Fractional statistics in some exactly solvable Calogero-like models with PT invariant interactions

Abstract

Here we review a method for constructing exact eigenvalues and eigenfunctions of a many-particle quantum system, which is obtained by adding some nonhermitian but PT invariant (i.e., combined parity and time reversal invariant) interaction to the Calogero model. It is shown that such extended Calogero model leads to a real spectrum obeying generalised exclusion statistics. It is also found that the corresponding exchange statistics parameter differs from the exclusion statistics parameter and exhibits a `reflection symmetry' provided the strength of the PT invariant interaction exceeds a critical value.

8 pages, Latex, Talk given at Joint APCTP-Nankai Symposium, Tianjin (China), Oct. 2001

References in corpus (1)

• On an exactly solvable $B_N$ type Calogero model with nonhermitian PT invariant interaction

Cited by in corpus (10)

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• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Pseudo-Hermitian Interactions in Dirac Theory: Examples
• Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential
• Entangled Quantum State Discrimination using Pseudo-Hermitian System
• Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
• Chiral bosons on Bargmann space associated with A${}_r$ Statistics
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models