62 research outputs found
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 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 controls the separation of time
scales and the limit corresponds to an adiabatic limit, in
which the slow and fast degrees of freedom decouple. At the same time
is the semiclassical limit for the slow degrees of freedom.
In this paper we show that the -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 -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 . 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.
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