16,805 research outputs found
AB and Berry phases for a quantum cloud of charge
We investigate the phase accumulated by a charged particle in an extended
quantum state as it encircles one or more magnetic fluxons, each carrying half
a flux unit. A simple, essentially topological analysis reveals an interplay
between the Aharonov-Bohm phase and Berry's phase.Comment: 10 pages, TAUP 2110-93. Te
Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)
A quantal guiding center theory allowing to systematically study the
separation of the different time scale behaviours of a quantum charged spinning
particle moving in an external inhomogeneous magnetic filed is presented. A
suitable set of operators adapting to the canonical structure of the problem
and generalizing the kinematical momenta and guiding center operators of a
particle coupled to a homogenous magnetic filed is constructed. The Pauli
Hamiltonian rewrites in this way as a power series in the magnetic length making the problem amenable to a perturbative analysis. The
first two terms of the series are explicitly constructed. The effective
adiabatic dynamics turns to be in coupling with a gauge filed and a scalar
potential. The mechanism producing such magnetic-induced geometric-magnetism is
investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include
Non-Abelian Geometric Quantum Memory with Atomic Ensemble
We study a quantum information storage scheme based on an atomic ensemble
with near (also exact) three-photon resonance electromagnetically induced
transparency (EIT). Each 4-level-atom is coupled to two classical control
fields and a quantum probe field. Quantum information is adiabatically stored
in the associated dark polariton manifold. An intrinsic non-trivial topological
structure is discovered in our quantum memory implemented through the symmetric
collective atomic excitations with a hidden SU(3) dynamical symmetry. By
adiabatically changing the Rabi frequencies of two classical control fields,
the quantum state can be retrieved up to a non-abelian holonomy and thus
decoded from the final state in a purely geometric way.Comment: 4 pages, 2 figure
The non-Abelian state-dependent gauge field in optics
The covariant formulation of the quantum dynamics in CP(1) should lead to the
observable geometrodynamical effects for the local dynamical variable of the
light polarization states.Comment: 8 pages, 3 figures, LaTe
Calculation of the Aharonov-Bohm wave function
A calculation of the Aharonov-Bohm wave function is presented. The result is
a series of confluent hypergeometric functions which is finite at the forward
direction.Comment: 12 pages in LaTeX, and 3 PostScript figure
Berry's phase in the multimode Peierls states
It is shown that Berry's phase associated with the adiabatic change of local
variables in the Hamiltonian can be used to characterize the multimode Peierls
state, which has been proposed as a new type of the ground state of the
two-dimensional(2D) systems with the electron-lattice interaction.Comment: 2 pages, 2 figure
Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework
While many existing formal concept analysis algorithms are efficient, they
are typically unsuitable for distributed implementation. Taking the MapReduce
(MR) framework as our inspiration we introduce a distributed approach for
performing formal concept mining. Our method has its novelty in that we use a
light-weight MapReduce runtime called Twister which is better suited to
iterative algorithms than recent distributed approaches. First, we describe the
theoretical foundations underpinning our distributed formal concept analysis
approach. Second, we provide a representative exemplar of how a classic
centralized algorithm can be implemented in a distributed fashion using our
methodology: we modify Ganter's classic algorithm by introducing a family of
MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the
algorithm's lineage. To evaluate the factors that impact distributed algorithm
performance, we compare our MR* algorithms with the state-of-the-art.
Experiments conducted on real datasets demonstrate that MRGanter+ is efficient,
scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201
Spatio-temporal vortex beams and angular momentum
We present a space-time generalization of the known spatial (monochromatic)
wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the
propagation direction. Generic spatio-temporal vortex beams are polychromatic
and can carry intrinsic OAM at an arbitrary angle to the mean momentum.
Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a
monochromatic Bessel beam, we construct a family of either (i) time-diffracting
or (ii) non-diffracting spatio-temporal Bessel beams, which are exact solutions
of the Klein-Gordon wave equations. The proposed spatio-temporal OAM states are
able to describe either photon or electron vortex states (both relativistic and
nonrelativistic), and can find applications in particle collisions, optics of
moving media, quantum communications, and astrophysics.Comment: 9 pages, 6 figures, to appear in Phys. Rev.
Topological vortex formation in a Bose-Einstein condensate
Vortices were imprinted in a Bose-Einstein condensate using topological
phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were
transformed from a non-rotating state to one with quantized circulation by
adiabatically inverting the magnetic bias field along the trap axis. Using
surface wave spectroscopy, the axial angular momentum per particle of the
vortex states was found to be consistent with or , depending
on the hyperfine state of the condensate.Comment: 5 pages, 3 figure
Entanglement entropy and the Berry phase in solid states
The entanglement entropy (von Neumann entropy) has been used to characterize
the complexity of many-body ground states in strongly correlated systems. In
this paper, we try to establish a connection between the lower bound of the von
Neumann entropy and the Berry phase defined for quantum ground states. As an
example, a family of translational invariant lattice free fermion systems with
two bands separated by a finite gap is investigated. We argue that, for one
dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band
is equal to and when the ground state respects a
discrete unitary particle-hole symmetry (chiral symmetry), the entanglement
entropy in the thermodynamic limit is at least larger than (per
boundary), i.e., the entanglement entropy that corresponds to a maximally
entangled pair of two qubits. We also discuss this lower bound is related to
vanishing of the expectation value of a certain non-local operator which
creates a kink in 1D systems.Comment: 11 pages, 4 figures, new references adde
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