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Superfluid helium-4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose–Einstein condensation must be heavily modified in order to describe it. Bose–Einstein condensation remains, however, fundamental to the superfluid properties of helium-4.
Bose's "error" leads to what is now called Bose–Einstein statistics. Bose and Einstein extended the idea to atoms and this led to the prediction of the existence of phenomena which became known as Bose–Einstein condensate, a dense collection of bosons (which are particles with integer spin, named after Bose), which was demonstrated to exist ...
As a result, at very low energies (or temperatures), a great majority of the bosons in a Bose gas can be crowded into the lowest energy state, creating a Bose–Einstein condensate. Bose and Einstein have established that the statistical properties of a Bose gas are governed by the Bose–Einstein statistics. In Bose–Einstein statistics, any ...
The theory of superfluidity was developed by Soviet theoretical physicists Lev Landau and Isaak Khalatnikov. Superfluidity often co-occurs with Bose–Einstein condensation , but neither phenomenon is directly related to the other; not all Bose–Einstein condensates can be regarded as superfluids, and not all superfluids are Bose–Einstein ...
A fermionic condensate is similar to the Bose–Einstein condensate but composed of fermions. The Pauli exclusion principle prevents fermions from entering the same quantum state, but a pair of fermions can behave as a boson, and multiple such pairs can then enter the same quantum state without restriction.
Bose–Einstein condensation can occur in quasiparticles, particles that are effective descriptions of collective excitations in materials. Some have integer spins and can be expected to obey Bose–Einstein statistics like traditional particles. Conditions for condensation of various quasiparticles have been predicted and observed.
A supersolid is a special quantum state of matter where particles form a rigid, spatially ordered structure, but also flow with zero viscosity.This is in contradiction to the intuition that flow, and in particular superfluid flow with zero viscosity, is a property exclusive to the fluid state, e.g., superconducting electron and neutron fluids, gases with Bose–Einstein condensates, or ...
The thermodynamics of an ideal Bose gas is best calculated using the grand canonical ensemble.The grand potential for a Bose gas is given by: = = (). where each term in the sum corresponds to a particular single-particle energy level ε i; g i is the number of states with energy ε i; z is the absolute activity (or "fugacity"), which may also be expressed in terms of the chemical ...