2,020 research outputs found
On the zero of the fermion zero mode
We argue that the fermionic zero mode in non-trivial gauge field backgrounds
must have a zero. We demonstrate this explicitly for calorons where its
location is related to a constituent monopole. Furthermore a topological
reasoning for the existence of the zero is given which therefore will be
present for any non-trivial configuration. We propose the use of this property
in particular for lattice simulations in order to uncover the topological
content of a configuration.Comment: 6 pages, 3 figures in 5 part
Designing Robust Unitary Gates: Application to Concatenated Composite Pulse
We propose a simple formalism to design unitary gates robust against given
systematic errors. This formalism generalizes our previous observation [Y.
Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing
dynamical phase in some composite gates is essential to suppress amplitude
errors. By employing our formalism, we naturally derive a new composite unitary
gate which can be seen as a concatenation of two known composite unitary
operations. The obtained unitary gate has high fidelity over a wider range of
the error strengths compared to existing composite gates.Comment: 7 pages, 4 figures. Major revision: improved presentation in Sec. 3,
references and appendix adde
Dual Formulation of the Lie Algebra S-expansion Procedure
The expansion of a Lie algebra entails finding a new, bigger algebra G,
through a series of well-defined steps, from an original Lie algebra g. One
incarnation of the method, the so-called S-expansion, involves the use of a
finite abelian semigroup S to accomplish this task. In this paper we put
forward a dual formulation of the S-expansion method which is based on the dual
picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of
the method is useful in finding a generalization to the case of a gauge free
differential algebra, which in turn is relevant for physical applications in,
e.g., Supergravity. It also sheds new light on the puzzling relation between
two Chern-Simons Lagrangians for gravity in 2+1 dimensions, namely the
Einstein-Hilbert Lagrangian and the one for the so-called "exotic gravity".Comment: 12 pages, no figure
Continuous vortex pumping into a spinor condensate with magnetic fields
We study the mechanisms and the limits of pumping vorticity into a spinor
condensate through manipulations of magnetic (B-) fields. We discover a
fundamental connection between the geometrical properties of the magnetic
fields and the quantized circulation of magnetically trapped atoms, a result
which generalizes several recent experimental and theoretical studies. The
optimal procedures are devised that are capable of continuously increasing or
decreasing a condensate's vorticity by repeating certain two step B-field
manipulation protocols. We carry out detailed numerical simulations that
support the claim that our protocols are highly efficient, stable, and robust
against small imperfections of all types. Our protocols can be implemented
experimentally within current technologies.Comment: 9 pages, 6 figure
Super coset space geometry
Super coset spaces play an important role in the formulation of
supersymmetric theories. The aim of this paper is to review and discuss the
geometry of super coset spaces with particular focus on the way the geometrical
structures of the super coset space G/H are inherited from the super Lie group
G. The isometries of the super coset space are discussed and a definition of
Killing supervectors - the supervectors associated with infinitesimal
isometries - is given that can be easily extended to spaces other than coset
spaces.Comment: 49 pages, 1 figure, AFK previously published under the name A. F.
Schunc
Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction
We construct a minimal robust controlled-NOT gate with an Ising-type
interaction by which elementary two-qubit gates are implemented. It is robust
against inaccuracy of the coupling strength and the obtained quantum circuits
are constructed with the minimal number (N=3) of elementary two-qubit gates and
several one-qubit gates. It is noteworthy that all the robust circuits can be
mapped to one-qubit circuits robust against a pulse length error. We also prove
that a minimal robust SWAP gate cannot be constructed with N=3, but requires
N=6 elementary two-qubit gates.Comment: 7 pages, 2 figure
Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor
The derivation of the helicon dispersion relation for a uniform plasma with
stationary ions subject to a constant background magnetic field is reexamined
in terms of the potential formulation of electrodynamics. Under the same
conditions considered by the standard derivation, the nonlinear self-coupling
between the perturbed electron flow and the potential it generates is
addressed. The plane wave solution for general propagation vector is determined
for all frequencies and expressed in terms of a vector phasor. The behavior of
the solution as described in vacuum units depends upon the ratio of
conductivity to the magnitude of the background field. Only at low conductivity
and below the cyclotron frequency can significant propagation occur as
determined by the ratio of skin depth to wavelength.Comment: 10 pages, 6 figures, major revision, final version, to appear in Po
Topological Protection and Quantum Noiseless Subsystems
Encoding and manipulation of quantum information by means of topological
degrees of freedom provides a promising way to achieve natural fault-tolerance
that is built-in at the physical level. We show that this topological approach
to quantum information processing is a particular instance of the notion of
computation in a noiseless quantum subsystem. The latter then provide the most
general conceptual framework for stabilizing quantum information and for
preserving quantum coherence in topological and geometric systems.Comment: 4 Pages LaTeX. Published versio
A gauge theoretical view of the charge concept in Einstein gravity
We will discuss some analogies between internal gauge theories and gravity in
order to better understand the charge concept in gravity. A dimensional
analysis of gauge theories in general and a strict definition of elementary,
monopole, and topological charges are applied to electromagnetism and to
teleparallelism, a gauge theoretical formulation of Einstein gravity.
As a result we inevitably find that the gravitational coupling constant has
dimension , the mass parameter of a particle dimension ,
and the Schwarzschild mass parameter dimension l (where l means length). These
dimensions confirm the meaning of mass as elementary and as monopole charge of
the translation group, respectively. In detail, we find that the Schwarzschild
mass parameter is a quasi-electric monopole charge of the time translation
whereas the NUT parameter is a quasi-magnetic monopole charge of the time
translation as well as a topological charge. The Kerr parameter and the
electric and magnetic charges are interpreted similarly. We conclude that each
elementary charge of a Casimir operator of the gauge group is the source of a
(quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio
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