAIN

We analyze integrable models associated to a multiparametric SU(N)R-matrix. We show that the Hamiltonians describe SU(N) chains with twisted boundary conditions and that the underlying algebraic structure is the multiparametric deformation of SU(N) enlarged by the introduction of a central element.

ν-DIMENSIONAL IDEAL QUANTUM q-GAS: BOSE-EINSTEIN CONDENSATION AND λ-POINT TRANSITION

We consider an ideal quantum q-gas in ν spatial dimensions and energy spectrum ωiα pα Departing from the Hamiltonian H=ω[N], we study the effect of the deformation on thermodynamic functions and equation of state of that system. The virial expansion is obtained for the high temperature (or low density) regime. The critical temperature is higher than in non-deformed ideal gases. We show that Bose-Einstein condensation always exists (unless when ν/α=1) for finite q but not for q=∞. Employing numerical calculations and selecting for v/α the values 3/2, 2 and 3, we show the critical temperature as a function of q, the specific heat CV and the chemical potential µ as functions of for q=1.05 and q=4.5. CV exhibits a λ-point discontinuity in all cases, instead of the cusp singularity found in the usual ideal gas. Our results indicate that physical systems which have quantum symmetries can exhibit Bose-Einstein condensation phenomenon, the critical temperature being favored by the deformation parameter.

Non-relativistic q-gases with low critical temperatures

We propose a deformed q-oscillator system that allows the study of its thermodynamic properties when a deformation parameter q<1. Our analysis shows that deformation is somehow connected to λ-point transitions and that the different values of the deformation parameters can either favor criticality or render it more difficult to attain. We show that in the non-relativistic case the critical temperature of condensation of the system presented can be much smaller than in the non-deformed ideal bosonic gas.

q-Deformation and Energy Deficit in Liquid Helium Phonon Spectrum

We present an application of an ideal bosonic q-gas in a ν0 inequivalent representation to the phonons in 4He and discuss the role of q-deformation as a possible mechanism to supply the energy deficit that forbiddens one-phonon decay into two phonons when the constant γ in the phonon anomalous dispersion relation (ωph = c0p(1 - γp2)) is positive.

VIRIAL EXPANSION FOR AN ε-DEFORMED SYSTEM

We compute the virial expansion of an ideal quantum q gas equation of state for small values of the deformation parameter.

From geodesics to metric

Abstract The inverse problem of general relativity is solved; the Einstein equations for a static spherically symmetruc perfect fluid are integrated from the given (measurable) orbital velocity of circular geodesics, which thus fixes both the geometry generated by and the equation of state of the fluid. The features of the matter content of a region are therefore determined from the (observed) rotational velocities in its surroundings.