Solitons and giants in matrix models

We present a method for solving BPS equations obtained in the collective-field approach to matrix models. The method enables us to find BPS solutions and quantum excitations around these solutions in the one-matrix model, and in general for the Calogero model. These semiclassical solutions correspond to giant gravitons described by matrix models obtained in the framework of AdS/CFT correspondence. The two-field model, associated with two types of giant gravitons, is investigated. In this duality-based matrix model we find the finite form of the $n$-soliton solution. The singular limit of this solution is examined and a realization of open-closed string duality is proposed.Comment: 17 pages, JHEP cls; v2: final version to appear in JHEP, 2 references added, physical motivation and interpretation clarifie

Multi-vortex solution in the Sutherland model

We consider the large-$N$ Sutherland model in the Hamiltonian collective-field approach based on the $1/N$ expansion. The Bogomol'nyi limit appears and the corresponding solutions are given by static-soliton configurations. They exist only for \l<1, i.e. for the negative coupling constant of the Sutherland interaction. We determine their creation energies and show that they are unaffected by higher-order corrections. For \l=1, the Sutherland model reduces to the free one-plaquette Kogut-Susskind model.Comment: Latex, using ioplppt.sty, 11 page

Solitons and fractional statistics

Solitons in the continuum limit of the Calogero model are derived and shown to correspond to one-particle excitations. The statistical mechanics of exclusion statistics particles is then formulated in terms of a priori probabilities and a path integral is thereoff constructed. (Talk delivered at the Trieste April 1995 Conference on statistical mechanics and QFT and at the Oslo August 1995 Worskhop on low-dimensional systems.)Comment: 7 pages, Latex, no figures; References correcte

Applications of the Collective Field Theory for the Calogero-Sutherland Model

We use the collective field theory known for the Calogero-Sutherland model to study a variety of low-energy properties. These include the ground state energy in a confining potential upto the two leading orders in the particle number, the dispersion relation of sound modes with a comparison to the two leading terms in the low temperature specific heat, large amplitude waves, and single soliton solutions. The two-point correlation function derived from the dispersion relation of the sound mode only gives its nonoscillatory asymptotic behavior correctly, demonstrating that the theory is applicable only for the low-energy and long wavelength excitations of the system.Comment: LaTeX, 31 page

How to achieve various gait patterns from single nominal

In this paper is presented an approach to achieving on-line modification of nominal biped gait without recomputing entire dynamics when steady motion is performed. Straight, dynamically balanced walk was used as a nominal gait, and applied modifications were speed-up and slow-down walk and turning left and right. It is shown that the disturbances caused by these modifications jeopardize dynamic stability, but they can be simply compensated to enable walk continuation

Dynamical and Quenched Random Matrices and Homolumo Gap

We consider a rather general type of matrix model, where the matrix M represents a Hamiltonian of the interaction of a bosonic system with a single fermion. The fluctuations of the matrix are partly given by some fundamental randomness and partly dynamically, even quantum mechanically. We then study the homolumo-gap effect, which means that we study how the level density for the single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In the case of the quenched randomness (the fundamental one) dominating the quantum mechanical one we show that in the first approximation the homolumo gap is characterized by the absence of single-fermion levels between two steep gap boundaries. The filled and empty level densities are in this first approximation just pushed, each to its side. In the next approximation these steep drops in the spectral density are smeared out to have an error-function shape. The studied model could be considered as a first step towards the more general case of considering a whole field of matrices - defined say on some phase space - rather than a single matrix.Comment: 15 pages, 2 figures; v2. substantial improvements, published in IJMP

Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries

We study the collective field formulation of a restricted form of the multispecies Calogero model, in which the three-body interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality transformations, which interchange, among other things, particles and antiparticles, and thus generalize the well-known strong-weak coupling duality symmetry of the ordinary Calogero model. We identify all these dualities, which form an Abelian group, and study their consequences. We also study the ground state and small fluctuations around it in detail, starting with the two-species model, and then generalizing to an arbitrary number of species.Comment: latex, 53 pages, no figures;v2-minor changes (a paragraph added following eq. (61)