TY - JOUR
T1 - On the entropy of quantum limits for 2-dimensional cat maps
AU - Brooks, Shimon
PY - 2009
Y1 - 2009
N2 - We study semiclassical measures, or quantum limits, for quantized hyperbolic automorphisms of T2. We show that any quantum limit has the following property: if a weight α is carried on ergodic components of low entropy (say, entropy less than h0), then a weight ≥ α must be carried on ergodic components of high entropy (≥ hmax-h0, where hmax is themaximal entropy). This combines some existing partial results towards the classification of quantum limits.
AB - We study semiclassical measures, or quantum limits, for quantized hyperbolic automorphisms of T2. We show that any quantum limit has the following property: if a weight α is carried on ergodic components of low entropy (say, entropy less than h0), then a weight ≥ α must be carried on ergodic components of high entropy (≥ hmax-h0, where hmax is themaximal entropy). This combines some existing partial results towards the classification of quantum limits.
UR - http://www.scopus.com/inward/record.url?scp=79957808047&partnerID=8YFLogxK
U2 - 10.1007/s00220-009-0897-y
DO - 10.1007/s00220-009-0897-y
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AN - SCOPUS:79957808047
SN - 0010-3616
VL - 293
SP - 231
EP - 255
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -