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In quantum physics and quantum chemistry, an avoided crossing (AC, sometimes called intended crossing, [1] non-crossing or anticrossing) is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on continuous real parameters cannot become equal in value ("cross") except on a manifold of dimension . [2]
Sketch of an avoided crossing.The graph represents the energies of the system along a parameter z (which may be vary in time). The dashed lines represent the energies of the diabatic states, which cross each other at z c, and the full lines represent the energy of the adiabatic states (eigenvalues of the Hamiltonian).
Simple railway underpass, with Warren truss girder. Most accommodation bridges, in the UK at least, were constructed during the railway building boom of the mid-19th century. [5] British practice avoided level crossings wherever possible, except in the flat parts of the country where building a raised approach to a bridge would be more costly ...
To describe situations in which economic users withdraw resources to secure short-term gains without regard for the long-term consequences, the term tragedy of the commons was coined. For example, forest exploitation leads to barren lands, and overfishing leads to a reduction of overall fish stocks, both of which eventually result in ...
English: Graphical representation of the variation of energy as a function of a spacial coordinate z (which may be varying in time) around an avoided crossing. The dashed lines represent the energy of the diabatic states (which cross each other at z_c) and the full lines represent the energy of the adiabatic states (eigenvalues of the Hamiltonian) which do not cross, appearing to avoid each other.
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In order to be able to observe it, the process would need to be slowed down from femtoseconds to milliseconds. A novel 2023 quantum experiment, involving trapped-ion quantum computer, slowed down interference pattern of a single atom (caused by a conical intersection) by a factor of 100 billion, making a direct observation possible.