Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids

Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for non-linear systems, propagating wave packets are unstable. At finite time shock wave singularities develop, the wave packet collapses, and oscillatory features arise. They evolve into regularly structured localized pulses carrying a fractionally quantized charge - {\it soliton trains}. We briefly discuss perspectives of observation of Quantum Shock Waves in edge states of Fractional Quantum Hall Effect and a direct measurement of the fractional charge

A Note on Dressed S-Matrices in Models with Long-Range Interactions

The {\sl dressed} Scattering matrix describing scattering of quasiparticles in various models with long-range interactions is evaluated by means of Korepin's method\upref vek1/. For models with ${1\over\sin^2(r)}$-interactions the S-matrix is found to be a momentum-independent phase, which clearly demonstrates the ideal gas character of the quasiparticles in such models. We then determine S-matrices for some models with ${1\over\sinh^2(r)}$-interaction and find them to be in general nontrivial. For the ${1\over r^2}$-limit of the ${1\over\sinh^2(r)}$-interaction we recover trivial S-matrices, thus exhibiting a crossover from interacting to noninteracting quasiparticles. The relation of the S-matrix to fractional statistics is discussed.Comment: 18 pages, jyTeX (macro included - just TeX the file) BONN-TH-94-13, revised version: analysis of models with 1/sinh^2 interaction adde

Multi-parameter deformed and nonstandard Y(glM)Y(gl_M) Yangian symmetry in integrable variants of Haldane-Shastry spin chain

By using `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax equations for these spin chains allow us to find out the related conserved quantities. However, it turns out that such spin chains also possess a few additional conserved quantities which are apparently not derivable from the Lax equations. Identifying these additional conserved quantities, and the usual ones related to Lax equations, with different modes of a monodromy matrix, it is shown that the above mentioned HS like spin chains exhibit multi-parameter deformed and `nonstandard' variants of $Y(gl_M)$ Yangian symmetry.Comment: 18 pages, latex, no figure

Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles

We give two formulations of exclusion statistics (ES) using a variable number of bosonic or fermionic single-particle states which depend on the number of particles in the system. Associated bosonic and fermionic ES parameters are introduced and are discussed for FQHE quasiparticles, anyons in the lowest Landau level and for the Calogero-Sutherland model. In the latter case, only one family of solutions is emphasized to be sufficient to recover ES; appropriate families are specified for a number of formulations of the Calogero-Sutherland model. We extend the picture of variable number of single-particle states to generalized ideal gases with statistical interaction between particles of different momenta. Integral equations are derived which determine the momentum distribution for single-particle states and distribution of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE

Spinless Calogero-Sutherland model with twisted boundary condition

In this work, the spinless Calogero-Sutherland model with twisted boundary condition is studied. The ground state wavefunctions, the ground state energies, the full energy spectrum are provided in details.Comment: preprint of ETH-L, appearing in recent PR

The spirit of sport: the case for criminalisation of doping in the UK

This article examines public perceptions of doping in sport, critically evaluates the effectiveness of current anti-doping sanctions and proposes the criminalisation of doping in sport in the UK as part of a growing global movement towards such criminalisation at national level. Criminalising doping is advanced on two main grounds: as a stigmatic deterrent and as a form of retributive punishment enforced through the criminal justice system. The ‘spirit of sport’ defined by the World Anti-Doping Agency (WADA) as being based on the values of ethics, health and fair-play is identified as being undermined by the ineffectiveness of existing anti-doping policy in the current climate of doping revelations, and is assessed as relevant to public perceptions and the future of sport as a whole. The harm-reductionist approach permitting the use of certain performance enhancing drugs (PEDs) is considered as an alternative to anti-doping, taking into account athlete psychology, the problems encountered in containing doping in sport through anti-doping measures and the effect of these difficulties on the ‘spirit of sport’. This approach is dismissed in favour of criminalising doping in sport based on the offence of fraud. It will be argued that the criminalisation of doping could act as a greater deterrent than existing sanctions imposed by International Federations, and, when used in conjunction with those sanctions, will raise the overall ‘price’ of doping. The revelations of corruption within the existing system of self-governance within sport have contributed to a disbelieving public and it will be argued that the criminalisation of doping in sport could assist in satisfying the public that justice is being done and in turn achieve greater belief in the truth of athletic performances

Elementary Excitations and Dynamical Correlation Functions of the Calogero-Sutherland Model with Internal Symmetry

We consider the physical properties of elementary excitations of the Calogero-Sutherland (CS) model with SU(K) internal symmetry. From the results on the thermodynamics of this model, we obtain the charge, spin, and statistics of elementary excitations. Combining this knowledge and the known results on the dynamics in the spinless CS model, we propose the expression for the dynamical correlation functions of the SU(K) CS model. In the asymptotic region, we confirm the consistency of our results with predictions from conformal field theory.Comment: 22 pages, REVTe

Long Range Interaction Models and Yangian Symmetry

The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is shown to generate both models. We finally introduce the reflection algebra K(u) to the long range models.Comment: 13 pages, preprint of Nankai Institute of Mathematics ( Theoretical Physics Division ), published in Physical Review E of 1995. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this accoun

Invariants of the Haldane-Shastry SU(N)SU(N) Chain

Using a formalism developed by Polychronakos, we explicitly construct a set of invariants of the motion for the Haldane-Shastry $SU(N)$ chain.Comment: 11 pages, UVA-92-0

Exclusion Statistics in a trapped two-dimensional Bose gas

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte