8,043 research outputs found
The dynamical equation of the spinning electron
We obtain by invariance arguments the relativistic and non-relativistic
invariant dynamical equations of a classical model of a spinning electron. We
apply the formalism to a particular classical model which satisfies Dirac's
equation when quantised. It is shown that the dynamics can be described in
terms of the evolution of the point charge which satisfies a fourth order
differential equation or, alternatively, as a system of second order
differential equations by describing the evolution of both the center of mass
and center of charge of the particle. As an application of the found dynamical
equations, the Coulomb interaction between two spinning electrons is
considered. We find from the classical viewpoint that these spinning electrons
can form bound states under suitable initial conditions. Since the classical
Coulomb interaction of two spinless point electrons does not allow for the
existence of bound states, it is the spin structure that gives rise to new
physical phenomena not described in the spinless case. Perhaps the paper may be
interesting from the mathematical point of view but not from the point of view
of physics.Comment: Latex2e, 14 pages, 5 figure
Symmetry-protected Topological Phases at Finite Temperature
We have applied the recently developed theory of topological Uhlmann numbers
to a representative model of a topological insulator in two dimensions, the
Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT)
phase under external thermal fluctuations in two-dimensions. A complete phase
diagram for this model is computed as a function of temperature and coupling
constants in the original Hamiltonian. It shows the appearance of large stable
phases of matter with topological properties compatible with thermal
fluctuations or external noise and the existence of critical lines separating
abruptly trivial phases from topological phases. These novel critical
temperatures represent thermal topological phase transitions. The initial part
of the paper comprises a self-contained explanation of the Uhlmann geometric
phase needed to understand the topological properties that it may acquire when
applied to topological insulators and superconductors.Comment: Contribution to the focus issue on "Artificial Graphene". Edited by
Maciej Lewenstein, Vittorio Pellegrini, Marco Polini and Mordechai (Moti)
Sege
Observation of a tricritical wedge filling transition in the 3D Ising model
In this Letter we present evidences of the occurrence of a tricritical
filling transition for an Ising model in a linear wedge. We perform Monte Carlo
simulations in a double wedge where antisymmetric fields act at the top and
bottom wedges, decorated with specific field acting only along the wegde axes.
A finite-size scaling analysis of these simulations shows a novel critical
phenomenon, which is distinct from the critical filling. We adapt to
tricritical filling the phenomenological theory which successfully was applied
to the finite-size analysis of the critical filling in this geometry, observing
good agreement between the simulations and the theoretical predictions for
tricritical filling.Comment: 5 pages, 3 figure
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