Related papers: The semi-classical approximation for modular opera…

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…

The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed…

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…

In this paper a new method for computation of higher order corrections to the saddle point approximation of the Feynman path integral is discussed. The saddle point approximation leads to local Schr\"odinger problems around classical…

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which…

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schr\"odinger type equations.…

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an…

We propose a new semiclassical approach based on the dynamical mean field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical (static) phonon modes are treated exactly whereas the…

We study the spectrum of the hydrogen atom in Snyder space in a semiclassical approximation based on a generalization of the Born-Sommerfeld quantization rule. While the corrections to the standard quantum mechanical spectrum arise at first…

We define a new congruence relation on the set of integers, leading to a group similar to the multiplicative group of integers modulo $n$. It makes use of a symmetry almost omnipresent in modular multiplications and halves the number of…

Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase…

We derive semiclassical expressions for spectra, weighted by matrix elements of a Gaussian observable, relevant to a range of molecular and mesoscopic systems. We apply the formalism to the particular example of the resonant tunneling diode…

Given a mixed Hodge module E on a scheme X over the complex numbers, and a quasi-projective morphism f:X->S, we construct in this paper a natural resolution of the nth exterior tensor power of E restricted to the nth configuration space of…

A major barrier in semiclassical calculations is the sheer number of terms that contribute as time increases; for classically chaotic dynamics, the proliferation is exponential. We have been able to overcome this ``exponential wall'' for…

This paper discusses the approximation by %semigroups of operators of class ($\mathscr{C}_0$) on the sphere and focuses on a class of so called exponential-type multiplier operators. It is proved that such operators form a strongly…

We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

We study approximation of functions by algebraic polynomials in the H\"older spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By using modifications of the classical moduli of…