Related papers: Time-domain scars: resolving the spectral form fac…
We present a novel extension of the concept of scars for the wave functions of classically chaotic few-body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space…
Quantum scars are enhancements of quantum probability density along classical periodic orbits. We study the recently discovered phenomenon of strong, perturbation-induced quantum scarring in the two-dimensional harmonic oscillator exposed…
We develop a semi-classical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic fringes,…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
We develop the theory of quantum scars for quantum fields. By generalizing the formalisms of Heller and Bogomolny from few-body quantum mechanics to quantum fields, we find that unstable periodic classical solutions of the field equations…
We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical orbit of a Hamiltonian system…
A quantum scar is a wave function which displays an high intensity in the region of a classical unstable periodic orbit. Saddle scars are states related to the unstable harmonic motions along the stable manifold of a saddle point of the…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by…
Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically…
A quantum scar - an enhancement of a quantum probability density in the vicinity of a classical periodic orbit - is a fundamental phenomenon connecting quantum and classical mechanics. Here we demonstrate that some of the eigenstates of the…
We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example,…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…
We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a…