Weakly Interacting, Dilute Bose Gases in 2D

This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to be realized. Nevertheless, first experimental indications supporting the formation of the condensate in low dimensional systems have been recently obtained. This unexpected behaviour appears to be due to the non-uniformity, introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. We survey a number of popular theoretical treatments of the dilute weakly interacting Bose gas and discuss their regions of applicability. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of perturbative t-matrix approximation and diluteness condition are issues that we discuss in detail.Comment: Survey, 25 pages RMP style, revised version, refs added, some changes made, accepted for publication in Rev. Mod. Phy

Multitemporal generalization of the Tangherlini solution

The n-time generalization of the Tangherlini solution [1] is considered. The equations of geodesics for the metric are integrated. For $n = 2$ it is shown that the naked singularity is absent only for two sets of parameters, corresponding to the trivial extensions of the Tangherlini solution. The motion of a relativistic particle in the multitemporal background is considered. This motion is governed by the gravitational mass tensor. Some generalizations of the solution, including the multitemporal analogue of the Myers-Perry charged black hole solution, are obtained.Comment: 14 pages. RGA-CSVR-005/9

Spectral signatures of the Luttinger liquid to charge-density-wave transition

Electron- and phonon spectral functions of the one-dimensional, spinless-fermion Holstein model at half filling are calculated in the four distinct regimes of the phase diagram, corresponding to an attractive or repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or polaronic insulator at strong coupling. The results obtained by means of kernel polynomial and systematic cluster approaches reveal substantially different physics in these regimes and further indicate that the size of the phonon frequency significantly affects the nature of the quantum Peierls phase transition.Comment: 5 pages, 4 figures; final version, accepted for publication in Physical Review

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.Comment: 14 pages, IOP styl

Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries

The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$ a three parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged center of the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a three-dimensional complex hypersurface which remains invariant under the action of an infinite-dimensional group of analytic transformations, called the quantum coadjoint action.Comment: 52 pages, TCI LaTex, v2: equation (167) corrected, two references adde

Enhancement of the Thermal Conductivity in gapped Quantum Spin Chains

We study mechanism of magnetic energy transport, motivated by recent measurements of the thermal conductivity in low dimensional quantum magnets. We point out a possible mechanism of enhancement of the thermal conductivity in gapped magnetic system, where the magnetic energy transport plays a crucial role. This mechanism gives an interpretation for the recent experiment of CuGeO_3, where the thermal conductivity depends on the crystal direction.Comment: 4 pages, 2 figure