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The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
Van Hove singularity. A Van Hove singularity is a singularity (non-smooth point) in the density of states (DOS) of a crystalline solid. The wavevectors at which Van Hove singularities occur are often referred to as critical points of the Brillouin zone. For three-dimensional crystals, they take the form of kinks (where the density of states is ...
Scientists. v. t. e. The thermal motions of the atoms or molecules in a gas are allowed to move freely, and the interactions between the two (the gas and the atoms/molecules) can be neglected. In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. [citation needed]
Electronic band structure. In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a ...
The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. [1] It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other ...
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix of two quantum mechanical systems and , to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2×2 and 2×3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where ...
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero, i.e., 0 K (−273.15 °C; −459.67 °F). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which ...
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