Related papers: Linear and Nonlinear Theory of Eigenfunction Scars
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal correspondence of their quantum spectral statistics with random matrix models. We argue…
We derive semiclassical laser equations valid in all orders of nonlinearity. With the help of a diagrammatic representation, the perturbation series in powers of electric field can be resummed in terms of a certain class of diagrams. The…
We show that on a suitable time scale, logarithmic in $\hbar$, the coherent states on the two-torus, evolved under a quantized perturbed hyperbolic toral automorphism, equidistribute on the torus. We then use this result to obtain control…
We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map…
We construct a class of quantum many-body systems hosting an $\mathfrak{su}(3)$-invariant scar subspace, extending the conventional paradigm of quantum many-body scars beyond equally spaced spectra and single-directional tower structures.…
Recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of dynamical behavior that challenged the conventional paradigms of integrability and thermalization. This…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs…
Classical periodic orbits responsible for emergence of the superdeformed shell structures for single-particle motions in spheroidal cavities are identified and their relative contributions to the shell structures are evaluated. Both prolate…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
The semiclassical origins of the enhancement of shell effects in exotic-shape mean-field potentials are investigated by focusing attention on the roles of the local symmetries associated with the periodic-orbit bifurcations. The deformed…
Shell structure of the single-particle spectrum for reflection-asymmetric deformed cavity is investigated. Remarkable shell structure emerges for certain combinations of quadrupole and octupole deformations. Semiclassical periodic-orbit…
The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find…
Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including…
We investigate statistical properties of the eigenfunctions of the Schrodinger operator on families of star graphs with incommensurate bond lengths. We show that these eigenfunctions are not quantum ergodic in the limit as the number of…
We study the landscape of solutions of the coherent quantum states in a ring shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical…
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…
We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle…