Takafumi Kita

Mermin-Ho vortex in ferromagnetic spinor Bose-Einstein condensates

The Mermin-Ho and Anderson-Toulouse coreless vortices are demonstrated to be thermodynamically stable in ferromagnetic F = 1 spinor Bose-Einstein condensates under rotation. We have carried out extensive calculations of the Gross-Pitaevskii equations by assuming uniform density along the z axis and comparing the energies of other competing non-axis-symmetric or singular vortices. The phase diagram is thereby established in a plane of the rotation drive vs the total magnetization. Their stability is also checked by calculating collective modes based on the Bogoliubov equations.

Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory

In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson’s equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson’s equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green’s function and the self-energy uniquely on the roundtrip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green’s functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the selfconsistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym’s Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the “Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy”. Aim (ii) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog’s expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with quantum field theory, including fluctuations. We also discuss a derivation of the quantum transport equations for electrons in electromagnetic fields based on the gauge-invariant Wigner transformation so that the Lorentz force is reproduced naturally. As for (iii), the Gibbs entropy of equilibrium statistical mechanics suffers from the flaw that it does not evolve in time. We show here that a microscopic expression of nonequilibrium dynamical entropy can be derived from the quantum transport equations so as to be compatible with the law of increase in entropy as well as equilibrium statistical mechanics. Subject Index: 052, 056, 062, 356, 512

QUASIPARTICLES OF D-WAVE SUPERCONDUCTORS IN FINITE MAGNETIC FIELDS

We study quasiparticles of d-wave superconductors in the vortex lattice by self-consistently solving the Bogoliubov-de Gennes equations. It is found for a pure

Gauge invariance and Hall terms in the quasiclassical equations of superconductivity

d_{x^2-y^2}

Ab initio calculations of Hc2 in type-II superconductors: Basic formalism and model calculations

state that: (i) low-energy quasiparticle bands in the magnetic Brillouin zone have rather large dispersion even in low magnetic fields, indicating absense of bound states for an isolated vortex; (ii) in finite fields with

Solving the Ginzburg-Landau Equations with Magnetic Translation Group

k_F \xi_0

Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws

small, the calculated tunneling conductance at the vortex core shows a double-peak structure near zero bias, as qualitatively consistent with the STM experiment by Maggio-Aprile et al. [Phys. Rev. Lett. {\bf 75} (1995) 2754]. We also find that mixing of a

Entropy in Nonequilibrium Statistical Mechanics

d_{xy}

Spinor Bose-Einstein condensates with many vortices

- or an s-wave component, if any, develops gradually without transitions as the field is increased, having little effect on the tunneling spectra.

Angular momentum of anisotropic superfluids at finite temperatures

This paper presents a careful derivation of the quasiclassical equations of superconductivity so that a manifest gauge invariance is retained with respect to the space-time arguments of the quasiclassical Greens function