Related papers: Quasi-Lie schemes and Emden--Fowler equations
Using the principles of the ETH - Approach to Quantum Mechanics we study fluorescence and the phenomenon of ``quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
We investigate quantum integrals of motion in the sine-Gordon, Zhiber-Shabat and similar systems. When the coupling constants in these models take special values a new quantum symmetry appears. In those cases, correlation functions can be…
Existence of nodal (i.e., sign changing) solutions and constant sign solutions for quasilinear elliptic equations involving convection-absorption terms are presented. A location principle for nodal solutions is obtained by means of constant…
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present…
Mathematical analysis of mass action models of large complex chemical systems is typically only possible if the models are reduced. The most common reduction technique is based on quasi-steady state assumptions. To increase the accuracy of…
The dynamics of a quantum system following a sudden, highly non-adiabatic change of its control parameter (quantum quench) is studied with quasiclassical techniques. Recent works have shown, using exact quantum mechanical approach, that…
A possible scheme of q-deformation, which was recently developed by the present authors, is reviewed by stressing the starting idea.
The experimental violation of Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
The Loschmidt echo (LE) is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to…
I present time-dependent analytical solutions of quasi-steady shocks with cooling, where quasi-steady shocks are objects composed of truncated steady-state models of shocks at any intermediate time. I compare these solutions to simulations…
A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
Modular pairs of some second order q-difference equations are considered. These equations may be interpreted as a quantum mechanics of a sort of hyperelliptic pendulum. It is shown the quantization of a spectrum may be provided by the…
The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…