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Superconductor–insulator Transition
The superconductor–insulator transition is an example of a quantum phase transition, whereupon tuning some parameter in the Hamiltonian, a dramatic change in the behavior of the electrons occurs. The nature of how this transition occurs is disputed, and many studies seek to understand how the order parameter, \Psi =\Delta \exp(i\theta), changes. Here \Delta is the amplitude of the order parameter, and \theta is the phase. Most theories involve either the destruction of the amplitude of the order parameter - by a reduction in the density of states at the Fermi surface, or by destruction of the phase coherence; which results from the proliferation of vortices. Destruction of superconductivity In two dimensions, the subject of superconductivity becomes very interesting because the existence of true long-range order is not possible. In the 1970s, J. Michael Kosterlitz and David J. Thouless (along with Vadim Berezinski) showed that a different kind of long-range order could exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Phase Transition
In physics, a quantum phase transition (QPT) is a phase transition between different quantum phases ( phases of matter at zero temperature). Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physical parameter—such as magnetic field or pressure—at absolute zero temperature. The transition describes an abrupt change in the ground state of a many-body system due to its quantum fluctuations. Such a quantum phase transition can be a second-order phase transition. Quantum phase transitions can also be represented by the topological fermion condensation quantum phase transition, see e.g. strongly correlated quantum spin liquid. In case of three dimensional Fermi liquid, this transition transforms the Fermi surface into a Fermi volume. Such a transition can be a first-order phase transition, for it transforms two dimensional structure ( Fermi surface) into three dimensional. As a result, the topological charge of Fermi li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (quantum Mechanics)
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's ''energy spectrum'' or its set of ''energy eigenvalues'', is the set of possible outcomes obtainable from a measurement of the system's total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory. The Hamiltonian is named after William Rowan Hamilton, who developed a revolutionary reformulation of Newtonian mechanics, known as Hamiltonian mechanics, which was historically important to the development of quantum physics. Similar to vector notation, it is typically denoted by \hat, where the hat indicates that it is an operator. It can also be written as H or \check. Introduction The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Surface
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic band structure, electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology. Theory Consider a Spin (physics), spin-less ideal Fermi gas of N particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy \epsilon_i is given by : \langle n_i\rangle =\frac, where * \left\langle n_i\right\rangle is the mean occupation number of the ith state * \epsilon_i is the kinetic energy of the ith state * \mu is the chemical potential (at zero temperature, this is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mermin–Wagner Theorem
In quantum field theory and statistical mechanics, the Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions . Intuitively, this theorem implies that long-range fluctuations can be created with little energy cost, and since they increase the entropy, they are favored. This preference is because if such a spontaneous symmetry breaking occurred, then the corresponding Goldstone bosons, being massless, would have an infrared divergent correlation function. The absence of spontaneous symmetry breaking in dimensional infinite systems was rigorously proved by David Mermin and Herbert Wagner (physicist), Herbert Wagner (1966), citing a more general unpublished proof by Pierre Hohenberg (published later in 1967) in statistical mechanics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
