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SUMMARY:Connections between Classical Integrable Models\, Log Gas and Rand
om Matrix Theory
DTSTART;VALUE=DATE-TIME:20190205T060000Z
DTEND;VALUE=DATE-TIME:20190205T070000Z
DTSTAMP;VALUE=DATE-TIME:20190220T062213Z
UID:indico-event-6896@cern.ch
DESCRIPTION:We present a deep connection between the classical Calogero-Mo
ser (CM) model\, Log-gas (LG) model and Random Matrix Theory (RMT). We sho
w that CM model has some remarkable connections with the 1D LG model. Both
models have the same minimum energy configuration with the particle posit
ions given by the zeros of the Hermite potential. Moreover the Hessian des
cribing small oscillations around equilibrium are also related for the two
models. We explore this connection further by studying finite temperature
equilibrium properties of the CM model through Monte-Carlo simulations an
d comparing them with known LG results. In particular\, our findings indic
ate that the single particle distribution and the marginal distribution of
the boundary particle of CM model are also given by Wigner semi-circle an
d the Tracy- Widom distribution respectively (similar to LG model). Compar
isons are made with analytical predictions from the small oscillation theo
ry and we find very good agreement. Parallels are also drawn with rigorous
mathematical results from RMT and implications of finite-size as well as
finite- temperature effects are observed. We also present some preliminary
results on large deviations in CM model by using field theory.\n\nhttps:/
/indico.tifr.res.in/indico/conferenceDisplay.py?confId=6896
LOCATION: A 304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6896
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