Larisa Jonke

Bosonic realization of algebras in the Calogero model

Abstract We study an N -body Calogero model in the S N -symmetric subspace of the positive definite Fock space. We construct a new algebra of S N -symmetric operators represented on the symmetric Fock space, and find a natural orthogonal basis by mapping the algebra onto the Heisenberg algebra. Our main result is the bosonic realization of non-linear dynamical symmetry algebra describing the structure of degenerate levels of the Calogero model.

Duality and quasiparticles in the Calogero-Sutherland model: Some exact results

A quantum-mechanical many-body system with a potential proportional to the pairwise inverse-square distance possesses a strong-weak coupling duality. Using this duality we construct a parent Hamiltonian describing the system of particles and quasiparticles. The construction of the Hamiltonian and the solutions found are of a hierarchical nature.

Dynamical symmetry algebra of the Calogero model

Abstract We study the dynamical symmetry algebra of the N -body Calogero model describing the structure of degenerate levels and demonstrate that the algebra is intrinsically polynomial. We discuss some general properties of an algebra of S N -symmetric operators acting on the S N -symmetric subspace of the Fock space for any statistical parameter ν . In the bosonic case ( ν =0) we find the algebra of generators for every N . For ν ≠0, we explicitly reproduce the finite algebra for the 4-particle model, demonstrating some general features of our construction.

Homolumo gap from dynamical energy levels

We introduce a dynamical matrix model where the matrix is interpreted as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show how a system of second-quantized fermions influences the ground state of the whole system by producing a gap between the highest eigenvalue of the occupied single-fermion states and the lowest eigenvalue of the unoccupied single-fermion states. We describe the development of the gap in both the strong and weak coupling regimes, while for the intermediate coupling strength we expect formation of homolumo kinks.

Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction

We consider the large-

MATRIX-MODEL DUALITIES FROM CONFORMAL FIELD THEORY

N

Perturbative spectrum of trapped weakly interacting bosons in two dimensions

Chern-Simons theory for attractive bosonic matter (Jackiw-Pi model) in the Hamiltonian collective-field approach based on the

Calogero model, deformed oscillators and the collapse

1/N

COLLECTIVE-FIELD EXCITATIONS IN THE CALOGERO MODEL

expansion. We show that the dynamics of low-lying density excitations around the ground-state vortex configuration is equivalent to that of the Sutherland model. The correspondence between the Chern-Simons coupling constant

Comment on 'Waves and solitons in the two-family Calogero model'

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