Propagation of Vortex Electron Wave Functions in a Magnetic Field

The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent prefactor. Hence adding OAM and propagating can in this case be replaced by first propagating then adding OAM. Also, the results shown provide an explicit illustration of the fact that the gyromagnetic ratio for OAM is unity. We also propose a novel version of the Bohm-Aharonov effect using vortex electron beams.Comment: 14 pages, 2 figures, submitted to Phys Rev

Ideal Linear Chain Polymers with Fixed Angular Momentum

The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This result is then compared to simulations done with a large number of non-interacting rigid links at fixed angular momentum. The simulation agrees with the theory up to finite size corrections. The simulations are also used to investigate the anisotropic nature of a spinning polymer. We find universal scaling of the polymer size along the direction of the angular momentum, as a function of rescaled angular momentum.Comment: 7 pages, 3 figure

Velocity acquired by an electron in a finite electric field in a polar crystal

The expectation value of the steady-state velocity acquired by an electron interacting with the longitudinal, optical phonons of a polar crystal in a finite electric field is analyzed quantum mechanically for arbitrary coupling strength, field strength, and temperature. The rate of loss of momentum by an electron drifting through the crystal in the applied field is expressed in a form in which the lattice coordinates (the phonons) have been eliminated exactly by path-integral methods. This expression is then evaluated by a path-integral approach similar to that used to calculate the impedance of electrons in polar crystals. We present numerical calculations of field (loss of energy per unit distance) versus velocity for three coupling strengths using the Fröhlich polaron model. In a single curve, all the expected phenomena appear, including a threshold field for producing hot electrons and a decreasing rate of energy loss with velocity for very fast electrons. Using only the experimentally measured values of the reststrahlen energy and the static and optical dielectric constants, we find an energy loss of 0.025 eV/Å for electrons near the threshold in Al2O3, which compares favorably with the experimental value of about 0.03 eV/Å. We conclude that optical-phonon scattering can indeed produce the high rate of energy loss that is present in tunnel-cathode structures

Feynman Lectures on the Strong Interactions

These twenty-two lectures, with exercises, comprise the extent of what was meant to be a full-year graduate-level course on the strong interactions and QCD, given at Caltech in 1987-88. The course was cut short by the illness that led to Feynman's death. Several of the lectures were finalized in collaboration with Feynman for an anticipated monograph based on the course. The others, while retaining Feynman's idiosyncrasies, are revised similarly to those he was able to check. His distinctive approach and manner of presentation are manifest throughout. Near the end he suggests a novel, nonperturbative formulation of quantum field theory in $D$ dimensions. Supplementary material is provided in appendices and ancillary files, including verbatim transcriptions of three lectures and the corresponding audiotaped recordings.Comment: 98 pages, 117 figures; Feynman's personal course notes and audio files for lectures 15, 17, 18 available at http://www.physics.mcgill.ca/~jcline/Feynman

Feynman Lectures on the Strong Interactions

These twenty-two lectures, with exercises, comprise the extent of what was meant to be a full-year graduate-level course on the strong interactions and QCD, given at Caltech in 1987-88. The course was cut short by the illness that led to Feynman's death. Several of the lectures were finalized in collaboration with Feynman for an anticipated monograph based on the course. The others, while retaining Feynman's idiosyncrasies, are revised similarly to those he was able to check. His distinctive approach and manner of presentation are manifest throughout. Near the end he suggests a novel, nonperturbative formulation of quantum field theory in D dimensions. Supplementary material is provided in appendices and ancillary files, including verbatim transcriptions of three lectures and the corresponding audiotaped recordings

An operator calculus having applications in quantum electrodynamics

An alteration in the notation used to indicate the order of operation of noncommuting quantities is suggested. Instead of the order being defined by the position on the paper, an ordering subscript is introduced so that AsBs′ means AB or BA depending on whether s exceeds s′ or vice versa. Then As can be handled as though it were an ordinary numerical function of s. An increase in ease of manipulating some operator expressions results. Connection to the theory of functionals is discussed in an appendix. Illustrative applications to quantum mechanics are made. In quantum electrodynamics it permits a simple formal understanding of the interrelation of the various present day theoretical formulations. The operator expression of the Dirac equation is related to the author's previous description of positrons. An attempt is made to interpret the operator ordering parameter in this case as a fifth coordinate variable in an extended Dirac equation. Fock's parametrization, discussed in an appendix, seems to be easier to interpret. In the last section a summary of the numerical constants appearing in formulas for transition probabilities is given

Very high-energy collisions of hadrons

Proposals are made predicting the character of longitudinal-momentum distributions in hadron collisions of extreme energies

Quantum Monte Carlo study of a magnetic-field-driven 2D superconductor-insulator transition

We numerically study the superconductor-insulator phase transition in a model disordered 2D superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the (2+1)D XY model in the presence of both disorder and magnetic field. The XY coupling is assumed to have the form -J\cos(\theta_i-\theta_j-A_{ij}), where A_{ij} has a mean of zero and a standard deviation \Delta A_{ij}. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The different values \Delta A_{ij} then corresponds to an applied field such that the average number of flux quanta per plaquette has various integer values N: larger N corresponds to larger \Delta A_{ij}. For any value of \Delta A_{ij}, there appears to be a critical coupling constant K_c(\Delta A_{ij})=\sqrt{[J/(2U)]_c}, where U is the charging energy, above which the system is a Mott insulator; there is also a corresponding critical conductivity \sigma^*(\Delta A_{ij}) at the transition. For \Delta A_{ij}=\infty, the order parameter of the transition is a renormalized coupling constant g. Using a numerical technique appropriate for disordered systems, we show that the transition at this value of \Delta A_{ij} takes place from an insulating (I) phase to a Bose glass (BG) phase, and that the dynamical critical exponent characterizing this transition is z \sim 1.3. By contrast, z=1 for this model at \Delta A_{ij}=0. We suggest that the superconductor to insulator transition is actually of this I to BG class at all nonzero \Delta A_{ij}'s, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion.Comment: 17 pages, 23 figures, accepted for publication in Phys. Rev.