Wigner and Husimi transforms have long been used for the phasespace reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the strong topology, i.e. approximation of Wigner functions by solutions of the Liou...

This paper concerns the use of phase information from band-pass signals for the measurement of binocular disparity, optic ow, and image orientation. Towards this end, one of the important properties of band-pass phase information is its stability with respect to small geometric deformations and contrast changes. However, in particular regions phase can also be very unstable due to the occurrenc...

There are several modern methods to visualize sounds, from oscilloscope and spectrometer to colour organs and strobe lights. Phase space is a relatively new way to visualize sounds. Originally used to better understand the chaos of strange attractors and other non-periodic systems, it can be used to observe the regularity of periodic and pseudo-periodic signals. Besides extracting information a...

Phase-space representations first arose from the attempt to describe quantum mechanics in terms of distributions over classical variables [1]. For example, Wigner introduced a function of phase-space variables W(x, p) that would classically correspond to a joint-probability distribution: an integration over x gives the marginal distribution for p and vice-versa. However in quantum mechanics, su...

The phase space of a particle or a mechanical system contains an intrinsic symplectic structure, and hence, it is a symplectic manifold. Recently, new invariants for symplectic manifolds in terms of cohomologies of differential forms have been introduced by Tseng and Yau. Here, we discuss the physical motivation behind the new symplectic invariants and analyze these invariants for phase space, ...

We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a crossover from the tunneling to the shuttling regime, thus extending the previously found classical results to the quantum domain. Further, a new dynamical regime is discovere...

Conformally compactified phase space is conceived as an automorphism space for the global action of the extended conformal group. Space time and momentum space appear then as conformally dual, that is conjugate with respect to conformal reflections. If now the former, as generally agreed, is appropriate for the description of classical mechanics in euclidean geometrical form, then the latter re...

Problems involving interacting spins or qubits are often regarded as computationally intractable. These are frequently considered as only being accessible using quantum computers, which are not yet developed. At the same time, there is a ‘chicken and egg’ problem: it is difficult to design a quantum computer with no effective means to simulate its behaviour, including inevitable sources of loss...

Quantum theory predicts probabilities for various events as well as relative phases (interference or geometric) between different alternatives of the system. The most general description of the latter is in terms of the Pancharatnam phase. A unified description of both probabilities and phases comes through generalisation of the notion of a density matrix for histories; this object is the decoh...

Speech production is essentially a nonlinear dynamic process. Motivated by ideas in dynamic system research, this paper seeks to recast the speech representation problem (front-end) as an attempt to reconstruct the phase space of the production process, or articulatory configurations. We point out that the use of the delta and double delta features, common in current ASR (Automatic Speech Recog...