Extra manipulations will be necessary to properly re-initialize the hidden pointers in the copy. Such a self-referential object cannot be copied by a simple raw memory copy routine (like memcpy). In order for a special member function to satisfy the above requirements, the class must have a very simplistic structure, it must not require any hidden initializations when an object is being created or destroyed, or any hidden additional internal manipulations when it is being copied.įor example, if class has virtual functions, it will require some extra hidden initializations when objects of this class are being created (initialize virtual method table and such), so the constructor for this class will not qualify as trivial.įor another example, if a class has virtual base classes, then each object of this class might contain hidden pointers that point to other parts of the very same object. Requiring real thought or significant computing power. Non-trivial mean trivial and non -trivial, respectively, from the perspective of a reasonable lender in PFG ’s position, as determined by PFG in its good faith business discretion, and Non-trivial includes a lesser level of significance that does the term material. If you define a constructor yourself, it is considered non-trivial, even if it doesn't do anything, so a trivial constructor must be implicitly defined by the compiler. Often, solutions or examples involving the number zero are considered trivial. For copy-constructor and copy-assignment operator, being "trivial" means literally "be equivalent to simple raw memory copying" (like copy with memcpy). A solution or example that is not trivial. The "straightforward manner" means different thing for different kinds of special member functions.įor a default constructor and destructor being "trivial" means literally "do nothing at all". In simple words a "trivial" special member function literally means a member function that does its job in a very straightforward manner. For example, the non-trivial factors of 8 are 2 and 4, and the nontrivial factors of 36 are. Recently on SO: What is a non-trivial constructor in C++? Concerning the integers, non-trivial factors are factors that are not the original integer or 1. Quick A: All constructors that you define are not trivial. If $C=0$ you have a trivial insulator, and if $C\neq0$ you have a non-trivial or topological insulator.« Prev Next » Quick Q: What is a non-trivial constructor in C++? Where the sum is over occupied bands, the integral is over the entire Brillouin zone, and the integrated quantity is the Berry curvature (analogue of the magnetic field in $\mathbf$ are the Bloch eigenvectors.
So whether the band structure is wound up or not is a topological property, and one can measure it with the topological index, also called a Chern number, defined as This is the interesting part of the topological insulators from the practical standpoint. This unwinding will will have to close the gap near the edge, hence the topologically protected edge states. This manifests itself in the fact that when you put the two in contact, the curled up band structure of the TI must unwind so that the band structure fits the one in the ordinary insulator. The twisting of the band structure is what the phrase non-trivial topology is referring to an analogy would be the way a Mobius strip is a twisted version of an ordinary strip. This twisting is protected by time-reversal invariance, and although still an insulator, the resulting phase is topologically different from an ordinary insulator. Now if you have a material with a sufficiently strong spin-orbit interaction for example ( not essential for the effect, but historically important approach), this can cause the energy bands above and below the gap to swap places. These states are localized at the edge however they are not robust, and as such not particularly useful. In this trivial insulator, although the bulk is insulating, there is possibility of for example dangling bonds introducing states that lie in an energy gap. No (small) electric field can perturb them enough to cause motion, and thus you have an insulator. adjective 0 0 (mathematics) Of, relating to, or being an expression in which at least one variable is not equal to zero. adjective 1 0 Not trivial of some importance.
adjective 1 0 (computing) Needing significant computing power to solve intractable. Energy bands (and gaps) appear as the result of hybridization of many atomic orbitals, and for a specific filling you can end up with the top most pair of bands being either entirely filled (valence band) or entirely empty (conduction band). non trivial See word origin Frequency: (mathematics) Having at least one non-zero variable. Kronig-Penney model) was the explanation of the insulating state of matter. One of the early triumphs of QM (through e.g.
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