30,173 research outputs found
UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square
functions associated with Poisson semigroups for Bessel operators are defined
by using fractional derivatives. If B is a UMD Banach space we obtain for
B-valued Hardy and BMO spaces equivalent norms involving -radonifying
operators and square functions. We also establish characterizations of UMD
Banach spaces by using Hardy and BMO-boundedness properties of g-functions
associated to Bessel-Poisson semigroup
Considerations on bubble fragmentation models
n this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30âD3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22 f(D; D0) = D2 f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) â«0D0 (D/D0)3 f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(Ï”, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, Ï”, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(Ï”, D0) D2/30 Ï”â1/3, with Wet ~ Ï Ï”2/3 D05/3/Ï, where Ï is the density of the continuous phase and Ï the surface tension
UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators
In this paper we define square functions (also called Littlewood-Paley-Stein
functions) associated with heat semigroups for Schr\"odinger and Laguerre
operators acting on functions which take values in UMD Banach spaces. We extend
classical (scalar) L^p-boundedness properties for the square functions to our
Banach valued setting by using \gamma-radonifying operators. We also prove that
these L^p-boundedness properties of the square functions actually characterize
the Banach spaces having the UMD property
New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
We reveal universal dynamical scaling behavior across adiabatic quantum phase
transitions (QPTs) in networks ranging from traditional spatial systems (Ising
model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our
findings, which lie beyond traditional critical exponent analysis and adiabatic
perturbation approximations, are applicable even where excitations have not yet
stabilized and hence provide a time-resolved understanding of QPTs encompassing
a wide range of adiabatic regimes. We show explicitly that even though two
systems may traditionally belong to the same universality class, they can have
very different adiabatic evolutions. This implies more stringent conditions
need to be imposed than at present, both for quantum simulations where one
system is used to simulate the other, and for adiabatic quantum computing
schemes.Comment: 5 pages, 3 figures, plus supplementary material (6 pages, 1 figure
Large dynamic light-matter entanglement from driving neither too fast nor too slow
A significant problem facing next-generation quantum technologies is how to
generate and manipulate macroscopic entanglement in light and matter systems.
Here we report a new regime of dynamical light-matter behavior in which a
giant, system-wide entanglement is generated by varying the light-matter
coupling at \emph{intermediate} velocities. This enhancement is far larger and
broader-ranged than that occurring near the quantum phase transition of the
same model under adiabatic conditions. By appropriate choices of the coupling
within this intermediate regime, the enhanced entanglement can be made to
spread system-wide or to reside in each subsystem separately.Comment: 7 pages, 7 figure
Robust quantum correlations in out-of-equilibrium matter-light systems
High precision macroscopic quantum control in interacting light-matter
systems remains a significant goal toward novel information processing and
ultra-precise metrology. We show that the out-of-equilibrium behavior of a
paradigmatic light-matter system (Dicke model) reveals two successive stages of
enhanced quantum correlations beyond the traditional schemes of near-adiabatic
and sudden quenches. The first stage features magnification of matter-only and
light-only entanglement and squeezing due to effective non-linear
self-interactions. The second stage results from a highly entangled
light-matter state, with enhanced superradiance and signatures of chaotic and
highly quantum states. We show that these new effects scale up consistently
with matter system size, and are reliable even in dissipative environments.Comment: 14 pages, 6 figure
Quantum Hysteresis in Coupled Light-Matter Systems
We investigate the non-equilibrium quantum dynamics of a canonical
light-matter system, namely the Dicke model, when the light-matter interaction
is ramped up and down through a cycle across the quantum phase transition. Our
calculations reveal a rich set of dynamical behaviors determined by the cycle
times, ranging from the slow, near adiabatic regime through to the fast, sudden
quench regime. As the cycle time decreases, we uncover a crossover from an
oscillatory exchange of quantum information between light and matter that
approaches a reversible adiabatic process, to a dispersive regime that
generates large values of light-matter entanglement. The phenomena uncovered in
this work have implications in quantum control, quantum interferometry, as well
as in quantum information theory.Comment: 9 pages and 4 figure
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