16,905 research outputs found
Gorensteinness of invariant subrings of quantum algebras
We prove Auslander-Gorenstein and \GKdim-Macaulay properties for certain
invariant subrings of some quantum algebras, the Weyl algebras, and the
universal enveloping algebras of finite dimensional Lie algebras.Comment: AMSTEX, 18 pages. Revised and corrected versio
Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States
Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev.
Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party
correlations in two families of -qutrit Greenberger-Horne-Zeilinger type
states. For the pure states in one of the families, the irreducible 2-party,
-party and -party () correlations are nonzero, which is
different from the -qubit case. We also derive the correlation distributions
in the -qutrit maximal slice state, which can be uniquely determined by its
-qutrit reduced density matrices among pure states. It is proved that
there is no irreducible -qutrit correlation in the maximal slice state. This
enlightens us to give a discussion about how to characterize the pure states
with irreducible -party correlation in arbitrarily high-dimensional systems
by the way of the continuity approach.Comment: 5p, no fi
Quantum speed limit for relativistic spin-0 and spin-1 bosons on commutative and noncommutative planes
Quantum speed limits of relativistic charged spin-0 and spin-1 bosons in the
background of a homogeneous magnetic field are studied on both commutative and
oncommutative planes. We show that, on the commutative plane, the average
speeds of wave packets along the radial direction during the interval in which
a quantum state evolving from an initial state to the orthogonal final one can
not exceed the speed of light, regardless of the intensities of the magnetic
field. However, due to the noncommutativity, the average speeds of the wave
packets on noncommutative plane will exceed the speed of light in vacuum
provided the intensity of the magnetic field is strong enough. It is a clear
signature of violating Lorentz invariance in quantum mechanics region.Comment: 8 pages, no figures. arXiv admin note: text overlap with
arXiv:1702.0316
Long-time self-similar asymptotic of the macroscopic quantum models
The unipolar and bipolar macroscopic quantum models derived recently for
instance in the area of charge transport are considered in spatial
one-dimensional whole space in the present paper. These models consist of
nonlinear fourth-order parabolic equation for unipolar case or coupled
nonlinear fourth-order parabolic system for bipolar case. We show for the first
time the self-similarity property of the macroscopic quantum models in large
time. Namely, we show that there exists a unique global strong solution with
strictly positive density to the initial value problem of the macroscopic
quantum models which tends to a self-similar wave (which is not the exact
solution of the models) in large time at an algebraic time-decay rate.Comment: 18 page
Two-parameter quantum general linear supergroups
The universal R-matrix of two-parameter quantum general linear supergroups is
computed explicitly based on the RTT realization of
Faddeev--Reshetikhin--Takhtajan.Comment: v1: 14 pages. v2: published version, 9 pages, title changed and the
section on central extension remove
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