223 research outputs found
On the stability of Hamiltonian relative equilibria with non-trivial isotropy
We consider Hamiltonian systems with symmetry, and relative equilibria with
isotropy subgroup of positive dimension. The stability of such relative
equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In
both papers the authors give sufficient conditions for stability which require
first determining a splitting of a subspace of the Lie algebra of the symmetry
group, with different splittings giving different criteria. In this note we
remove this splitting construction and so provide a more general and more
easily computed criterion for stability. The result is also extended to apply
to systems whose momentum map is not coadjoint equivariant
Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a
base for the construction of conformally invariant quantum (field) theory,
either as phase or configuration spaces. We follow a gauge-invariant Lagrangian
approach (of nonlinear sigma-model type) and use a generalized Dirac method for
the quantization of constrained systems, which resembles in some aspects the
standard approach to quantizing coadjoint orbits of a group G. Physical wave
functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels
are explicitly calculated in and holomorphic picture in these Cartan domains
for both scalar and spinning quantum particles. Similarities and differences
with other results in the literature are also discussed and an extension of
Schwinger's Master Theorem is commented in connection with closure relations.
An adaptation of the Born's Reciprocity Principle (BRP) to the conformal
relativity, the replacement of space-time by the 8-dimensional conformal domain
at short distances and the existence of a maximal acceleration are also put
forward.Comment: 33 pages, no figures, LaTe
Mathisson's helical motions for a spinning particle --- are they unphysical?
It has been asserted in the literature that Mathisson's helical motions are
unphysical, with the argument that their radius can be arbitrarily large. We
revisit Mathisson's helical motions of a free spinning particle, and observe
that such statement is unfounded. Their radius is finite and confined to the
disk of centroids. We argue that the helical motions are perfectly valid and
physically equivalent descriptions of the motion of a spinning body, the
difference between them being the choice of the representative point of the
particle, thus a gauge choice. We discuss the kinematical explanation of these
motions, and we dynamically interpret them through the concept of hidden
momentum. We also show that, contrary to previous claims, the frequency of the
helical motions coincides, even in the relativistic limit, with the
zitterbewegung frequency of the Dirac equation for the electron
Models for Modules
We recall the structure of the indecomposable sl(2) modules in the
Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise
as quantized phase spaces of physical models. In particular, we demonstrate in
a path integral discretization how a redefined action of the sl(2) algebra over
the complex numbers can glue finite dimensional and infinite dimensional
highest weight representations into indecomposable wholes. Furthermore, we
discuss how projective cover representations arise in the tensor product of
finite dimensional and Verma modules and give explicit tensor product
decomposition rules. The tensor product spaces can be realized in terms of
product path integrals. Finally, we discuss relations of our results to brane
quantization and cohomological calculations in string theory.Comment: 18 pages, 6 figure
On transversally elliptic operators and the quantization of manifolds with -structure
An -structure on a manifold is an endomorphism field
\phi\in\Gamma(M,\End(TM)) such that . Any -structure
determines an almost CR structure E_{1,0}\subset T_\C M given by the
-eigenbundle of . Using a compatible metric and connection
on , we construct an odd first-order differential operator ,
acting on sections of , whose principal symbol is of the
type considered in arXiv:0810.0338. In the special case of a CR-integrable
almost -structure, we show that when is the generalized
Tanaka-Webster connection of Lotta and Pastore, the operator is given by D
= \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann
operator.
We then describe two "quantizations" of manifolds with -structure that
reduce to familiar methods in symplectic geometry in the case that is a
compatible almost complex structure, and to the contact quantization defined in
\cite{F4} when comes from a contact metric structure. The first is an
index-theoretic approach involving the operator ; for certain group actions
will be transversally elliptic, and using the results in arXiv:0810.0338,
we can give a Riemann-Roch type formula for its index. The second approach uses
an analogue of the polarized sections of a prequantum line bundle, with a CR
structure playing the role of a complex polarization.Comment: 31 page
Reduction and approximation in gyrokinetics
The gyrokinetics formulation of plasmas in strong magnetic fields aims at the
elimination of the angle associated with the Larmor rotation of charged
particles around the magnetic field lines. In a perturbative treatment or as a
time-averaging procedure, gyrokinetics is in general an approximation to the
true dynamics. Here we discuss the conditions under which gyrokinetics is
either an approximation or an exact operation in the framework of reduction of
dynamical systems with symmetryComment: 15 pages late
C^{2} formulation of Euler fluid
The Hamiltonian formalism for the continuous media is constructed using the
representation of Euler variables in phase
space.Comment: 8 page
Anisotropic Hubble expansion of large scale structures
We investigate the dynamics of an homogenous distribution of galaxies moving
under the cosmological expansion through Euler-Poisson equations system. The
solutions are interpreted with the aim of understanding the cosmic velocity
fields in the Local Super Cluster, and in particular the presence of a bulk
flow. Among several solutions, we shows a planar kinematics with constant
(eternal) and rotational distortion, the velocity field is not potential
SOT-MRAM 300mm integration for low power and ultrafast embedded memories
We demonstrate for the first time full-scale integration of top-pinned
perpendicular MTJ on 300 mm wafer using CMOS-compatible processes for
spin-orbit torque (SOT)-MRAM architectures. We show that 62 nm devices with a
W-based SOT underlayer have very large endurance (> 5x10^10), sub-ns switching
time of 210 ps, and operate with power as low as 300 pJ.Comment: presented at VLSI2018 session C8-
Non-abelian Harmonic Oscillators and Chiral Theories
We show that a large class of physical theories which has been under
intensive investigation recently, share the same geometric features in their
Hamiltonian formulation. These dynamical systems range from harmonic
oscillations to WZW-like models and to the KdV dynamics on . To the
same class belong also the Hamiltonian systems on groups of maps.
The common feature of these models are the 'chiral' equations of motion
allowing for so-called chiral decomposition of the phase space.Comment: 1
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