3,315 research outputs found
A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation
We give a short proof of asymptotic completeness and global existence for the
cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing
with the long range behavior of the asymptotic solution is by reducing it, in
hyperbolic coordinates to the study of an ODE. Similar arguments extend to
higher dimensions and other long range type nonlinear problems.Comment: To appear in Lett. Math. Phy
Simple Non Linear Klein-Gordon Equations in 2 space dimensions, with long range scattering
We establish that solutions, to the most simple NLKG equations in 2 space
dimensions with mass resonance, exhibits long range scattering phenomena.
Modified wave operators and solutions are constructed for these equations. We
also show that the modified wave operators can be chosen such that they
linearize the non-linear representation of the Poincar\'e group defined by the
NLKG.Comment: 19 pages, LaTeX, To appear in Lett. Math. Phy
Chains of Quasi-Classical Informations for Bipartite Correlations and the Role of Twin Observables
Having the quantum correlations in a general bipartite state in mind, the
information accessible by simultaneous measurement on both subsystems is shown
never to exceed the information accessible by measurement on one subsystem,
which, in turn is proved not to exceed the von Neumann mutual information. A
particular pair of (opposite- subsystem) observables are shown to be
responsible both for the amount of quasi-classical correlations and for that of
the purely quantum entanglement in the pure-state case: the former via
simultaneous subsystem measurements, and the latter through the entropy of
coherence or of incompatibility, which is defined for the general case. The
observables at issue are so-called twin observables. A general definition of
the latter is given in terms of their detailed properties.Comment: 7 pages, Latex2e, selected for the December 2002 issue of the Virtual
Journal of Quantum Informatio
The fidelity of general bosonic channels with pure state input
We first derive for the general form of the fidelity for various bosonic
channels. Thereby we give the fidelity of different quantum bosonic channel,
possibly with product input and entangled input respectively, as examples. The
properties of the fidelity are carefully examined.Comment: 3 pages, comments welcom
Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
We argue from the point of view of statistical inference that the quantum
relative entropy is a good measure for distinguishing between two quantum
states (or two classes of quantum states) described by density matrices. We
extend this notion to describe the amount of entanglement between two quantum
systems from a statistical point of view. Our measure is independent of the
number of entangled systems and their dimensionality.Comment: 11 pages no figures, to appear in Phys. Rev.
Kinematic approach to the mixed state geometric phase in nonunitary evolution
A kinematic approach to the geometric phase for mixed quantal states in
nonunitary evolution is proposed. This phase is manifestly gauge invariant and
can be experimentally tested in interferometry. It leads to well-known results
when the evolution is unitary.Comment: Minor changes; journal reference adde
Correlations in optically-controlled quantum emitters
We address the problem of optically controlling and quantifying the
dissipative dynamics of quantum and classical correlations in a set-up of
individual quantum emitters under external laser excitation. We show that both
types of correlations, the former measured by the quantum discord, are present
in the system's evolution even though the emitters may exhibit an early stage
disentanglement. In the absence of external laser pumping,we demonstrate
analytically, for a set of suitable initial states, that there is an entropy
bound for which quantum discord and entanglement of the emitters are always
greater than classical correlations, thus disproving an early conjecture that
classical correlations are greater than quantum correlations. Furthermore, we
show that quantum correlations can also be greater than classical correlations
when the system is driven by a laser field. For scenarios where the emitters'
quantum correlations are below their classical counterparts, an optimization of
the evolution of the quantum correlations can be carried out by appropriately
tailoring the amplitude of the laser field and the emitters' dipole-dipole
interaction. We stress the importance of using the entanglement of formation,
rather than the concurrence, as the entanglement measure, since the latter can
grow beyond the total correlations and thus give incorrect results on the
actual system's degree of entanglement.Comment: 11 pages, 10 figures, this version contains minor modifications; to
appear in Phys. Rev.
Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint
In this paper it was proved that the quantum relative entropy can be asymptotically attained by Kullback Leibler divergences of
probabilities given by a certain sequence of POVMs. The sequence of POVMs
depends on , but is independent of the choice of .Comment: LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment
for Quantum Relative Entropy
Steady state entanglement in open and noisy quantum systems at high temperature
We show that quantum mechanical entanglement can prevail even in noisy open
quantum systems at high temperature and far from thermodynamical equilibrium,
despite the deteriorating effect of decoherence. The system consists of a
number N of interacting quantum particles, and it can interact and exchange
particles with some environment. The effect of decoherence is counteracted by a
simple mechanism, where system particles are randomly reset to some standard
initial state, e.g. by replacing them with particles from the environment. We
present a master equation that describes this process, which we can solve
analytically for small N. If we vary the interaction strength and the reset
against decoherence rate, we find a threshold below which the equilibrium state
is classically correlated, and above which there is a parameter region with
genuine entanglement.Comment: 5 pages, 3 figure
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
We study self-adjoint operators defined by factorizing second order
differential operators in first order ones. We discuss examples where such
factorizations introduce singular interactions into simple quantum mechanical
models like the harmonic oscillator or the free particle on the circle. The
generalization of these examples to the many-body case yields quantum models of
distinguishable and interacting particles in one dimensions which can be solved
explicitly and by simple means. Our considerations lead us to a simple method
to construct exactly solvable quantum many-body systems of Calogero-Sutherland
type.Comment: 17 pages, LaTe
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