Structure, dynamics and spectroscopy of single molecules: A challenge to quantum mechanics
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 right-handed state? What is the stochastic dynamics for such a decay? Similarly, superpositions of states of different molecular isomers (having the same Hamiltonian and the same thermal state) seem to be unstable under external perturbations. Or superpositions of states of a magnet having positive and negative permanent magnetization seem to be unstable under external perturbations. What is the transition time between such unstable superpositions and stable states? The latter are usually not eigenstates of the molecular Hamiltonian in question. Which is the observable measured in a single-molecule spectroscopic experiment? The Hamiltonian or the dipole moment operator? Does an arbitrary initial state become an eigenstate of the molecular Hamiltonian (Bohr's point of view) or an eigenstate of the dipole moment operator (von Neumann's point of view)?
scientific article; zbMATH DE number 1036976
scientific article