Article

# Emergence of Quantum Ergodicity in Rough Billiards

Physical Review Letters (Impact Factor: 7.73). 02/1997; DOI: 10.1103/PhysRevLett.79.1833

Source: arXiv

- [Show abstract] [Hide abstract]

**ABSTRACT:**We show that using the concept of the two-dimensional level number N⊥ one can experimentally study of the nodal domains in a three-dimensional (3D) microwave chaotic rough billiard with the translational symmetry. Nodal domains are regions where a wave function has a definite sign. We found the dependence of the number of nodal domains ℵN⊥ lying on the cross-sectional planes of the cavity on the two-dimensional level number N⊥. We demonstrate that in the limit N⊥→∞ the least squares fit of the experimental data reveals the asymptotic ratio ℵN⊥/N⊥≃0.059±0.029 that is close to the theoretical prediction ℵN⊥/N⊥≃0.062. This result is in good agreement with the predictions of percolation theory.Physics Letters A 03/2009; · 1.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A rigorous solution for the spectrum of a quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained. To accomplish this task, we have developed a method for the separation of variables in a wave equation, which enables one, in principle, to rigorously examine any limiting case-from negligibly weak to arbitrarily strong disorder at the resonator boundary. It is shown that the effect of disorder-induced scattering can be properly described in terms of two geometric potentials, specifically, the "amplitude" and the "gradient" potentials, which appear in wave equations in the course of conformal smoothing of the resonator boundaries. The scattering resulting from the gradient potential appears to be dominant, and its impact on the whole spectrum is governed by the unique sharpness parameter Ξ, the mean tangent of the asperity slope. As opposed to the resonator with bulk disorder, the distribution of nearest-neighbor spacings (NNS) in the rough-resonator spectrum acquires Wigner-like features only when the governing wave operator loses its unitarity, i.e., with the availability in the system of either openness or dissipation channels. It is shown that the reason for this is that the spectral line broadening related to the oscillatory mode scattering due to random inhomogeneities is proportional to the dissipation rate. Our numeric experiments suggest that in the absence of dissipation loss the randomly rough resonator spectrum is always regular, whatever the degree of roughness. Yet, the spectrum structure is quite different in the domains of small and large values of the parameter Ξ. For the dissipation-free resonator, the NNS distribution changes its form with growing the asperity sharpness from poissonian-like distribution in the limit of Ξ≪1 to the bell-shaped distribution in the domain where Ξ≫1.Physical Review E 08/2011; 84(2 Pt 2):026209. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the classical and quantum properties of the "Chirikov typical map," proposed by Boris Chirikov in 1969. This map is obtained from the well-known Chirikov standard map by introducing a finite-number T of random phase-shift angles. These angles induce a random behavior for small time-scales (t<T) and a T -periodic iterated map which is relevant for larger time-scales (t>T) . We identify the classical chaos border k(c) approximately T (-3/2)1 for the kick parameter k and two regimes with diffusive behavior on short and long time scales. The quantum dynamics is characterized by the effect of Chirikov localization (or dynamical localization). We find that the localization length depends in a subtle way on the two classical diffusion constants in the two time-scale regime.Physical Review E 07/2009; 80(1 Pt 2):016210. · 2.31 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.