Exclusion statistics: A resolution of the problem of negative weights

We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which describes an ideal exclusion statistics system and deduce the general counting rules for occupancy of states obeyed by these particles. We show that the problem of negative probabilities may be avoided with these new counting rules.Comment: REVTEX 3.0, 14 page

Fractional Exclusion Statistics and Anyons

Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and anti-anyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the non-relativistic limit.Comment: 9 pages, latex, IFT-498-UN

Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics

We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.Comment: 10pp, REVTE

Exclusion Statistics of Quasiparticles in Condensed States of Composite Fermion Excitations

The exclusion statistics of quasiparticles is found at any level of the hierarchy of condensed states of composite fermion excitations (for which experimental indications have recently been found). The hierarchy of condensed states of excitations in boson Jain states is introduced and the statistics of quasiparticles is found. The quantum Hall states of charged $\alpha$-anyons ($\alpha$ -- the exclusion statistics parameter) can be described as incompressible states of $(\alpha+2p)$-anyons ($2p$ -- an even number).Comment: 4 page

Entropic C-theorems in free and interacting two-dimensional field theories

The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative entropy analogous to Zamolodchikov's $c$ function. The one-dimensional quantum thermodynamic entropy gives rise to another monotonic dimensionless quantity. I illustrate these monotonicity theorems with examples ranging from free field theories to interacting models soluble with the thermodynamic Bethe ansatz. Both dimensionless entropies are explicitly shown to be monotonic in the examples that we analyze.Comment: 34 pages, 3 figures (8 EPS files), Latex2e file, continuation of hep-th/9710241; rigorous analysis of sufficient conditions for universality of the dimensionless relative entropy, more detailed discussion of the relation with Zamolodchikov's theorem, references added; to appear in Phys. Rev.

Algebra of the observables in the Calogero model and in the Chern-Simons matrix model

The algebra of observables of an N-body Calogero model is represented on the S_N-symmetric subspace of the positive definite Fock space. We discuss some general properties of the algebra and construct four different realizations of the dynamical symmetry algebra of the Calogero model. Using the fact that the minimal algebra of observables is common to the Calogero model and the finite Chern-Simons (CS) matrix model, we extend our analysis to the CS matrix model. We point out the algebraic similarities and distinctions of these models.Comment: 24 pages, misprints corrected, reference added, final version, to appear in PR

Нове технологічне рішення для створення багатошарових систем на основі кремнію з бінарними нанокластерами та елементами III та V груп

Розроблено дифузійну технологію формування бінарних кластерів в кремії за участю елементів III і V груп. Показано, що шляхом контролю концентрації елементів атомів III і V групи можна сформувати багатошарові гетеропереходи на основі кремнію в поверхневій області кремнію зі збагаченими нанокристалами AIIIBV, а потім збагаченими різними комбінаціями елементарних комірок Si2AIIIBV (1 – 5 мкм товщиною). Це створює практичний новий матеріал на основі кремнію - безперервну варизонну структуру завдяки плавному переходу від забороненої зони напівпровідникових сполук III – V до забороненої зони кремнію.The diffusion technology has been developed for the formation of binary clusters involving elements of group III and V in silicon. It is shown that by controlling the concentration of elements of group III and V atoms, multilayer silicon-based heterojuns can be formed in the surface region of silicon with enriched AIIIBV nanocrystals, followed by enriched with various combinations of Si2AIIIBV unit cells (1 – 5 µm thick). This creates a practical new material based on silicon - a continuous graded-gap structure, i.e. heterojuns by a smooth transition from the band gap of III – V semiconductor compounds to the band gap of silicon