Related papers: Matrix formalism of synchrobetatron coupling
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths…
We extend the previous construction of loop transfer matrix to the case of nonzero self-intersection coupling constant $\kappa$. The loop generalization of Fourier transformation allows to diagonalize transfer matrices depending on…
Longitudinal oscillations of bunched beams in synchrotrons have been analyzed by accelerator physicists for decades, and a closed theory is well-known [1]. The first modes of oscillation are the coherent dipole mode, quadrupole mode, and…
The influence of spin-orbit coupling in two-dimensional systems is investigated within the framework of the Landauer-Buettiker coherent scattering formalism. This formalism usually deals with spin-independent stationary states and,…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
Symplectic tracking of beam particles using point magnets is achieved using a reference orbit made of circular arcs and straight lines that join smoothly with each other. For this choice of the reference orbit, results are given for the…
The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
Within the quantum sine-Gordon model a transmission matrix describing the scattering of a soliton with a fused pair of integrable defects is proposed. The result is consistent with the classical picture of scattering and highlights the…
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…
We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and with a connection for a trivial GL(n,C) bundle over that manifold. To each light ray on the manifold we assign the data of paralel transport along that light ray. It…
We found an exact analytical solution of the wave equation for a transient electromagnetic field of synchrotron radiation in the frequency domain. The exact solution represents the field which consists of the coherent and incoherent…
Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle $\omega =S\theta$ in terms of the incoming angle…
We present a linear coordinate transform to expand the solution of scattering and emission problems into a basis of forward and backward directional vector harmonics. The transform provides intuitive algebraic and geometric interpretations…
An effective Hamiltonian which could model the interaction between a tunneling proton and the conduction electrons of a metal is investigated. A remarkably simple correlation between the motion of the $TLS$-atom and an angular-momentum…
Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems…
Light transport in periodic waveguides coupled to a two-level atom is investigated. By using optical Bloch equations and a photonic modal formalism, we derive semi-analytical expressions for the scattering matrix of one atom trapped in a…
We revise a previous version of this paper proposing a method to transfer emittances from the transverse planes to the longitudinal. It turned out the system showed non-Hamiltonian behavior because the longitudinal component of the…
We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the…
We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a…