22,756 research outputs found
S-regular functions which preserve a complex slice
We study global properties of quaternionic slice regular functions (also
called s-regular) defined on symmetric slice domains. In particular, thanks to
new techniques and points of view, we can characterize the property of being
one-slice preserving in terms of the projectivization of the vectorial part of
the function. We also define a "Hermitian" product on slice regular functions
which gives us the possibility to express the -product of two s-regular
functions in terms of the scalar product of suitable functions constructed
starting from and . Afterwards we are able to determine, under different
assumptions, when the sum, the -product and the -conjugation of two slice
regular functions preserve a complex slice. We also study when the -power of
a slice regular function has this property or when it preserves all complex
slices. To obtain these results we prove two factorization theorems: in the
first one, we are able to split a slice regular function into the product of
two functions: one keeping track of the zeroes and the other which is
never-vanishing; in the other one we give necessary and sufficient conditions
for a slice regular function (which preserves all complex slices) to be the
symmetrized of a suitable slice regular one.Comment: 23 pages, to appear in Annali di Matematica Pura e Applicat
Heritage, gentrification, participation : remaking urban landscapes in the name of culture and historic preservation : introduction
This special issue explores the relationship between heritagization, shifting economies, and urban struggles in different cities around the globe. Our aim is to examine the conditions that have brought history, culture, an old/new urban aesthetics, real estate values, and housing struggles in a relational nexus by looking at the ways in which differently-situated actors mobilize the language of cultural heritage to act upon urban spaces. Ideas of what constitutes a beautiful and livable city are changing along with capital accumulation strategies and urban social geographies. The growing heritagization of historic neighborhoods enables local governments and real-estate developers to engender massive spatial and social changes in the urban landscape. City authorities renovate last swaths of urban fabrics in the name of historic preservation and of the ‘common good’, but this often means that local residents are evicted while private developers allied with these authorities realize huge profits by ‘regenerating’ depressed areas. Yet, local residents also resort to the language of cultural heritage to combat the destruction of their urban worlds. What are the consequences for those who cannot afford to live in the newly restored quarters? What kinds of heritage rhetoric are being mobilized by involved actors? How do rooted political cultures shape the local instantiation of this globalizing phenomenon? Recent urban struggles in the Middle East and Europe reveal an inextricable link between heritagization, gentrification, and urban politics. We invite contributors to submit papers dealing with such links between heritagization and housing struggles, evictions, cultural capitalism, and changing urban aesthetics.
-exponential of slice-regular functions
According to [5] we define the -exponential of a slice-regular function,
which can be seen as a generalization of the complex exponential to
quaternions. Explicit formulas for are provided, also in terms of
suitable sine and cosine functions. We completely classify under which
conditions the -exponential of a function is either slice-preserving or
-preserving for some and show that
is never-vanishing. Sharp necessary and sufficient conditions are given in
order that , finding an exceptional and
unexpected case in which equality holds even if and do not commute. We
also discuss the existence of a square root of a slice-preserving regular
function, characterizing slice-preserving functions (defined on the
circularization of simply connected domains) which admit square roots. Square
roots of this kind of functions are used to provide a further formula for
. A number of examples is given throughout the paper.Comment: 15 pages; to appear in Proceedings of the American Mathematical
Societ
Reduction of pre-Hamiltonian actions
We prove a reduction theorem for the tangent bundle of a Poisson manifold
endowed with a pre-Hamiltonian action of a Poisson Lie group . In the special case of a Hamiltonian action of a Lie group, we are
able to compare our reduction to the classical Marsden-Ratiu reduction of .
If the manifold is symplectic and simply connected, the reduced tangent
bundle is integrable and its integral symplectic groupoid is the
Marsden-Weinstein reduction of the pair groupoid .Comment: 18 pages, final version, to appear in Journal of Geometry and Physic
Cavity assisted measurements of heat and work in optical lattices
We propose a method to experimentally measure the internal energy of a system
of ultracold atoms trapped in optical lattices by coupling them to the fields
of two optical cavities. We show that the tunnelling and self-interaction terms
of the one-dimensional Bose-Hubbard Hamiltonian can be mapped to the field and
photon number of each cavity, respectively. We compare the energy estimated
using this method with numerical results obtained using the density matrix
renormalisation group algorithm. Our method can be employed for the assessment
of power and efficiency of thermal machines whose working substance is a
strongly correlated many-body system.Comment: Accepted version in Quantum. Updates: New results for the work in
quenching a Bose-Hubbard model; new references; v3 fixed doi links in
references to make paper compliant with Quantu
Detection of entanglement in ultracold lattice gases
We propose the use of quantum polarization spectroscopy for detecting
multi-particle entanglement of ultracold atoms in optical lattices. This
method, based on a light-matter interface employing the quantum Farady effect,
allows for the non destructive measurement of spin-spin correlations. We apply
it to the specific example of a one dimensional spin chain and reconstruct its
phase diagram using the light signal, readily measurable in experiments with
ultracold atoms. Interestingly, the same technique can be extended to detect
quantum many-body entanglement in such systems.Comment: Submitted to the Special Issue: "Strong correlations in Quantum
Gases" in The Journal of Low Temperature Physic
Genuine quantum correlations in quantum many-body systems: a review of recent progress
Quantum information theory has considerably helped in the understanding of
quantum many-body systems. The role of quantum correlations and in particular,
bipartite entanglement, has become crucial to characterise, classify and
simulate quantum many body systems. Furthermore, the scaling of entanglement
has inspired modifications to numerical techniques for the simulation of
many-body systems leading to the, now established, area of tensor networks.
However, the notions and methods brought by quantum information do not end with
bipartite entanglement. There are other forms of correlations embedded in the
ground, excited and thermal states of quantum many-body systems that also need
to be explored and might be utilised as potential resources for quantum
technologies. The aim of this work is to review the most recent developments
regarding correlations in quantum many-body systems focussing on multipartite
entanglement, quantum nonlocality, quantum discord, mutual information but also
other non classical measures of correlations based on quantum coherence.
Moreover, we also discuss applications of quantum metrology in quantum
many-body systems.Comment: Review. Close to published version. Comments are welcome! Please
write an email to g.dechiara[(at)]qub.ac.u
Quantum correlations and thermodynamic performances of two-qubit engines with local and collective baths
We investigate heat engines whose working substance is made of two coupled
qubits performing a generalised Otto cycle by varying their applied magnetic
field or their interaction strength during the compression and expansion
strokes. During the heating and cooling strokes, the two qubits are coupled to
local and common environments that are not necessarily at equilibrium. We find
instances of quantum engines coupled to non equilibrium common environments
exhibiting non-trivial connections to quantum correlations as witnessed by a
monotonic dependence of the work produced on quantum discord and entanglement.Comment: Close to published versio
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