Search results for "Explicit formulae"
showing 5 items of 5 documents
Exact solution of generalized Tavis - Cummings models in quantum optics
1996
Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogen…
Insights into Kelvin probe force microscopy data of insulator-supported molecules
2015
We present a detailed analysis and understanding of Kelvin probe force microscopy (KPFM) data for a system of point charges in a vacuum-dielectric tip-sample system. Explicit formulae describing the KPFM signal $\ensuremath{\Delta}V$ are derived for the two KPFM operation modes, namely amplitude modulation and frequency modulation (FM). The formulae allow for a physical interpretation of the resulting KPFM signal, reveal contributing parameters, and especially disclose an additive behavior. We numerically evaluate these equations and show exemplary KPFM slice data for a single point charge. The theoretical analysis is complemented by two-dimensional FM-KPFM maps obtained experimentally on 2…
On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
2005
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arb…
On the numerical evaluation of algebro-geometric solutions to integrable equations
2011
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis no…
Unitary Representations of the Modular and Two-Particle Q-Deformed Toda Chains
2001
The paper deals with the analytic theory of the quantum two-particle q-deformed Toda chains. This is the simplest nontrivial example clarifying the role of the modular duality concept (first discovered by L.Faddeev) in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors and Whittaker functions are presented in terms of the double sine functions.