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

By Yoshio Kuramoto, Yusuke Kato

One-dimensional quantum platforms express interesting houses past the scope of the mean-field approximation. besides the fact that, the advanced arithmetic concerned is a excessive barrier to non-specialists. Written for graduate scholars and researchers new to the sector, this publication is a self-contained account of ways to derive the unique quasi-particle photo from the precise resolution of versions with inverse-square interparticle interactions. The publication offers readers with an intuitive figuring out of tangible dynamical homes when it comes to unique quasi-particles that are neither bosons nor fermions. robust innovations, 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 is additionally given. Derivations of dynamics are made more uncomplicated, and are extra concise than within the unique papers, so readers can study the physics of one-dimensional quantum structures in the course of the least difficult version.

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Extra resources for Dynamics of One-Dimensional Quantum Systems

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8. Young diagram of the states with a right-moving quasi-particle and λ quasi-holes. 116). This diagram consists of a quasi-particle, represented by shaded squares, and quasi-holes, represented by unshaded squares. One quasi-particle excitation accompanies λ quasi-hole excitations. 117) where ep and eh denote the charge of a quasi-particle and a quasi-hole, respectively. ∆N (= 0 in the present case) is the difference of the particle numbers between excited states and the ground state. Excitation of one quasi-particle and λ quasi-holes is the minimum set of neutral excitation.

48 Single-component Sutherland model ∆E 8p 2d 2 4p 2d 2 Q 2pd 0 4pd Fig. 9. Excitation spectrum with one quasi-particle and λ(= 2) quasi-holes in the case of N = 7 and the density n = N/L. 43) is given relative to the ground-state energy E0,N by ∆E[ν] = 2π L 2 κ2 ν(κ) + κ λ 2 |κ − κ |ν(κ)ν(κ ) . 126) following the method of [177]. Here µ is the chemical potential and β = 1/T . First we take {κi }N i as an index of one-particle states. We divide the set of one-particle states into many subsets which consist of a macroscopic number of κi (see Fig.

We define the weight of µ as N |µ| = µi . i=1 The Young diagram of a partition µ consists of squares, the coordinates of which are (i, j) with 1 ≤ i ≤ l(µ) and 1 ≤ j ≤ µi . The set of those (i, j) is denoted by D(µ). In drawing diagrams, the first coordinate i (the row index) increases as one goes downwards and the second coordinate j (the column index) increases from left to right. In Fig. 4(a), we show the diagram of the partition µ = (5, 4, 3, 3, 2), where 5(= µ1 ) squares are in the first row, 4(= µ2 ) squares are in the second row, and so on.

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