Download Dynamics of One-Dimensional Quantum Systems: Inverse-Square by Yoshio Kuramoto, Yusuke Kato PDF

By Yoshio Kuramoto, Yusuke Kato

One-dimensional quantum structures express interesting houses past the scope of the mean-field approximation. notwithstanding, the complex arithmetic concerned is a excessive barrier to non-specialists. Written for graduate scholars and researchers new to the sphere, this booklet is a self-contained account of ways to derive the unique quasi-particle photo from the precise answer of versions with inverse-square interparticle interactions. The e-book offers readers with an intuitive realizing of tangible dynamical homes when it comes to unique quasi-particles that are neither bosons nor fermions. strong recommendations, reminiscent of the Yangian symmetry within the Sutherland version and its lattice models, are defined. A self-contained account of non-symmetric and symmetric Jack polynomials can be given. Derivations of dynamics are made more straightforward, and are extra concise than within the unique papers, so readers can research the physics of one-dimensional quantum structures in the course of the least difficult version.

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Extra info for Dynamics of One-Dimensional Quantum Systems: Inverse-Square Interaction Models

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The most striking feature of the Sutherland model is that one can derive not only the energy spectrum but also the dynamics for the many-particle case with an exact account of interaction effects. Thus, the Sutherland model provides an ideal framework to study a one-dimensional quantum liquid in detail. 1, we derive the eigenenergies of eigenstates. 2, we present different but equivalent physical pictures for the energy spectrum. Namely, the energy spectrum is naturally regarded as that of interacting bosons or fermions.

6(b). 92) consists of the Fermi sea for an N -particle system and an additional particle. We call this particle outside the Fermi sea a quasi-particle. 3 Elementary excitations 41 (a) · · · 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0· · · (b) · · · 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1· · · (c) · · · 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0· · · Fig. 6. Motif representation of eigenstates for λ = 2 and N = 7: (a) the ground state; (b) a one-particle addition state; (c) a one-particle removal state.

Part I Physical properties 2 Single-component Sutherland model In the present chapter, we discuss the Sutherland model for particles without internal degrees of freedom such as spin. We call this model the singlecomponent Sutherland model. 3) have been obtained explicitly in the previous chapter. The most striking feature of the Sutherland model is that one can derive not only the energy spectrum but also the dynamics for the many-particle case with an exact account of interaction effects. Thus, the Sutherland model provides an ideal framework to study a one-dimensional quantum liquid in detail.

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