Universality in the Large N_c Dynamics of Flavour: Thermal Vs. Quantum Induced Phase Transitions

We show how two important types of phase transition in large N_c gauge theory with fundamental flavours can be cast into the same classifying framework as the meson-melting phase transition. These are quantum fluctuation induced transitions in the presence of an external electric field, or a chemical potential for R-charge. The classifying framework involves the study of the local geometry of a special D-brane embedding, which seeds a self-similar spiral structure in the space of embeddings. The properties of this spiral, characterized by a pair of numbers, capture some key universal features of the transition. Computing these numbers for these non-thermal cases, we find that these transitions are in the same universality class as each other, but have different universal features from the thermal case. We present a natural generalization that yields new universality classes that may pertain to other types of transition.Comment: 22 pages, 4 figures, pdfLaTe

Double-valuedness of the electron wave function and rotational zero-point motion of electrons in rings

I propose that the phase of an electron's wave function changes by $\pi$ when the electron goes around a loop maintaining phase coherence. Equivalently, that the minimum orbital angular momentum of an electron in a ring is $\hbar/2$ rather than zero as generally assumed, hence that the electron in a ring has azimuthal zero point motion. This proposal provides a physical explanation for the origin of electronic `quantum pressure', it implies that a spin current exists in the ground state of aromatic ring molecules, and it suggests an explanation for the ubiquitousness of persistent currents observed in mesoscopic rings

Quantum transport properties of two-dimensional electron gases under high magnetic fields

We study quantum transport properties of two-dimensional electron gases under high perpendicular magnetic fields. For this purpose, we reformulate the high-field expansion, usually done in the operatorial language of the guiding-center coordinates, in terms of vortex states within the framework of real-time Green functions. These vortex states arise naturally from the consideration that the Landau levels quantization can follow directly from the existence of a topological winding number. The microscopic computation of the current can then be performed within the Keldysh formalism in a systematic way at finite magnetic fields $B$ (i.e. beyond the semi-classical limit $B = \infty$). The formalism allows us to define a general vortex current density as long as the gradient expansion theory is applicable. As a result, the total current is expressed in terms of edge contributions only. We obtain the first and third lowest order contributions to the current due to Landau-levels mixing processes, and derive in a transparent way the quantization of the Hall conductance. Finally, we point out qualitatively the importance of inhomogeneities of the vortex density to capture the dissipative longitudinal transport.Comment: 21 pages, 5 figures ; main change: the discussion about the longitudinal transport (Part A of Section VI) is rewritten and enhance

The Pauli equation in scale relativity

In standard quantum mechanics, it is not possible to directly extend the Schrodinger equation to spinors, so the Pauli equation must be derived from the Dirac equation by taking its non-relativistic limit. Hence, it predicts the existence of an intrinsic magnetic moment for the electron and gives its correct value. In the scale relativity framework, the Schrodinger, Klein-Gordon and Dirac equations have been derived from first principles as geodesics equations of a non-differentiable and continuous spacetime. Since such a generalized geometry implies the occurence of new discrete symmetry breakings, this has led us to write Dirac bi-spinors in the form of bi-quaternions (complex quaternions). In the present work, we show that, in scale relativity also, the correct Pauli equation can only be obtained from a non-relativistic limit of the relativistic geodesics equation (which, after integration, becomes the Dirac equation) and not from the non-relativistic formalism (that involves symmetry breakings in a fractal 3-space). The same degeneracy procedure, when it is applied to the bi-quaternionic 4-velocity used to derive the Dirac equation, naturally yields a Pauli-type quaternionic 3-velocity. It therefore corroborates the relevance of the scale relativity approach for the building from first principles of the quantum postulates and of the quantum tools. This also reinforces the relativistic and fundamentally quantum nature of spin, which we attribute in scale relativity to the non-differentiability of the quantum spacetime geometry (and not only of the quantum space). We conclude by performing numerical simulations of spinor geodesics, that allow one to gain a physical geometric picture of the nature of spin.Comment: 22 pages, 2 figures, accepted for publication in J. Phys. A: Math. & Ge