An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations

Abstract

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.

arXiv comment10 pages

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• Classes of Exactly Solvable Generalized Semi-Classical Rabi Systems
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• Cooling of Many-Body Systems via Selective Interactions
• Landau-Majorana-Stuckelberg-Zener dynamics driven by coupling for two interacting qutrit systems
• Coupling-assisted Landau-Majorana-Stuckelberg-Zener transition in two-interacting-qubit systems
• Dynamics of a harmonic oscillator coupled with a Glauber amplifier
• Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-Stückelberg-Zener transitions
• Lie-algebraic approach to one-dimensional translationally invariant free-fermionic dissipative systems
• New approach to describe two coupled spins in a variable magnetic field
• Quantum-based solution of time-dependent complex Riccati equations