Comment on "Solitons and excitations in the duality-based matrix model"

It is shown that a method for constructing exact multi-solitonic solutions of the coupled BPS equations in the duality-based generalization of the hermitean matrix model, which was put forward in a recent paper, is not correct.Comment: 5 pages, no figures, JHEP-style, submitted to JHE

Analytical Results for Trapped Weakly Interacting Bosons in Two Dimensions

We consider a model of N two-dimensional bosons in a harmonic trap with translational and rotational invariant, weak two-particle interaction. We present in configuration space a systematical recursive method for constructing all wave functions with angular momentum L and corresponding energies and apply it to L\leq 6 for all N. The lower and the upper bounds for interaction energy are estimated. We analitically confirm the conjecture of Smith et al. that elementary symmetric polynomial is the ground state for repulsive delta interaction, for all N\geq L up to L\leq 6. Additionally, we find that there exist vanishing-energy solutions for L\geq N(N-1), signalizing the exclusive statistics. Finally, we consider briefly the case of attractive power-like potential r^k, k>-2, and prove that the lowest-energy state is still the one in which all angular momentum is absorbed by the center-of-mass motion.Comment: RevTex, 13 page

Deformed Heisenberg algebras, a Fock-space representation and the Calogero model

We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space representation. One solution of these conditions leads to a q-deformed oscillator already studied by Lorek et al., and reduces to the harmonic oscillator only in the infinite-momentum frame. The other solution leads to the Calogero model in ordinary quantum mechanics, but reduces to the harmonic oscillator in the absence of deformation.Comment: 13 pages, to appear in Eur. Phys. J.

Example of q-deformed Field Theory

The non-relativistic Chern-Simons theory with the single-valued anyonic field is proposed as an example of q-deformed field theory. The corresponding q-deformed algebra interpolating between bosons and fermions,both in position and momentum spaces, is analyzed.A possible generalization to a space with an arbitrary dimension is suggested.Comment: 13 pages,LaTe

Solutions of coupled BPS equations for two-family Calogero and matrix models

We consider a large N, two-family Calogero and matrix model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by the static soliton configurations. We find all solutions close to constant and construct exact one-parameter solutions in the strong-weak dual case. Full classification of these solutions is presented.Comment: latex, 15 pages, no figure

Partition function for general multi-level systems

We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach. Anyonic- like systems are briefly discussed.Comment: Latex file, 16 page

Fluktuacije kolektivnog polja oko zidnog rješenja Chern-Simonsove teorije

We consider a large-N Chern-Simons theory for the attractive bosonic matter (Jackiw-Pi model) in the Hamiltonian collective-field approach based on the 1/N expansion. We show that the dynamics of low-lying density fluctuations around the semiclassical wall solution is governed by the Calogero Hamiltonian . The relationship between the Chern-Simons coupling constant κ and the statistical parameter α signalizes some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.Razmatra se Chern-Simonsova teorija za privlačnu bozonsku tvar (Jackiw-Pi model) u pristupu hamiltonijana kolektivnog polja zasnovanog na 1q N razvoju. Pokazuje se da dinamikom niskoležećih fluktuacija gustoće oko poluklasičnog zidnog rješenja upravlja Calogerov hamiltonijan. Odnos između Chern-Simonsove konstante vezanja κ i Calogerovog statističkog parametra λ ukazuje na neku vrstu statističke transmutacije koja prati smanjenje dimenzija početnog problema