764 research outputs found
THE VALUE OF JULIUS CAESAR AS ETHNOGRAPHER
Caesar's campaigns in Gaul, Germany and Britain occasioned great excitement in Rome.
For Catullus "the Gaulish Rhine, the formidable Britons, remotest of men" represented
"the memorials of great Caesar" (Cat. 11.10-11). Cicero too considered Caesar's exploits
against the Britons the stuff of poetry (Q Fr. 2.16.14). The reading public must have been
interested in what he had to say about his foreign adversaries
Test for entanglement using physically observable witness operators and positive maps
Motivated by the Peres-Horodecki criterion and the realignment criterion we
develop a more powerful method to identify entangled states for any bipartite
system through a universal construction of the witness operator. The method
also gives a new family of positive but non-completely positive maps of
arbitrary high dimensions which provide a much better test than the witness
operators themselves. Moreover, we find there are two types of positive maps
that can detect 2xN and 4xN bound entangled states. Since entanglement
witnesses are physical observables and may be measured locally our construction
could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl
An efficient direct solver for a class of mixed finite element problems
In this paper we present an efficient, accurate and parallelizable direct method for the solution of the (indefinite) linear algebraic systems that arise in the solution of fourth-order partial differential equations (PDEs) using mixed finite element approximations. The method is intended particularly for use when multiple right-hand sides occur, and when high accuracy is required in these solutions.
The algorithm is described in some detail and its performance is illustrated through the numerical solution of a biharmonic eigenvalue problem where the smallest eigenpair is approximated using inverse iteration after discretization via the Ciarlet–Raviart mixed finite element method
Nonlinear Inequalities and Entropy-Concurrence Plane
Nonlinear inequalities based on the quadratic Renyi entropy for mixed
two-qubit states are characterized on the Entropy-Concurrence plane. This class
of inequalities is stronger than Clauser-Horne-Shimony-Holt (CHSH) inequalities
and, in particular, are violated "in toto" by the set of Type I
Maximally-Entangled-Mixture States (MEMS I)
An alternative approach to the construction of Schur-Weyl transform
We propose an alternative approach for the construction of the unitary matrix
which performs generalized unitary rotations of the system consisting of
independent identical subsystems (for example spin system). This matrix, when
applied to the system, results in a change of degrees of freedom, uncovering
the information hidden in non-local degrees of freedom. This information can be
used, inter alia, to study the structure of entangled states, their
classification and may be useful for construction of quantum algorithms.Comment: 6 page
A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements
A generic model of measurement device which is able to directly measure
commonly used quantum-state characteristics such as fidelity, overlap, purity
and Hilbert-Schmidt distance for two general uncorrelated mixed states is
proposed. In addition, for two correlated mixed states, the measurement
realizes an entanglement witness for Werner's separability criterion. To
determine these observables, the estimation only one parameter - the visibility
of interference, is needed. The implementations in cavity QED, trapped ion and
electromagnetically induced transparency experiments are discussed.Comment: 6 pages, 3 figure
Trapped ions in the strong excitation regime: ion interferometry and non--classical states
The interaction of a trapped ion with a laser beam in the strong excitation
regime is analyzed. In this regime, a variety of non--classical states of
motion can be prepared either by using laser pulses of well defined area, or by
an adiabatic passage scheme based on the variation of the laser frequency. We
show how these states can be used to investigate fundamental properties of
quantum mechanics. We also study possible applications of this system to build
an ion interferometer.Comment: 9 pages, Revtex format, 5 compressed postscript figure
Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
We introduce a new set of generalized Fokker-Planck equations that conserve
energy and mass and increase a generalized entropy until a maximum entropy
state is reached. The concept of generalized entropies is rigorously justified
for continuous Hamiltonian systems undergoing violent relaxation. Tsallis
entropies are just a special case of this generalized thermodynamics.
Application of these results to stellar dynamics, vortex dynamics and Jupiter's
great red spot are proposed. Our prime result is a novel relaxation equation
that should offer an easily implementable parametrization of geophysical
turbulence. This relaxation equation depends on a single key parameter related
to the skewness of the fine-grained vorticity distribution. Usual
parametrizations (including a single turbulent viscosity) correspond to the
infinite temperature limit of our model. They forget a fundamental systematic
drift that acts against diffusion as in Brownian theory. Our generalized
Fokker-Planck equations may have applications in other fields of physics such
as chemotaxis for bacterial populations. We propose the idea of a
classification of generalized entropies in classes of equivalence and provide
an aesthetic connexion between topics (vortices, stars, bacteries,...) which
were previously disconnected.Comment: Submitted to Phys. Rev.
Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions
A N-sized inertial classical Heisenberg ferromagnet, which consists in a
modification of the well-known standard model, where the spins are replaced by
classical rotators, is studied in the limit of infinite-range interactions. The
usual canonical-ensemble mean-field solution of the inertial classical
-vector ferromagnet (for which recovers the particular Heisenberg
model considered herein) is briefly reviewed, showing the well-known
second-order phase transition. This Heisenberg model is studied numerically
within the microcanonical ensemble, through molecular dynamics.Comment: 18 pages text, and 7 EPS figure
Generalizations of entanglement based on coherent states and convex sets
Unentangled pure states on a bipartite system are exactly the coherent states
with respect to the group of local transformations. What aspects of the study
of entanglement are applicable to generalized coherent states? Conversely, what
can be learned about entanglement from the well-studied theory of coherent
states? With these questions in mind, we characterize unentangled pure states
as extremal states when considered as linear functionals on the local Lie
algebra. As a result, a relativized notion of purity emerges, showing that
there is a close relationship between purity, coherence and (non-)entanglement.
To a large extent, these concepts can be defined and studied in the even more
general setting of convex cones of states. Based on the idea that entanglement
is relative, we suggest considering these notions in the context of partially
ordered families of Lie algebras or convex cones, such as those that arise
naturally for multipartite systems. The study of entanglement includes notions
of local operations and, for information-theoretic purposes, entanglement
measures and ways of scaling systems to enable asymptotic developments. We
propose ways in which these may be generalized to the Lie-algebraic setting,
and to a lesser extent to the convex-cones setting. One of our original
motivations for this program is to understand the role of entanglement-like
concepts in condensed matter. We discuss how our work provides tools for
analyzing the correlations involved in quantum phase transitions and other
aspects of condensed-matter systems.Comment: 37 page
- …