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Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit
Dmitri A. Ivanov, Alexander G. Abanov, Vadim V. Cheianov
We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansi…
Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants
Alexander G. Abanov, Dmitri A. Ivanov, Yachao Qian
We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating functi…
Soliton solutions of Calogero model in harmonic potential
Alexander G. Abanov, Andrey Gromov, Manas Kulkarni
A classical Calogero model in an external harmonic potential is known to be integrable for any number of particles. We consider here reductions which play a role of "soliton" solut…