Scarring for quantum maps with simple spectrum

Dubi Kelmer

Type: Article

Publication Date: 2011-03-18

Citations: 4

DOI: https://doi.org/10.1112/s0010437x10005270

Abstract

We previously introduced a family of symplectic maps of the torus whose quantization exhibits scarring on invariant co-isotropic submanifolds. The purpose of this note is to show that in contrast to other examples, where failure of Quantum Unique Ergodicity is attributed to high multiplicities in the spectrum, for these examples the spectrum is (generically) simple.

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Compositio Mathematica - View - PDF

Similar Works

Action	Title	Year	Authors
+	Invariant Spectra of Orbits in Multidimensional Symplectic Maps	1999	N. Voglis Christos Efthymiopoulos G. Contopoulos
+ PDF Chat	Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus	2010	Dubi Kelmer
+	Arithmetic Quantum Unique Ergodicity for Symplectic Linear Maps of the Multidimensional Torus	2005	Dubi Kelmer
+	Arithmetic Quantum Unique Ergodicity for Symplectic Linear Maps of the Multidimensional Torus	2005	Dubi Kelmer
+ PDF Chat	Scarring on Invariant Manifolds for Perturbed Quantized Hyperbolic Toral Automorphisms	2007	Dubi Kelmer
+	Quantization of nilpotent coadjoint orbits	1996	Diko Mihov
+ PDF Chat	Quantization of Compact Symplectic Manifolds	2015	Laurent Charles
+	Toric manifolds	1991	Michèle Audin
+	Periodic maps in symplectic topology	1989	Alexander Givental
+	Bloch varieties and quantum ergodicity for periodic graph operators	2024	Wencai Liu
+	Quantization of affine coadjoint orbits	2015	Guangzhong Peng
+	Universality and scaling of zeros on symplectic manifolds: MSRI Publications 40	2001	Pavel Bleher Bernard Shiffman Steve Zelditch
+	Breakdown of tori in symplectic maps	2014	Víctor Álvarez López
+	Integrable symplectic maps	1991	M. Bruschi O. Ragnisco P. M. Santini Tu Gui-Zhang
+	Integrable symplectic maps	1999	Allan P. Fordy
+	Nekhoroshev estimate for isochronous non resonant symplectic maps	1990	Armando Bazzani Stefano Marmi G. Turchetti
+ PDF Chat	Quantization of symplectic orbifolds and group actions	1999	Ana Cannas da Silva Victor Guillemin
+ PDF Chat	Fukaya category of Grassmannians: Rectangles	2020	Marco Castronovo
+	Strict Quantizations of Symplectic Manifolds	2003	Toshikazu Natsume Ryszard Nest I. Peter
+	Bundle of quantizations of a symplectic torus	1996	Andrés Viña

Works That Cite This (4)

Action	Title	Year	Authors
+	Superscars for Arithmetic Point Scatterers II	2019	Pär Kurlberg Stephen Lester Lior Rosenzweig
+	Periodic orbits in cosmological billiards: the Selberg trace formula for asymptotic Bianchi IX universes, evidence for scars in the wavefunction of the quantum universe and large-scale structure anisotropies of the present universe	2013	Orchidea Maria Lecian
+	Problems in Number Theory related to Mathematical Physics	2008	Rikard Olofsson
+ PDF Chat	Superscars for Arithmetic Toral Point Scatterers	2016	Pär Kurlberg Lior Rosenzweig

Works Cited by This (8)

Action	Title	Year	Authors
+ PDF Chat	Scarring on Invariant Manifolds for Perturbed Quantized Hyperbolic Toral Automorphisms	2007	Dubi Kelmer
+ PDF Chat	Entropy of Semiclassical Measures of the Walsh-Quantized Baker’s Map	2006	Nalini Anantharaman Stéphane Nonnenmacher
+ PDF Chat	Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus	2010	Dubi Kelmer
+ PDF Chat	Hecke theory and equidistribution for the quantization of linear maps of the torus	2000	Pär Kurlberg Zeév Rudnick
+ PDF Chat	Invariant measures and arithmetic quantum unique ergodicity	2006	Elon Lindenstrauss
+ PDF Chat	Scarred Eigenstates for Quantum Cat Maps of Minimal Periods	2003	Frédéric Faure Stéphane Nonnenmacher Stephan De Bièvre
+ PDF Chat	The behaviour of eigenstates of arithmetic hyperbolic manifolds	1994	Zeév Rudnick Peter Sarnak
+	Arithmetic Quantum Unique Ergodicity for Symplectic Linear Maps of the Multidimensional Torus	2005	Dubi Kelmer