1,452 research outputs found
Universal Measure of Entanglement
A general framework is developed for separating classical and quantum
correlations in a multipartite system. Entanglement is defined as the
difference in the correlation information encoded by the state of a system and
a suitably defined separable state with the same marginals. A generalization of
the Schmidt decomposition is developed to implement the separation of
correlations for any pure, multipartite state. The measure based on this
decomposition is a generalization of the entanglement of formation to
multipartite systems, provides an upper bound for the relative entropy of
entanglement, and is directly computable on pure states. The example of pure
three-qubit states is analyzed in detail, and a classification based on
minimal, four-term decompositions is developed.Comment: 4 page
Multi-center MICZ-Kepler system, supersymmetry and integrability
We propose the general scheme of incorporation of the Dirac monopoles into
mechanical systems on the three-dimensional conformal flat space. We found that
any system (without monopoles) admitting the separation of variables in the
elliptic or parabolic coordinates can be extended to the integrable system with
the Dirac monopoles located at the foci of the corresponding coordinate
systems. Particular cases of this class of system are the two-center
MICZ-Kepler system in the Euclidean space, the limiting case when one of the
background dyons is located at the infinity as well as the model of particle in
parabolic quantum dot in the presence of parallel constant uniform electric and
magnetic fields.Comment: 5 pages, revtex, revised versio
Coulomb-oscillator duality in spaces of constant curvature
In this paper we construct generalizations to spheres of the well known
Levi-Civita, Kustaanheimo-Steifel and Hurwitz regularizing transformations in
Euclidean spaces of dimensions 2, 3 and 5. The corresponding classical and
quantum mechanical analogues of the Kepler-Coulomb problem on these spheres are
discussed.Comment: 33 pages, LaTeX fil
Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
We study the relation between the recently defined localizable entanglement
and generalized correlations in quantum spin systems. Differently from the
current belief, the localizable entanglement is always given by the average of
a generalized string. Using symmetry arguments we show that in most spin 1/2
and spin 1 systems the localizable entanglement reduces to the spin-spin or
string correlations, respectively. We prove that a general class of spin 1
systems, which includes the Heisenberg model, can be used as perfect quantum
channel. These conclusions are obtained in analytic form and confirm some
results found previously on numerical grounds.Comment: 5 pages, RevTeX
The relation between the model of a crystal with defects and Plebanski's theory of gravity
In the present investigation we show that there exists a close analogy of
geometry of spacetime in GR with a structure of defects in a crystal. We
present the relation between the Kleinert's model of a crystal with defects and
Plebanski's theory of gravity. We have considered the translational defects -
dislocations, and the rotational defects - disclinations - in the 3- and
4-dimensional crystals. The 4-dimensional crystalline defects present the
Riemann-Cartan spacetime which has an additional geometric property - "torsion"
- connected with dislocations. The world crystal is a model for the gravitation
which has a new type of gauge symmetry: the Einstein's gravitation has a zero
torsion as a special gauge, while a zero connection is another equivalent gauge
with nonzero torsion which corresponds to the Einstein's theory of
"teleparallelism". Any intermediate choice of the gauge with nonzero connection
A^{IJ}_\mu is also allowed. In the present investigation we show that in the
Plebanski formulation the phase of gravity with torsion is equivalent to the
ordinary or topological gravity, and we can exclude a torsion as a separate
dynamical variable.Comment: 13 pages, 2 figure
Statistical description of small quantum systems beyond weak-coupling limit
An explicit expression is derived for the statistical description of small
quantum systems, which are relatively-weakly and directly coupled to only small
parts of their environments. The derived expression has a canonical form, but
is given by a renormalized self-Hamiltonian of the studied system, which
appropriately takes into account the influence of the system-environment
interaction. In the case that the system has a narrow spectrum and the
environment is sufficiently large, the modification to the self-Hamiltonian
usually has a mean-field feature, given by an environmental average of the
interaction Hamiltonian. In other cases, the modification may be beyond the
mean-field approximation.Comment: 9 pages, published versio
On the nonsymmetric purely affine gravity
We review the vacuum purely affine gravity with the nonsymmetric connection
and metric. We also examine dynamical effects of the second Ricci tensor and
covariant second-rank tensors constructed from the torsion tensor in the
gravitational Lagrangian.Comment: 15 pages; published versio
Weak momentum scattering and the conductivity of graphene
Electrical transport in graphene offers a fascinating parallel to spin
transport in semiconductors including the spin-Hall effect. In the weak
momentum scattering regime the steady-state density matrix contains two
contributions, one linear in the carrier number density and characteristic
scattering time , the other independent of either. In this paper we take
the Liouville equation as our starting point and demonstrate that these two
contributions can be identified with pseudospin conservation and
non-conservation respectively, and are connected in a non-trivial manner by
scattering processes. The scattering term has a distinct form, which is
peculiar to graphene and has important consequences in transport. The
contribution linear in is analogous to the part of the spin density
matrix which yields a steady state spin density, while the contribution
independent of , is analogous to the part of the spin density matrix
which yields a steady state spin current. Unlike in systems with spin-orbit
interactions, the and -independent part of the conductivity is
reinforced in the weak momentum scattering regime by scattering between the
conserved and non-conserved pseudospin distributions.Comment: 10 pages. Accepted for publication in Phys. Rev.
Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional
We study a gauge-invariant variational framework for the Yang-Mills vacuum
wave functional. Our approach is built on gauge-averaged Gaussian trial
functionals which substantially extend previously used trial bases in the
infrared by implementing a general low-momentum expansion for the vacuum-field
dispersion (which is taken to be analytic at zero momentum). When completed by
the perturbative Yang-Mills dispersion at high momenta, this results in a
significantly enlarged trial functional space which incorporates both dynamical
mass generation and asymptotic freedom. After casting the dynamics associated
with these wave functionals into an effective action for collections of soft
vacuum-field orbits, the leading infrared improvements manifest themselves as
four-gradient interactions. Those turn out to significantly lower the minimal
vacuum energy density, thus indicating a clear overall improvement of the
vacuum description. The dimensional transmutation mechanism and the dynamically
generated mass scale remain almost quantitatively robust, however, which
ensures that our prediction for the gluon condensate is consistent with
standard values. Further results include a finite group velocity for the soft
gluonic modes due to the higher-gradient corrections and indications for a
negative differential color resistance of the Yang-Mills vacuum.Comment: 47 pages, 5 figures (vs2 contains a few minor stylistic adjustments
to match the published version
Berry phase in entangled systems: a proposed experiment with single neutrons
The influence of the geometric phase, in particular the Berry phase, on an
entangled spin-1/2 system is studied. We discuss in detail the case, where the
geometric phase is generated only by one part of the Hilbert space. We are able
to cancel the effects of the dynamical phase by using the ``spin-echo'' method.
We analyze how the Berry phase affects the Bell angles and the maximal
violation of a Bell inequality. Furthermore we suggest an experimental
realization of our setup within neutron interferometry.Comment: 10 pages, 6 figures, Introduction extended, References adde
- …