Elements of Modern Physics
246
There is no widely accepted theory to explain their properties. Cuprate
superconductors (and other unconventional superconductors) differ in many
important ways from conventional superconductors, such as elemental mercury
or lead, which are adequately explained by the BCS theory. There also has been
much debate as to high-temperature superconductivity coexisting with magnetic
ordering in YBCO, iron-based superconductors, several other exotic
superconductors, and the search continues for other families of materials. HTS
are Type-II superconductors, which allow magnetic fields to penetrate their
interior in quantized units of flux, meaning that much higher magnetic fields
are required to suppress superconductivity. The layered structure also gives a
directional dependence to the magnetic field response.
Several commercial applications of high temperature superconducting
materials have been realized. For example, superconducting materials are finding
use as magnets in magnetic resonance imaging, magnetic levitation, and
Josephson junctions. (The most used material for power cables and magnets is
BSCCO (bismuth strontium calcium copper oxide).
(Source: Wikipedia)
7.7 EXAMPLES
In this section, some examples which illustrate and extend the main ideas
quantum statistics are discussed.
Example 1
Consider the statistical distributions of two identical particles among three sets
of states g 1 = 1, g 2 = 2, g 3 = 1 with energies 0, ε, 2ε, respectively (both the g 2
states have energy ε). The populations of these sets are (n 1 , n 2 , n 3 ). The most
probable distribution with total energy 2ε has to be found.
Distinguishable particles: The allowed population distributions are:
1. (1, 0, 1) has two distinguishable arrangements (A, 0, B), (B, 0, A)
2. (0, 2, 0) with four possible distinguishable arrangements (AB, 0), (0, A, B),
(A, B) and (B, A) in the g 2 set, where A and B represent the two
distinguishable particles.
Thus, the second distribution is twice as probable as the first distribution.
Bosons: For bosons, the (1, 0, 1) distribution has only one distinguishable
arrangement while (0, 2, 0) has three distinguishable arrangements (AA, 0),
(A, A) (0, AA) in the g 2 set. Therefore, the (0, 2, 0) is three times as probable as
the (1, 0, 1) distribution.
Fermions: For fermions, of the two distribution (1, 0, 1) and (0, 2, 0), each
has only one possible distinguishable arrangement (it should be recalled that
246
There is no widely accepted theory to explain their properties. Cuprate
superconductors (and other unconventional superconductors) differ in many
important ways from conventional superconductors, such as elemental mercury
or lead, which are adequately explained by the BCS theory. There also has been
much debate as to high-temperature superconductivity coexisting with magnetic
ordering in YBCO, iron-based superconductors, several other exotic
superconductors, and the search continues for other families of materials. HTS
are Type-II superconductors, which allow magnetic fields to penetrate their
interior in quantized units of flux, meaning that much higher magnetic fields
are required to suppress superconductivity. The layered structure also gives a
directional dependence to the magnetic field response.
Several commercial applications of high temperature superconducting
materials have been realized. For example, superconducting materials are finding
use as magnets in magnetic resonance imaging, magnetic levitation, and
Josephson junctions. (The most used material for power cables and magnets is
BSCCO (bismuth strontium calcium copper oxide).
(Source: Wikipedia)
7.7 EXAMPLES
In this section, some examples which illustrate and extend the main ideas
quantum statistics are discussed.
Example 1
Consider the statistical distributions of two identical particles among three sets
of states g 1 = 1, g 2 = 2, g 3 = 1 with energies 0, ε, 2ε, respectively (both the g 2
states have energy ε). The populations of these sets are (n 1 , n 2 , n 3 ). The most
probable distribution with total energy 2ε has to be found.
Distinguishable particles: The allowed population distributions are:
1. (1, 0, 1) has two distinguishable arrangements (A, 0, B), (B, 0, A)
2. (0, 2, 0) with four possible distinguishable arrangements (AB, 0), (0, A, B),
(A, B) and (B, A) in the g 2 set, where A and B represent the two
distinguishable particles.
Thus, the second distribution is twice as probable as the first distribution.
Bosons: For bosons, the (1, 0, 1) distribution has only one distinguishable
arrangement while (0, 2, 0) has three distinguishable arrangements (AA, 0),
(A, A) (0, AA) in the g 2 set. Therefore, the (0, 2, 0) is three times as probable as
the (1, 0, 1) distribution.
Fermions: For fermions, of the two distribution (1, 0, 1) and (0, 2, 0), each
has only one possible distinguishable arrangement (it should be recalled that