The phenomenon of Bose-like condensation, the continuous change of the dimensionality of the particle distribution as a consequence of freezing out of one or more degrees of freedom in the limit of low particle density, is investigated theoretically in the case of closed systems of massive bosons and fermions, described by general single-particle Hamiltonians. This phenomenon is similar for both types of particles and, for some energy spectra, exhibits features specific to multiple-step Bose-Einstein condensation, for instance, the appearance of maxima in the specific heat. In the case of fermions, as the particle density increases, another phenomenon is also observed. For certain types of single particle Hamiltonians, the specific heat is approaching asymptotically a divergent behavior at zero temperature, as the Fermi energy epsilon(F) is converging towards any value from an infinite discrete set of energies epsilon(i)(i>/=1). If epsilon(F)=epsilon(i), for any i, the specific heat is divergent at T=0 just in infinite systems, whereas for any finite system the specific heat approaches zero at low enough temperatures. The results are particularized for particles trapped inside parallelepipedic boxes and harmonic potentials.The phenomenon of Bose-like condensation, the continuous change of the dimensionality of the particle distribution as a consequence of freezing out of one or more degrees of freedom in the limit of low particle density, is investigated theoretically in the case of closed systems of massive bosons and fermions, described by general single-particle Hamiltonians. This phenomenon is similar for both types of particles and, for some energy spectra, exhibits features specific to multiple-step Bose-Einstein condensation, for instance, the appearance of maxima in the specific heat. In the case of fermions, as the particle density increases, another phenomenon is also observed. For certain types of single particle Hamiltonians, the specific heat is approaching asymptotically a divergent behavior at zero temperature, as the Fermi energy epsilon(F) is converging towards any value from an infinite discrete set of energies epsilon(i)(i>/=1). If epsilon(F)=epsilon(i), for any i, the specific heat is divergent at T=0 just in infinite systems, whereas for any finite system the specific heat approaches zero at low enough temperatures. The results are particularized for particles trapped inside parallelepipedic boxes and harmonic potentials.

arXiv:cond-mat/0006430Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsDec 1, 20004 citations

Test of the low-energy model for one-dimensional interacting Fermi systems

Andrey V. Chubukov, Dmitrii L. Maslov, Fabian H. L. Eßler

Bosonization predicts that the specific heat $C(T)$ of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing $T$ . We verify whether this result is reproduced in the $g$ -ology model. Of specific interest are the anomalous terms in $C(T)$ that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for $C(T)$ obtained within the $g$ -ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.Bosonization predicts that the specific heat $C(T)$ of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing $T$. We verify whether this result is reproduced in the $g$-ology model. Of specific interest are the anomalous terms in $C(T)$ that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for $C(T)$ obtained within the $g$-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.

arXiv:0801.1837Physical Review BApr 14, 20084 citations

Bosonization predicts that the specific heat

C(T)

of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing

T

. We verify whether this result is reproduced in the

g

-ology model. Of specific interest are the anomalous terms in

C(T)

that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for

C(T)

obtained within the

g

-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.