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Register a new userRole of guiding center in Landau level system and mechanical and pseudo orbital angular momenta
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There is an interesting but not so popular quantity called pseudo orbital angular momentum (OAM) in the Landau-level system, besides the well-known canonical and mechanical OAMs. The pseudo OAM can be regarded as a gauge-invariant extension of the canonical OAM, which is formally gauge invariant and reduces to the canonical OAM in a certain gauge. Since both of the pseudo OAM and the mechanical OAM are gauge invariant, it is impossible to judge which of those is superior to the other solely from the gauge principle. However, these two OAMs have totally different physical meanings. The mechanical OAM shows manifest observability and clear correspondence with the classical OAM of the cyclotron motion. On the other hand, we demonstrate that the standard canonical OAM as well as the pseudo OAM in the Landau problem are the concepts which crucially depend on the choice of the origin of the coordinate system. We try to reveal the relation between the pseudo OAM and the mechanical OAM as well as their observability by paying special attention to the role of guiding-center operator in the Landau problem.
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One intriguing issue in the nucleon spin decomposition problem is the existence of two types of decompositions, which are representably characterized by two different orbital angular momenta (OAMs) of quarks. The one is the manifestly gauge-invariant mechanical OAM, while the other is the so-called gauge-invariant canonical (g.i.c.) OAM, the concept of which was introduced by Chen et al. To get a deep insight into the difference of these two decompositions, it is therefore vitally important to understand the the physical meanings of the above two OAMs correctly. Also to be clarified is the implication of the gauge symmetry that is immanent in the concept of g.i.c. OAM. We find that the famous Landau problem provides us with an ideal tool to answer these questions owing to its analytically solvable nature. After deriving a complete relation between the standard eigen-functions of the Landau Hamiltonian in the Landau gauge and in the symmetric gauge, we try to unravel the physics of the the canonical OAM and the mechanical OAM, by paying special attention to their gauge-dependence. We also argue that, different from the mechanical OAM of the electron, the canonical OAM or its gauge-invariant version would not correspond to any direct observables at least in the Landau problem. Also briefly discussed is the uniqueness or non-uniqueness problem of the nucleon spin decomposition, which arises from the arbitrariness in the definition of the so-called physical component of the gauge field.
This paper analyzes the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre--Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.
We report the experimental preparation of optical superpositions of high orbital angular momenta(OAM). Our method is based on the use of spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices. We demonstrate the surprising performance of a traditional Mach-Zehnder interferometer with one inserted Dove prism to identify these superposed twisted lights, where the high OAM numbers as well as their possible superpositions can be inferred directly from the interfered bright multiring lattices. The possibility of present scheme working at photon-count level is also shown using an electron multiplier CCD camera. Our results hold promise in high-dimensional quantum information applications when high quanta are beneficial.
We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with $Z_4$ noise, and the signal-to-noise is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a $16^3 times 24$ quenched lattice at $beta = 6.0$ for Wilson fermions with $kappa=0.154, 0.155$, and $0.1555$ which correspond to pion masses at $650, 538$, and $478$~MeV, respectively. The chirally extrapolated $u$ and $d$ quark momentum/angular momentum fraction is found to be $0.64(5)/0.70(5)$, the strange momentum/angular momentum fraction is $0.024(6)/0.023(7)$, and that of the glue is $0.33(6)/0.28(8)$. The previous study of quark spin on the same lattice revealed that it carries a fraction of $0.25(12)$ of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes $0.47(13)$ of the proton spin with almost all of it coming from the disconnected insertions.
As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron. The eigen-energies of the system depend only on the first quantum number $n$, and the second quantum number $m$ does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a {it gauge-variant} quantity, and observation of a gauge-variant quantity would contradict a fundamental principle of physics called the {it gauge principle}. In recent researches, however, Bliohk et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly non-trivial $m$-dependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number $m$ in the Landau eigen-states corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number $m$ in the Landau eigen-states was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the {it particle-like} aspect but also to the {it wave-like} aspect of the Landau electron.
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