相关论文: Hyperbolic Scar Patterns in Phase Space

The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…

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…

Strong repelling interactions between a few fermions or bosons confined in two-dimensional circular traps lead to particle localization and formation of quantum Wigner molecules (QWMs) possessing definite point-group space symmetries. These…

We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations…

We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is…

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…

Recent developments in the semiclassical analysis of chaotic systems are reviewed and illustrated for Wigner's time delay in elastic scattering of a point particle from three disks in the plane. The convergence of the cycle expanded…

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…

Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant…

The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid…

We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential. Surprisingly in a strong resonance regime, we show that the model can be described by the kinetically constrained effective…

Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…

The Fast Lyapunov Indicators are functions defined on the tangent fiber of the phase-space of a discrete (or continuous) dynamical system, by using a finite number of iterations of the dynamics. In the last decade, they have been largely…

In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an…

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in…

We show that the cross Wigner function can be written in the form $W(\psi, \phi)= \hat S (\psi \otimes \overline{\hat\phi})$ where ${\hat\phi}$ is the Fourier transform of $\phi$ and $\hat S$ is a metaplectic operator that projects onto a…

Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular…

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wavefunctions localized around unstable periodic orbits. The formalism applies to the description of…

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…

The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…