Structure, dynamics and spectroscopy of single molecules: A challenge to quantum mechanics
type: Item
instance of: scholarly article
title: Structure, dynamics and spectroscopy of single molecules: A challenge to quantum mechanics
zbMATH Open document ID: 0883.92030
DOI: 10.1007/BF01164662
author: A. Amann
publication date: 1997-07-17T00:00:00Z
review text: Spectroscopy of an ensemble of molecules gives information about (differences of) eigenvalues of the molecular Hamiltonian and ``transition probabilities''. All this information is encoded in the thermal non-pure state with density operator \(D_\beta\). No information is offered on the pure states of the actual individual molecules. In response theory, for example, a spectroscopic experiment is described by an input-output equation which depends only on the thermal density operator \(D_\beta\) and not on a particular decomposition of \(D_\beta\) into pure states. Spectroscopy of single molecules gives more information than just (differences of) eigenvalues of the molecular Hamiltonian and transition probabilities. One has, for example, an additional stochastic (``migrating'') behaviour of lines, which is not reconcilable with response theory. Also, the derivation of dissipative single-molecule behaviour cannot be done by usual response theory, since expectation values (of the output observable) with respect to a pure state cannot be measured without perturbing this pure state itself. Only averaging over the stochastic behaviour of many molecules results in the regular dynamics used in response theory. Here ``single-molecule spectroscopy'' is always meant to refer to the quantum joint system \{single molecule \& environment\}, where the environment can, for example, consist of the matrix in which the single molecule is embedded or the quantum radiation field. The question ``What is the influence of the molecular environment?'' will be an important background for the discussions in this paper. Single molecule-spectroscopy should finally give answers to questions like the following always referring to pure states of individual molecules and not to the thermal non-pure state \(D_\beta\): Superpositions of left- and right-handed states of a chiral molecule seem to be unstable under small external perturbations. What is the time necessary to decay into either a left- or a…
Mathematics Subject Classification ID: 92E10
Mathematics Subject Classification ID: 81V55
Mathematics Subject Classification ID: 92E99
zbMATH DE Number: 1036976
zbMATH Keywords: spectroscopy of single molecules
zbMATH Keywords: superpositions
zbMATH Keywords: external perturbations
zbMATH Keywords: stochastic dynamics
zbMATH Keywords: molecular Hamiltonian
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01164662
OpenAlex ID: W2044743365
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 1036976