128 citations · 160 across the 5 of their papers we have counts for
7 papers
Fractal upper bounds on the density of semiclassical resonances
J. Sjoestrand, M. Zworski
For semiclassical problems we establish upper bounds on the number of resonances in boxes of size along the real axis, in terms of the dimension of the set of trapped trajector…
Eigenfunctions for partially rectangular billiards
N. Burq, M. Zworski
In this note we further develop the idea of using a ``black box'' point of view (see our previous work) to study eigenfunctions for billiards which have rectangular components: the…
Bouncing ball modes and quantum chaos
N. Burq, M. Zworski
Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we…
Quantum resonances and partial differential equations
Maciej Zworski
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, t…
Fractal Weyl laws for chaotic open systems
W. T. Lu, S. Sridhar, Maciej Zworski
We present a result relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. The result is supported by…
Birkhoff Normal Forms in Semi-Classical Inverse Problems
A. Iantchenko, J. Sjoestrand, M. Zworski
We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energ…