Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Bose–Einstein statistics
Summary
In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles can be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose.
The Bose–Einstein statistics applies only to the particles not limited to single occupancy of the same state – that is, particles that do not obey the Pauli exclusion principle restrictions. Such particles have integer values of spin and are named bosons. Particles with half-integer spins are called fermions and obey Fermi-Dirac statistics.
At low temperatures, bosons behave differently from fermions (which obey the Fermi–Dirac statistics) in a way that an unlimited number of them can "condense" into the same energy state. This apparently unusual property also gives rise to the special state of matter – the Bose–Einstein condensate. Fermi–Dirac and Bose–Einstein statistics apply when quantum effects are important and the particles are "indistinguishable". Quantum effects appear if the concentration of particles satisfies
where N is the number of particles, V is the volume, and nq is the quantum concentration, for which the interparticle distance is equal to the thermal de Broglie wavelength, so that the wavefunctions of the particles are barely overlapping.
Fermi–Dirac statistics applies to fermions (particles that obey the Pauli exclusion principle), and Bose–Einstein statistics applies to bosons.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related lectures (2)
Diagonalizability of Linear Transformations
Explores the conditions and implications of diagonalizability of linear transformations, including eigenvectors, eigenvalues, and distinct matrices.
Convergence of Series
Covers convergence criteria, geometric series, and Taylor series applications.