Related papers: A new class of semiclassical wave function uniform…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…
We derive semiclassical quantization conditions for systems with spin. To this end one has to define the notion of integrability for the corresponding classical system which is given by a combination of the translational motion and…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical…
We use a factorization technique and representation of canonical transformations to construct globally valid closed form expressions without singularities of semi-classical wave functions for arbitrary smooth potentials over a…
We derive a semiclassical theory for the detection of matter-waves. This theory draws on the theories of semiclassical optical detection and fluid mechanics. We observe that the intrinsically dispersive nature of matter-waves is important…
We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This gives a new solution of the the long standing problem of quantizing the resonances generically appearing…
Passive imaging is a new technique which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields, computed from the fields recorded at different points, is strongly related to the Green function…
In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of \hbar can be constructed for them without referring to the…
In this paper, we prove the equidistribution property of high-frequency eigensections of a certain series of unitary flat bundles, using the mixture of semiclassical and geometric quantizations.
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant…