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A macroscopic quantum state is a state of matter in which macroscopic properties, such as mechanical motion, [1] thermal conductivity, electrical conductivity [2] and viscosity, can be described only by quantum mechanics rather than merely classical mechanics. [3]
Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect, Josephson effect and topological order.
As such, condensation can be associated with phase transition, and the macroscopic occupation of the state is the order parameter. Bose–Einstein condensate was first predicted, generally, in 1924–1925 by Albert Einstein , [ 2 ] crediting a pioneering paper by Satyendra Nath Bose on the new field now known as quantum statistics . [ 3 ]
Measurements, macroscopic operations on quantum states, filter the state. [1]: 196 Whatever the input quantum state might be, repeated identical measurements give consistent values. For this reason, measurements 'prepare' quantum states for experiments, placing the system in a partially defined state.
Quantum anomalous Hall state: A state which has a quantized Hall resistance even in the absence of external magnetic field. Topological insulator: a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor. Fractional Chern insulator: A generalization of fractional quantum Hall state to ...
This leads to quantum systems expressed in the Dirac bra-ket notation: [1]: 245 | = | + | This approach is especially effect for systems like quantum spin with no classical coordinate analog. Such shorthand notation is very common in textbooks and papers on quantum mechanics and superposition of basis states is a fundamental tool in quantum ...
A quantum state can be an eigenvector of an observable, in which case it is called an eigenstate, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. More generally, a quantum state will be a linear combination of the eigenstates, known as a quantum superposition.
In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltage U that controls the chemical potential of the island.