Equation of Motion for a Spin Vortex and Geometric Force

The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The resultant equation shows the existence of a geometric force that is analogous to the so-called Magnus force in superfluid. This specific force plays a significant role for a quantum dynamics for a single vortex, e.g, the determination of the bound state of the vortex trapped by a pinning force arising from the interaction of the vortex with an impurity.Comment: 13 pages, plain te

Dynamics of a Vortex in Two-Dimensional Superfluid He3-A: Force Caused by the l-Texture

Based on the Landau-Ginzburg Lagrangian, the dynamics of a vortex is studied for superfluid He3-A characterized by the l-texture. The resultant equation of motion for a vortex leads to the Magnus-type force caused by the l-texture. The force is explicitly written in terms of the mapping degree from the compactified 2-dimensional plane to the space of l-vector, which reflects the quantitative differences of vortex configurations, especially the Mermin-Ho and Anderson-Toulouse vortices. The formulation is applied to anisotropic superconductors in which the Hall current is shown to incorporate changes between vortex configurations.Comment: 4 pages, RevTex(twocolumn

Generalized Coherent States and Spin S≥1S\geq 1 Systems

Generalized Coherent States (GCS) are constructed (and discussed) in order to study quasiclassical behaviour of quantum spin models of the Heisenberg type. Several such models are taken to their semiclassical limits, whose form depends on the spin value as well as the Hamiltonian symmetry. In the continuum approximation, SU(2)/U(1) GCS when applied give rise to the well-known Landau-Lifshitz classical phenomenology. For arbitrary spin values one obtains a lattice of coupled nonlinear oscillators. Corresponding classical continuum models are described as well.Comment: 18 pages, LaTeX. Submitted to J. of Phys. A: Math. and Ge

Long wavelength spin dynamics of ferromagnetic condensates

We obtain the equations of motion for a ferromagnetic Bose condensate of arbitrary spin in the long wavelength limit. We find that the magnetization of the condensate is described by a non-trivial modification of the Landau-Lifshitz equation, in which the magnetization is advected by the superfluid velocity. This hydrodynamic description, valid when the condensate wavefunction varies on scales much longer than either the density or spin healing lengths, is physically more transparent than the corresponding time-dependent Gross-Pitaevskii equation. We discuss the conservation laws of the theory and its application to the analysis of the stability of magnetic helices and Larmor precession. Precessional instabilities in particular provide a novel physical signature of dipolar forces. Finally, we discuss the anisotropic spin wave instability observed in the recent experiment of Vengalattore et. al. (Phys. Rev. Lett. 100, 170403, (2008)).Comment: arXiv version contains additional Section V relevant to the experiment of Vengalattore et. al. (Phys. Rev. Lett. 100, 170403, (2008)

Semiclassical theory of spin-orbit interactions using spin coherent states

We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula for the density of states. For a two-dimensional quantum dot with a spin-orbit interaction of Rashba type, we obtain satisfactory agreement with fully quantum-mechanical calculations. The mode-conversion problem, which arose in an earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review Letters; final version (v2) for publication with minor editorial change

Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Semiclassical theory of spin-orbit interaction in the extended phase space

We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density of states. We discuss special cases, such as weak and strong spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B; minor corrections elsewher

Geometric phases and hidden local gauge symmetry

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published in Phys. Rev.