8 research outputs found
Gauge Invariant Fractional Electromagnetic Fields
Fractional derivatives and integrations of non-integers orders was introduced
more than three centuries ago but only recently gained more attention due to
its application on nonlocal phenomenas. In this context, several formulations
of fractional electromagnetic fields was proposed, but all these theories
suffer from the absence of an effective fractional vector calculus, and in
general are non-causal or spatially asymmetric. In order to deal with these
difficulties, we propose a spatially symmetric and causal gauge invariant
fractional electromagnetic field from a Lagrangian formulation. From our
fractional Maxwell's fields arose a definition for the fractional gradient,
divergent and curl operators.Comment: accepted for publication in Physics Letters
Fractional Vector Calculus and Fractional Maxwell's Equations
The theory of derivatives and integrals of non-integer order goes back to
Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional
vector calculus (FVC) has only 10 years. The main approaches to formulate a
FVC, which are used in the physics during the past few years, will be briefly
described in this paper. We solve some problems of consistent formulations of
FVC by using a fractional generalization of the Fundamental Theorem of
Calculus. We define the differential and integral vector operations. The
fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of
these theorems are realized for simplest regions. A fractional generalization
of exterior differential calculus of differential forms is discussed.
Fractional nonlocal Maxwell's equations and the corresponding fractional wave
equations are considered.Comment: 42 pages, LaTe
Exciton entanglement in two coupled semiconductor microcrystallites
Entanglement of the excitonic states in the system of two coupled
semiconductor microcrystallites, whose sizes are much larger than the Bohr
radius of exciton in bulk semiconductor but smaller than the relevant optical
wavelength, is quantified in terms of the entropy of entanglement. It is
observed that the nonlinear interaction between excitons increases the maximum
values of the entropy of the entanglement more than that of the linear coupling
model. Therefore, a system of two coupled microcrystallites can be used as a
good source of entanglement with fixed exciton number. The relationship between
the entropy of the entanglement and the population imbalance of two
microcrystallites is numerically shown and the uppermost envelope function for
them is estimated by applying the Jaynes principle.Comment: 16 pages, 6 figure
Dynamics of entanglement for coherent excitonic states in a system of two coupled quantum dots and cavity QED
The dynamics of the entanglement for coherent excitonic states in the system
of two coupled large semiconductor quantum dots () mediated by a
single-mode cavity field is investigated. Maximally entangled coherent
excitonic states can be generated by cavity field initially prepared in odd
coherent state. The entanglement of the excitonic coherent states between two
dots reaches maximum when no photon is detected in the cavity. The effects of
the zero-temperature environment on the entanglement of excitonic coherent
state are also studied using the concurrence for two subsystems of the excitonsComment: 7 pages, 6 figure
Multipartite entangled states in coupled quantum dots and cavity-QED
We investigate the generation of multipartite entangled state in a system of
N quantum dots embedded in a microcavity and examine the emergence of genuine
multipartite entanglement by three different characterizations of entanglement.
At certain times of dynamical evolution one can generate multipartite entangled
coherent exciton states or multiqubit states by initially preparing the
cavity field in a superposition of coherent states or the Fock state with one
photon, respectively. Finally we study environmental effects on multipartite
entanglement generation and find that the decay rate for the entanglement is
proportional to the number of excitons.Comment: 9 pages, 4 figures, to appear in Phys. Rev.