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From the quantum statistics of a completely degenerate electron gas (all the lowest quantum states are occupied), the pressure and the density of a white dwarf are calculated in terms of the maximum electron momentum standardized as = /, with pressure = and density =, where
The free electron model of metals derives their physical properties by considering the conduction electrons alone as a degenerate gas, while the majority of the electrons are regarded as occupying bound quantum states. This solid state contrasts with degenerate matter that forms the body of a white dwarf, where most of the electrons would be ...
In white dwarf stars, the positive nuclei are completely ionized – disassociated from the electrons – and closely packed – a million times more dense than the Sun. At this density gravity exerts immense force pulling the nuclei together. This force is balanced by the electron degeneracy pressure keeping the star stable. [4]
A quantum Hall state gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow. A quantum spin Hall state is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat. This is a derivation of the Quantum Hall state of matter.
This is a derivative of the quantum Hall state of matter. Quantum anomalous Hall state: A state which has a quantized Hall resistance even in the absence of external magnetic field. Topological insulator: a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor.
The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is =, which means that its energy density decreases as =, where is a volume.In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.
The demonstration by Subrahmanyan Chandrasekhar that white dwarf stars have a maximum allowed mass because of the exclusion principle caused a revolution in the theory of star evolution. [44] Degenerate matter includes the part of the universe that is made up of neutron stars and white dwarfs.
As the quantum concentration depends on temperature, most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit, unless they also have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration.