Related papers: The semiclassical limit of chaotic eigenfunctions
We study the quantum-interference effect in the ballistic Aharonov-Bohm (AB) billiard. The wave-number averaged conductance and the correlation function of the non-averaged conductance are calculated by use of semiclassical theory. Chaotic…
Chaos plays a crucial role in numerous natural phenomena, but its quantum nature has remained large elusive. One intriguing quantum-chaotic phenomenon is the scarring of a single-particle wavefunction, where the quantum probability density…
We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows…
We consider the case of a cubic nonlinear Schr\"{o}dinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate…
A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily…
We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of…
We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a…
Semiclassical methods form a bridge between classical systems and their quantum counterparts. An interesting phenomenon discovered in this connection is the scar effect, whereby energy eigenstates display enhancement structures resembling…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
We consider quantum scattering from a compactly supported potential $q$. The semiclassical limit amounts to letting the wavenumber $k \to \infty$ while rescaling the potential as $k^2 q$ (alternatively, one can scale Planck's constant…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
In the periodic orbit quantization of physical systems, usually only the leading-order hbar contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae…
The eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence, but the characterization of the spectrum even for the simplest plasma model, ideal magnetohydrodynamics (MHD), is not…
We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors…
Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories.…
We consider the energy averaged two-point correlator of spectral determinants and calculate contributions beyond the diagonal approximation using semiclassical methods. Evaluating the contributions originating from pseudo-orbit correlations…