Abstract
In a recent series of articles, the authors have studied the transition behavior of partial Bergman kernels Πk,[E1,E2 ](z, w) and the associated DOS (density of states) Πk,[E1,E2 ](z) across the interface C between the allowed and forbidden regions. Partial Bergman kernels are Toeplitz Hamiltonians quantizing Morse functions H:M →ℝ on a Kähler manifold. The allowed region is H−1([E1,E2 ]) and the interface C is its boundary. In prior articles it was assumed that the endpoints Ej were regular values of H. This article completes the series by giving parallel results when an endpoint is a critical value of H. In place of the Erf scaling asymptotics in a k−12 tube around C for regular interfaces, one obtains δ-asymptotics in k−14-tubes around singular points of a critical interface. In k−12 tubes, the transition law is given by the osculating metaplectic propagator.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 471-492 |
| Number of pages | 22 |
| Journal | Arkiv for Matematik |
| Volume | 57 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 1 2019 |
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ASJC Scopus subject areas
- Mathematics(all)
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Interface asymptotics of Partial Bergman kernels around a critical level. / Zelditch, Steve; Zhou, Peng.
In: Arkiv for Matematik, Vol. 57, No. 2, 01.01.2019, p. 471-492.Research output: Contribution to journal › Article
TY - JOUR
T1 - Interface asymptotics of Partial Bergman kernels around a critical level
AU - Zelditch, Steve
AU - Zhou, Peng
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In a recent series of articles, the authors have studied the transition behavior of partial Bergman kernels Πk,[E1,E2 ](z, w) and the associated DOS (density of states) Πk,[E1,E2 ](z) across the interface C between the allowed and forbidden regions. Partial Bergman kernels are Toeplitz Hamiltonians quantizing Morse functions H:M →ℝ on a Kähler manifold. The allowed region is H−1([E1,E2 ]) and the interface C is its boundary. In prior articles it was assumed that the endpoints Ej were regular values of H. This article completes the series by giving parallel results when an endpoint is a critical value of H. In place of the Erf scaling asymptotics in a k−12 tube around C for regular interfaces, one obtains δ-asymptotics in k−14-tubes around singular points of a critical interface. In k−12 tubes, the transition law is given by the osculating metaplectic propagator.
AB - In a recent series of articles, the authors have studied the transition behavior of partial Bergman kernels Πk,[E1,E2 ](z, w) and the associated DOS (density of states) Πk,[E1,E2 ](z) across the interface C between the allowed and forbidden regions. Partial Bergman kernels are Toeplitz Hamiltonians quantizing Morse functions H:M →ℝ on a Kähler manifold. The allowed region is H−1([E1,E2 ]) and the interface C is its boundary. In prior articles it was assumed that the endpoints Ej were regular values of H. This article completes the series by giving parallel results when an endpoint is a critical value of H. In place of the Erf scaling asymptotics in a k−12 tube around C for regular interfaces, one obtains δ-asymptotics in k−14-tubes around singular points of a critical interface. In k−12 tubes, the transition law is given by the osculating metaplectic propagator.
UR - http://www.scopus.com/inward/record.url?scp=85074101574&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85074101574&partnerID=8YFLogxK
U2 - 10.4310/ARKIV.2019.v57.n2.a12
DO - 10.4310/ARKIV.2019.v57.n2.a12
M3 - Article
AN - SCOPUS:85074101574
VL - 57
SP - 471
EP - 492
JO - Arkiv for Matematik
JF - Arkiv for Matematik
SN - 0004-2080
IS - 2
ER -