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Quantum Phases
Quantum phases are quantum states of matter at zero temperature. Even at zero temperature a quantum-mechanical system has quantum fluctuations and therefore can still support phase transitions. As a physical parameter is varied, quantum fluctuations can drive a phase transition into a different phase of matter. An example of a canonical quantum phase transition is the well-studied Superconductor Insulator Transition in disordered thin films which separates two quantum phases having different symmetries. Quantum magnets provide another example of QPT. The discovery of new quantum phases is a pursuit of many scientists. These phases of matter exhibit properties and symmetries which can potentially be exploited for technological purposes and the benefit of mankind. The difference between these states and classical states of matter is that classically, materials exhibit different phases which ultimately depends on the change in temperature and/or density or some other macroscopic proper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta''. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics. Overview Phase space coordinates (p,q) and Hamiltonian H Let (M, \mathcal L) be a mechanical system with the configuration space M and the smooth Lagrangian \mathcal L. Select a standard coordinate system (\boldsymbol,\boldsymbol) on M. The quantities \textstyle p_i(\boldsymbol,\boldsymbol,t) ~\stackrel~ / are called ''momenta''. (Also ''generalized momenta'', ''conjugate momenta'', and ''canonical momenta''). For a time instant t, the Legendre transformat ... [...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 liquid changes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transitions
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition At the phase transition point for a substance, for instance the boiling point, the two phases involved - liquid and vapor, have identic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Critical Point
A quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero. A quantum critical point is typically achieved by a continuous suppression of a nonzero temperature phase transition to zero temperature by the application of a pressure, field, or through doping. Conventional phase transitions occur at nonzero temperature when the growth of random thermal fluctuations leads to a change in the physical state of a system. Condensed matter physics research over the past few decades has revealed a new class of phase transitions called quantum phase transitions which take place at absolute zero. In the absence of the thermal fluctuations which trigger conventional phase transitions, quantum phase transitions are driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle. Overview Within the class of phase transitions, there are two main categories: at a ''first-order phase t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Phases
Quantum phases are quantum states of matter at zero temperature. Even at zero temperature a quantum-mechanical system has quantum fluctuations and therefore can still support phase transitions. As a physical parameter is varied, quantum fluctuations can drive a phase transition into a different phase of matter. An example of a canonical quantum phase transition is the well-studied Superconductor Insulator Transition in disordered thin films which separates two quantum phases having different symmetries. Quantum magnets provide another example of QPT. The discovery of new quantum phases is a pursuit of many scientists. These phases of matter exhibit properties and symmetries which can potentially be exploited for technological purposes and the benefit of mankind. The difference between these states and classical states of matter is that classically, materials exhibit different phases which ultimately depends on the change in temperature and/or density or some other macroscopic proper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
