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In quantum chemistry, size consistency and size extensivity are concepts relating to how the behaviour of quantum-chemistry calculations changes with the system size. Size consistency (or strict separability) is a property that guarantees the consistency of the energy behaviour when interaction between the involved molecular subsystems is nullified (for example, by distance).
Some intensive properties do not apply at very small sizes. For example, viscosity is a macroscopic quantity and is not relevant for extremely small systems. Likewise, at a very small scale color is not independent of size, as shown by quantum dots, whose color depends on the size of the "dot".
The separability problem is a subject of current research. A separability criterion is a necessary condition a state must satisfy to be separable. In the low-dimensional ( 2 X 2 and 2 X 3 ) cases, the Peres-Horodecki criterion is actually a necessary and sufficient condition for separability.
The definition of entanglement witnesses and the Choi–Jamiołkowski isomorphism that links PnCP maps to entanglement witnesses in the bipartite case can also be generalized to the multipartite setting. We therefore get a separability condition from entanglement witnesses for multipartite states: the state …
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane ) by thinking of one set of points as being colored blue and the other set of points as being colored red.
Separability may refer to: Mathematics. Separable algebra, a generalization to associative algebras of the notion of a separable field extension;
While the above ansatz for the wave function itself has no natural truncation, however, for other properties, such as energy, there is a natural truncation when examining expectation values, which has its basis in the linked- and connected-cluster theorems, and thus does not suffer from issues such as lack of size extensivity, like the ...
In statistical process control (SPC), the ¯ and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process. [1]