Search results for "Unitary evolution."
showing 3 items of 3 documents
Target states and control of molecular alignment in a dissipative medium
2006
Received 17 August 2006; published 14 November 2006We investigate how and to what extent molecular alignment can be controlled in a dissipative medium by asuitable train of laser pulses. We focus primarily on the extension of a scheme of control originally constructedfor unitary evolution. The procedure is applied to control the alignment of CO molecules in an Ar gas. Theparameters of the train of kicks—i.e., the intensity of each kick and the delay between them—are eitherobtained by a systematic procedure maximum strategy or by optimization by evolutionary algorithms.DOI: 10.1103/PhysRevA.74.053411 PACS number s : 32.80.Lg, 33.80. b, 42.50.Hz
Analytically solvable Hamiltonians for quantum two-level systems and their dynamics
2014
A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented. In this method, a time-dependent Hamiltonian and the resulting unitary evolution operator are connected through an arbitrary function of time, furnishing us with new analytically solvable cases. The method is surprisingly simple, direct, and transparent and is applicable to a wide class of two-level Hamiltonians with no involved constraint on the input function. A few examples illustrate how the method leads to simple solvable Hamiltonians and dynamics.
An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations
2017
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.