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The mystery of the Fermi energy: Why does motion exist at absolute zero?
In the field of physics, there are many mysterious concepts, and "Fermi energy" is one of them. It not only affects the properties of metals and superconductors, but also plays an important role in cryogenic liquids and nuclear physics. This article will take you to explore the mysteries behind this theory and connect it to movement at absolute zero.
"At absolute zero, particles can continue to move, challenging our basic understanding of the relationship between energy and motion."
According to the definition in quantum mechanics, the Fermi energy is the difference between the highest energy state and the lowest energy state occupied by all non-interacting fermions (such as electrons, protons and neutrons) at absolute zero. . This concept plays a key role in many phenomena, especially in solid-state physics.
To understand Fermi energy, we must first recognize the Pauli exclusion principle followed by fermions. This principle states that two fermions cannot occupy the same quantum state. With this knowledge, scientists were able to deduce that when we fill up the energy states of a system, the highest occupied state is the source of the Fermi energy.
"Even though the Fermi gas is cooled to near absolute zero, we can still see the rapid motion of particles."
In an ideal non-interacting Fermi gas, we can take an empty system and add particles one by one to fill the unoccupied lowest energy states. Once all particles are filled, the kinetic energy of the highest occupied state is defined as the Fermi energy. Due to this phenomenon, fermions continue to move even in the coldest environments, which also explains why particles still have kinetic energy at "absolute zero".
Further analysis shows that the Fermi energy has found significant applications in metals. In the free electron model, the electrons in the metal can be viewed as a Fermi gas. The number density of conductive electrons in metals is generally between 1028 and 1029, which also means that their Fermi energies are usually between 2 and 10 electron volts.
"The Fermi energy of a white dwarf is about 0.3 MeV, which shows the important effect of high density on the behavior of electrons."
In addition to metals, white dwarfs also demonstrate the influence of Fermi energy in the universe. The mass of a white dwarf is usually comparable to that of the sun, but its radius is only one percent of that of the sun. This high-density state causes the electrons to no longer be fixed around a single atomic nucleus, but to form a degenerate electron gas. In such an environment, the Fermi energy can reach a value of 0.3 MeV.
In nuclear physics, something similar happens to the nucleons in the nucleus of an atom. Since the radius of an atomic nucleus can vary, the typical value of its Fermi energy is about 38 MeV, which is of great significance for understanding the stability of the atomic nucleus.
"The definition of Fermi temperature is to relate the Fermi energy to the Boltzmann constant. Its significance lies in comparing the mutual influence of thermal effects and quantum effects."
Here, we should also note the existence of the concept of Fermi temperature. The Fermi temperature is defined as the ratio of the Fermi energy to the Boltzmann constant. This temperature index can be regarded as the relative influence of thermal effects and quantum effects caused by Fermi statistics at this temperature. For metals, this temperature is usually much higher than room temperature, which allows the metal to maintain its conductive properties under common conditions.
Combining the above observations, the Fermi energy not only reveals the motion characteristics of particles at low temperatures, but also provides profound insights into many physical phenomena. Today's scientific research on quantum fluids, solid-state physics, and astronomical phenomena continues to rely on a deeper understanding of this concept. So, in this context, are there other physical concepts that we have not considered that have such a profound influence?
