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- W4211020123 endingPage "36" @default.
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- W4211020123 abstract "According to the postulates of quantum mechanics, a quantum system is completely specified by the state $$vert psi left (tright )rangle$$ whose evolution is provided by the Schrödinger equation 1.1 $$begin{array}{rlrlrl} ihslash frac{partial } {partial t}vert psi left (tright )rangle & =hat{ H}vert psi left (tright )rangle. &end{array}$$ Here, $$hat{H}$$ is the Hamiltonian describing the interactions of all of the microscopic degrees of freedom in the system under study. Unfortunately, the dimension of the Hilbert space in which the state $$vert psi left (tright )rangle$$ lives grows exponentially with the number of constituents in a many-body system, rendering Eq. (1.1) essentially useless for extracting physically relevant information from systems with more than a few particles. Practical concerns aside, there is a more fundamental reason why Eq. (1.1) does not enable us to answer all relevant questions in many-body physics. This reason is put succinctly by P.W. Anderson in his now famous article “More is different” [1] when he says that “The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.” That is to say, many-body systems can display very different, emergent, behavior from their microscopic constituents. In particular, the ground state of a many-body system need not have the same symmetry as its governing Hamiltonian due to the phenomenon of spontaneous symmetry breaking." @default.
- W4211020123 created "2022-02-13" @default.
- W4211020123 creator A5049902273 @default.
- W4211020123 date "2015-01-01" @default.
- W4211020123 modified "2023-10-16" @default.
- W4211020123 title "General Introduction" @default.
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