This paper deals with non-adiabatic processes (i.e.?processes excluded by the adiabatic theorem) from the geometrical (group-theoretical) point of view. An approximate formula for the probabilities of the non-adiabatic transitions is derived in the adiabatic regime for the case when the parameter-dependent Hamiltonian represents a smooth curve in the Lie algebra and the quantal dynamics is determined by the corresponding Lie group evolution operator. We treat the spin precession in a time-dependent magnetic field and the over-barrier reflection problem in a uniform way using the first-order dynamical equations on SU(2) and SU(1.1) group manifolds, respectively. A comparison with analytic solutions for simple solvable models is provided.

A geometrical approach to non-adiabatic transitions in quantum theory: applications to NMR, over-barrier reflection and parametric excitation of quantum oscillator

We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano, and (iii) the use of the thermofield technique for describing a finite temperature reservoir. We recover in this way a number of well-known and some, perhaps, less familiar results. An example of the latter is an ab initio proof that the oscillator relaxes to the mean-force Gibbs state. We find that special care is necessary when comparing the damped oscillator with its undamped counterpart as the former has two distinct natural frequencies, one associated with short time evolution and the other with longer times.

pdf/revisiting-the-damped-quantum-harmonic-oscillator-wwwwrcws.pdf

Revisiting the damped quantum harmonic oscillator

Simple quantum dynamics

A decade ago this magazine devoted a special issue to laser chemistry (see PHYSICS TODAY, November 1980). One of the articles emphasized the importance of time scales in chemical reactions and the possible use of ultrashort lasser pulses to induce chemistry. Over the past 10 years new laser techniques, and gas‐phase and molecular‐beam experiments, have revealed much about the fundamental steps of elementary chemical reactions. These approaches and the tremendous detail they have exposed about the dynamics of chemical reactions are the subject of the present article.

With new laser techniques and with gas phase and molecular beam experiments, it is now possible to determine the ultrafast motion in isolated chemical reactions—chemistry on the 10^(−13)‐second time scale.

/pdf/ultrafast-reaction-dynamics-2pesg52zq9.pdf

Ultrafast Reaction Dynamics

Profile: vive la différence. Doreen Kimura plumbs male and female brains.

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Simple quantum dynamics

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A geometrical approach to non-adiabatic transitions in quantum theory: applications to NMR, over-barrier reflection and parametric excitation of quantum oscillator

Revisiting the damped quantum harmonic oscillator

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Ultrafast Reaction Dynamics

Profile: vive la différence. Doreen Kimura plumbs male and female brains.

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