A Non-concentration Estimate for Partially Rectangular Billiards
نویسندگان
چکیده
We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ǫ0 > 0, an O(λ0 ) quasimode must have L mass in the “wings” (in phase space) bounded below by λ for any δ > 0. The proof uses the author’s recent work on 0-Gevrey smooth domains to approximate quasimodes on C domains. There is an improvement for C and C domains.
منابع مشابه
Ergodic Billiards That Are Not Quantum Unique Ergodic
Partially rectangular domains are compact two-dimensional Riemannian manifolds X, either closed or with boundary, that contain a flat rectangle or cylinder. In this paper we are interested in partially rectangular domains with ergodic billiard flow; examples are the Bunimovich stadium, the Sinai billiard or Donnelly surfaces. We consider a one-parameter family Xt of such domains parametrized by...
متن کاملPeriodic orbits and semiclassical form factor in barrier billiards
Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p/q from the side. To do this, we first obtain the asymptotic density of lengths for each family of periodic orb...
متن کاملNumerical and Experimental Studies of the Elastic Enhancement Factor for 2D Open Systems
We present the results of numerical and experimental studies of the elastic enhancement factorW for microwave rough and rectangular cavities simulating two-dimensional chaotic and partially chaotic quantum billiards in the presence of moderate absorption. We show that for the frequency range ν = 15.0−18.5 GHz, in which the coupling between antennas and the system is strong enough, the values of...
متن کاملLogarithmic contribution to the density of states of rectangular Andreev billiards
We demonstrate that the exact quantum mechanical calculations are in good agreement with the semiclassical predictions for rectangular Andreev billiards, and therefore for a large number of open channels it is sufficient to investigate the Bohr-Sommerfeld approximation of the density of states. We present exact calculations of the classical path length distribution P(s), which is a nondifferent...
متن کاملWave chaos in quantum billiards with a small but finite-size scatterer.
We study the low energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is formulated in terms of self-adjoint extension theory of functional analysis. The condition for the appearance of so-called wave chaos is clarified. We then rela...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014