3,593 research outputs found
Plurisubharmonic polynomials and bumping
We wish to study the problem of bumping outwards a pseudoconvex, finite-type
domain \Omega\subset C^n in such a way that pseudoconvexity is preserved and
such that the lowest possible orders of contact of the bumped domain with
bdy(\Omega), at the site of the bumping, are explicitly realised. Generally,
when \Omega\subset C^n, n\geq 3, the known methods lead to bumpings with high
orders of contact -- which are not explicitly known either -- at the site of
the bumping. Precise orders are known for h-extendible/semiregular domains.
This paper is motivated by certain families of non-semiregular domains in C^3.
These families are identified by the behaviour of the least-weight
plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study
how to perturb certain homogeneous plurisubharmonic polynomials without
destroying plurisubharmonicity.Comment: 24 pages; corrected typos, fixed errors in Lemma 3.3; accepted for
publication in Math.
Most Complex Regular Right-Ideal Languages
A right ideal is a language L over an alphabet A that satisfies L = LA*. We
show that there exists a stream (sequence) (R_n : n \ge 3) of regular right
ideal languages, where R_n has n left quotients and is most complex under the
following measures of complexity: the state complexities of the left quotients,
the number of atoms (intersections of complemented and uncomplemented left
quotients), the state complexities of the atoms, the size of the syntactic
semigroup, the state complexities of the operations of reversal, star, and
product, and the state complexities of all binary boolean operations. In that
sense, this stream of right ideals is a universal witness.Comment: 19 pages, 4 figures, 1 tabl
Ground state of a polydisperse electrorheological solid: Beyond the dipole approximation
The ground state of an electrorheological (ER) fluid has been studied based
on our recently proposed dipole-induced dipole (DID) model. We obtained an
analytic expression of the interaction between chains of particles which are of
the same or different dielectric constants. The effects of dielectric constants
on the structure formation in monodisperse and polydisperse electrorheological
fluids are studied in a wide range of dielectric contrasts between the
particles and the base fluid. Our results showed that the established
body-centered tetragonal ground state in monodisperse ER fluids may become
unstable due to a polydispersity in the particle dielectric constants. While
our results agree with that of the fully multipole theory, the DID model is
much simpler, which offers a basis for computer simulations in polydisperse ER
fluids.Comment: Accepted for publications by Phys. Rev.
Large Aperiodic Semigroups
The syntactic complexity of a regular language is the size of its syntactic
semigroup. This semigroup is isomorphic to the transition semigroup of the
minimal deterministic finite automaton accepting the language, that is, to the
semigroup generated by transformations induced by non-empty words on the set of
states of the automaton. In this paper we search for the largest syntactic
semigroup of a star-free language having left quotients; equivalently, we
look for the largest transition semigroup of an aperiodic finite automaton with
states.
We introduce two new aperiodic transition semigroups. The first is generated
by transformations that change only one state; we call such transformations and
resulting semigroups unitary. In particular, we study complete unitary
semigroups which have a special structure, and we show that each maximal
unitary semigroup is complete. For there exists a complete unitary
semigroup that is larger than any aperiodic semigroup known to date.
We then present even larger aperiodic semigroups, generated by
transformations that map a non-empty subset of states to a single state; we
call such transformations and semigroups semiconstant. In particular, we
examine semiconstant tree semigroups which have a structure based on full
binary trees. The semiconstant tree semigroups are at present the best
candidates for largest aperiodic semigroups.
We also prove that is an upper bound on the state complexity of
reversal of star-free languages, and resolve an open problem about a special
case of state complexity of concatenation of star-free languages.Comment: 22 pages, 1 figure, 2 table
Clifford algebras and universal sets of quantum gates
In this paper is shown an application of Clifford algebras to the
construction of computationally universal sets of quantum gates for -qubit
systems. It is based on the well-known application of Lie algebras together
with the especially simple commutation law for Clifford algebras, which states
that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR
Effective nonlinear optical properties of composite media of graded spherical particles
We have developed a nonlinear differential effective dipole approximation
(NDEDA), in an attempt to investigate the effective linear and third-order
nonlinear susceptibility of composite media in which graded spherical
inclusions with weak nonlinearity are randomly embedded in a linear host
medium. Alternatively, based on a first-principles approach, we derived exactly
the linear local field inside the graded particles having power-law dielectric
gradation profiles. As a result, we obtain also the effective linear dielectric
constant and third-order nonlinear susceptibility. Excellent agreement between
the two methods is numerically demonstrated. As an application, we apply the
NDEDA to investigate the surface plasma resonant effect on the optical
absorption, optical nonlinearity enhancement, and figure of merit of
metal-dielectric composites. It is found that the presence of gradation in
metal particles yields a broad resonant band in the optical region, and further
enhances the figure of merit.Comment: 20 pages, 5 figure
On the Shuffle Automaton Size for Words
We investigate the state size of DFAs accepting the shuffle of two words. We
provide words u and v, such that the minimal DFA for u shuffled with v requires
an exponential number of states. We also show some conditions for the words u
and v which ensure a quadratic upper bound on the state size of u shuffled with
v. Moreover, switching only two letters within one of u or v is enough to
trigger the change from quadratic to exponential
Schwinger model on a half-line
We study the Schwinger model on a half-line in this paper. In particular, we
investigate the behavior of the chiral condensate near the edge of the line.
The effect of the chosen boundary condition is emphasized. The extension to the
finite temperature case is straightforward in our approach.Comment: 4 pages, no figure. Final version to be published on Phys. Rev.
Decoherence and Relaxation of a Quantum Bit in the Presence of Rabi Oscillations
Dissipative dynamics of a quantum bit driven by a strong resonant field and
interacting with a heat bath is investigated. We derive generalized Bloch
equations and find modifications of the qubit's damping rates caused by Rabi
oscillations. Nonequilibrium decoherence of a phase qubit inductively coupled
to a LC-circuit is considered as an illustration of the general results. It is
argued that recent experimental results give a clear evidence of effective
suppression of decoherence in a strongly driven flux qubit.Comment: 14 pages; misprints correcte
Theory of weak continuous measurements in a strongly driven quantum bit
Continuous spectroscopic measurements of a strongly driven superconducting
qubit by means of a high-quality tank circuit (a linear detector) are under
study. Output functions of the detector, namely, a spectrum of voltage
fluctuations and an impedance, are expressed in terms of the qubit spectrum and
magnetic susceptibility. The nonequilibrium spectrum of the current
fluctuations in the qubit loop and the linear response function of the driven
qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating
wave approximations. Backaction effects of the qubit on the tank and the tank
on the qubit are analyzed quantitatively. We show that the voltage spectrum of
the tank provides detailed information about a frequency and a decay rate of
Rabi oscillations in the qubit. It is found that both an efficiency of
spectroscopic measurement and measurement-induced decoherence of the qubit
demonstrate a resonant behaviour as the Rabi frequency approaches the resonant
frequency of the tank. We determine conditions when the spectroscopic
observation of the Rabi oscillations in the flux qubit with the tank circuit
can be considered as a weak continuous quantum measurement.Comment: 28 page
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