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I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
Quantum semitoric systems form a large class of quantum Hamiltonian integrable systems with circular symmetry which has received great attention in the past decade. They include systems of high interest to physicists and mathematicians such…
The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.
Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…
We investigate static charge and spin density modulation patterns along a ferromagnet/semiconductor single junction quantum wire in the presence of spin-orbit coupling. Coherent scattering theory is used to calculate the charge and spin…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its…
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point $x_0$ of the phase function with zero critical value. We relate to an…
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su_q(2). The spectrum of position in this discrete…
Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the…
We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization in the classical spirit by superposing…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
String theory is the leading contemporary framework to explore the synthesis of quantum mechanics with gravity. String phenomenology aims to study string theory while maintaining contact with observational data. The fermionic $Z_2\times…
We present a derivation of the energy spectrum of the harmonic oscillator by using the alternative approach of topological quantization. The spectrum is derived from the topological invariants of a particular principal fiber bundle which…
The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to…
Let $f: D \rightarrow \Omega$ be a complex analytic function. The Julia quotient is given by the ratio between the distance of $f(z)$ to the boundary of $\Omega$ and the distance of $z$ to the boundary of $D.$ A classical…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…