Spin systems Definition and 7 Discussions

Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies. For photons, spin is the quantum-mechanical counterpart of the polarization of light; for electrons, the spin has no classical counterpart.The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The existence of the electron spin can also be inferred theoretically from spin–statistics theorem and from the Pauli exclusion principle—and vice versa, given the particular spin of the electron, one may derive the Pauli exclusion principle.
Spin is described mathematically as a vector for some particles such as photons, and as spinors and bispinors for other particles such as electrons. Spinors and bispinors behave similarly to vectors: they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of a given kind have the same magnitude of spin angular momentum, though its direction may change. These are indicated by assigning the particle a spin quantum number.The SI unit of spin is the same as classical angular momentum (i.e. N·m·s or kg·m2·s−1). In practice, spin is given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant ħ, which has the same dimensions as angular momentum, although this is not the full computation of this value. Very often, the "spin quantum number" is simply called "spin". The fact that it is a quantum number is implicit.
Wolfgang Pauli in 1924 was the first to propose a doubling of the number of available electron states due to a two-valued non-classical "hidden rotation". In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested the simple physical interpretation of a particle spinning around its own axis, in the spirit of the old quantum theory of Bohr and Sommerfeld. Ralph Kronig anticipated the Uhlenbeck–Goudsmit model in discussion with Hendrik Kramers several months earlier in Copenhagen, but did not publish. The mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it.

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  1. W

    Coding of Spin Spin correlation function

    I tried to code spinoperators who act like $S_x^iS_x^j$ (y and z too) and to apply them to the states, which works fine. I am not sure about how to code the expectation value in the product Space. Has anyone pseudo Code to demonstrate that?
  2. Narayanan KR

    Interesting Links Between Faraday's EM Induction and EPR

    Imagine a magnet moving up and down so that its flux 'B' cuts the copper rod to produce an alternating emf, suppose if the movement is fast enough such that its frequency equals to the electron spin resonance frequency given by F = B x 2.8 Mhz per gauss, neglecting skin effect, more copper...
  3. W

    A Ground state of the one-dimensional spin-1/2 Ising model

    Hi, I know that the ground state of the spin-1/2 Ising model is the ordered phase (either all spin up or all spin down). But how do I actually go about deriving this from say the one-dimensional spin hamiltonian itself, without having to solve system i.e. finding the partition function? $$...
  4. Narayanan KR

    A Right Hand Rule in NMR and EPR?

  5. Llukis

    A Experimental point of view of this Hamiltonian

    Dear everybody, I am involved with a system of two spins and I ended up with the following Hamiltonian: $$H_c(t) = W\sin(2J_+ t) \big( \mathbb{1} \otimes \sigma_z - \sigma_z \otimes \mathbb{1}\big) + W \cos(2J_+ t) \big( \sigma_y \otimes \sigma_x - \sigma_x \otimes \sigma_y \big) \: ,$$ where...
  6. S

    A Can Fluctuation-Dissipation Theorem Apply to Magnetic Forces

    Let's say I have multiple spin systems (atoms in a protein) in a solution of water and the spin systems are all producing a magnetic field \mathrm{B_{loc}} that affects nearby spin systems. Will the fluctuation-dispersion theorem apply to the force generated by a spin's magnetic field...
  7. pinu

    Good references for quantum spin chains

    Hi folks, I work in theoretical high energy physics. Recently I got interested in condensed matter theory. But each time I see some spin system I get scared thinking another one must be waiting for me! Can some one suggest me some reference(s) where these spin chains, specially those which are...