16,070 research outputs found
Pancharatnam and Berry Phases in Three-Level Photonic Systems
A theoretical analysis of Pancharatnam and Berry phases is made for biphoton
three-level systems, which are produced via frequency degenerate co-linear
spontaneous parametric down conversion (SPDC). The general theory of
Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in
Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical
phases are derived for the transformations produced by linear phase-converters.
The problem of gauge invariance is treated along all the article
Phase Dynamics of Two Entangled Qubits
We make a geometric study of the phases acquired by a general pure bipartite
two level system after a cyclic unitary evolution. The geometric representation
of the two particle Hilbert space makes use of Hopf fibrations. It allows for a
simple description of the dynamics of the entangled state's phase during the
whole evolution. The global phase after a cyclic evolution is always an entire
multiple of for all bipartite states, a result that does not depend on
the degree of entanglement. There are three different types of phases combining
themselves so as to result in the global phase. They can be identified
as dynamical, geometrical and topological. Each one of them can be easily
identified using the presented geometric description. The interplay between
them depends on the initial state and on its trajectory and the results
obtained are shown to be in connection to those on mixed states phases.Comment: 9 figures, slightly different version from the accepted on
The twistor geometry of three-qubit entanglement
A geometrical description of three qubit entanglement is given. A part of the
transformations corresponding to stochastic local operations and classical
communication on the qubits is regarded as a gauge degree of freedom. Entangled
states can be represented by the points of the Klein quadric a space
known from twistor theory. It is shown that three-qubit invariants are
vanishing on special subspaces of . An invariant vanishing for the
class is proposed. A geometric interpretation of the canonical
decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX
Multi-particle Correlations in Quaternionic Quantum Systems
We investigate the outcomes of measurements on correlated, few-body quantum
systems described by a quaternionic quantum mechanics that allows for regions
of quaternionic curvature. We find that a multi-particle interferometry
experiment using a correlated system of four nonrelativistic, spin-half
particles has the potential to detect the presence of quaternionic curvature.
Two-body systems, however, are shown to give predictions identical to those of
standard quantum mechanics when relative angles are used in the construction of
the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1
Labeling Schemes for Bounded Degree Graphs
We investigate adjacency labeling schemes for graphs of bounded degree
. In particular, we present an optimal (up to an additive
constant) adjacency labeling scheme for bounded degree trees.
The latter scheme is derived from a labeling scheme for bounded degree
outerplanar graphs. Our results complement a similar bound recently obtained
for bounded depth trees [Fraigniaud and Korman, SODA 10], and may provide new
insights for closing the long standing gap for adjacency in trees [Alstrup and
Rauhe, FOCS 02]. We also provide improved labeling schemes for bounded degree
planar graphs. Finally, we use combinatorial number systems and present an
improved adjacency labeling schemes for graphs of bounded degree with
Quaternionic Electroweak Theory and CKM Matrix
We find in our quaternionic version of the electroweak theory an apparently
hopeless problem: In going from complex to quaternions, the calculation of the
real-valued parameters of the CKM matrix drastically changes. We aim to explain
this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published
Approximate well-supported Nash equilibria in symmetric bimatrix games
The -well-supported Nash equilibrium is a strong notion of
approximation of a Nash equilibrium, where no player has an incentive greater
than to deviate from any of the pure strategies that she uses in
her mixed strategy. The smallest constant currently known for
which there is a polynomial-time algorithm that computes an
-well-supported Nash equilibrium in bimatrix games is slightly
below . In this paper we study this problem for symmetric bimatrix games
and we provide a polynomial-time algorithm that gives a
-well-supported Nash equilibrium, for an arbitrarily small
positive constant
Run-and-tumble particles with hydrodynamics: sedimentation, trapping and upstream swimming
We simulate by lattice Boltzmann the nonequilibrium steady states of
run-and-tumble particles (inspired by a minimal model of bacteria), interacting
by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic
interactions barely perturb the steady state found without them, but for
particles in a harmonic trap such a state is quite changed if the run length is
larger than the confinement length: a self-assembled pump is formed. Particles
likewise confined in a narrow channel show a generic upstream flux in
Poiseuille flow: chiral swimming is not required
Topological Phase Transitions and Holonomies in the Dimer Model
We demonstrate that the classical dimer model defined on a toroidal hexagonal
lattice acquires holonomy phases in the thermodynamic limit. When all
activities are equal the lattice sizes must be considered mod 6 in which case
the finite size corrections to the bulk partition function correspond to a
massless Dirac Fermion in the presence of a flat connection with nontrivial
holonomy. For general bond activities we find that the phase transition in this
model is a topological one, where the torus degenerates and its modular
parameter becomes real at the critical temperature. We argue that these
features are generic to bipartite dimer models and we present a more general
lattice whose continuum partition function is that of a massive Dirac Fermion.Comment: 7 pages, 4 figures. Minor corrections with additional figure
The gap exponent of XXZ model in a transverse field
We have calculated numerically the gap exponent of the anisotropic Heisenberg
model in the presence of the transverse magnetic field. We have implemented the
modified Lanczos method to obtain the excited states of our model with the same
accuracy of the ground state. The coefficient of the leading term in the
perturbation expansion diverges in the thermodynamic limit (N --> infinity). We
have obtained the relation between this divergence and the scaling behaviour of
the energy gap. We have found that the opening of gap in the presence of
transverse field scales with a critical exponent which depends on the
anisotropy parameter (Delta). Our numerical results are in well agreement with
the field theoretical approach in the whole range of the anisotropy parameter,
-1 < Delta < 1.Comment: 6 pages and 4 figure
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