665 research outputs found
Tilings, tiling spaces and topology
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic
tiling), we construct a space of similar tilings, on which the group of
translations acts naturally. This space is then an (abstract) dynamical system.
Dynamical properties of the space (such as mixing, or the spectrum of the
translation operator) are closely related to bulk properties of the individual
tilings (such as the diffraction pattern). The topology of the space of
tilings, particularly the Cech cohomology, gives information on how the
original tiling can be deformed. Tiling spaces can be constructed as inverse
limits of branched manifolds.Comment: 8 pages, including 2 figures, talk given at ICQ
Tiling Spaces are Inverse Limits
Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space
of tilings of M, with finite local complexity (relative to some symmetry group
Gamma) and closed in the natural topology. Then Omega is the inverse limit of a
sequence of compact finite-dimensional branched manifolds. The branched
manifolds are (finite) unions of cells, constructed from the tiles themselves
and the group Gamma. This result extends previous results of Anderson and
Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and
of G\"ahler. In particular, the construction in this paper is a natural
generalization of G\"ahler's.Comment: Latex, 6 pages, including one embedded figur
Transport and Dissipation in Quantum Pumps
This paper is about adiabatic transport in quantum pumps. The notion of
``energy shift'', a self-adjoint operator dual to the Wigner time delay, plays
a role in our approach: It determines the current, the dissipation, the noise
and the entropy currents in quantum pumps. We discuss the geometric and
topological content of adiabatic transport and show that the mechanism of
Thouless and Niu for quantized transport via Chern numbers cannot be realized
in quantum pumps where Chern numbers necessarily vanish.Comment: 31 pages, 10 figure
Efficient Optimal Minimum Error Discrimination of Symmetric Quantum States
This paper deals with the quantum optimal discrimination among mixed quantum
states enjoying geometrical uniform symmetry with respect to a reference
density operator . It is well-known that the minimal error probability
is given by the positive operator-valued measure (POVM) obtained as a solution
of a convex optimization problem, namely a set of operators satisfying
geometrical symmetry, with respect to a reference operator , and
maximizing . In this paper, by resolving the dual
problem, we show that the same result is obtained by minimizing the trace of a
semidefinite positive operator commuting with the symmetry operator and
such that . The new formulation gives a deeper insight into the
optimization problem and allows to obtain closed-form analytical solutions, as
shown by a simple but not trivial explanatory example. Besides the theoretical
interest, the result leads to semidefinite programming solutions of reduced
complexity, allowing to extend the numerical performance evaluation to quantum
communication systems modeled in Hilbert spaces of large dimension.Comment: 5 pages, 1 Table, no figure
Angioarchitectural evolution of clival dural arteriovenous fistulas in two patients.
Dural arteriovenous fistulas (dAVFs) may present in a variety of ways, including as carotid-cavernous sinus fistulas. The ophthalmologic sequelae of carotid-cavernous sinus fistulas are known and recognizable, but less commonly seen is the rare clival fistula. Clival dAVFs may have a variety of potential anatomical configurations but are defined by the involvement of the venous plexus just overlying the bony clivus. Here we present two cases of clival dAVFs that most likely evolved from carotid-cavernous sinus fistulas
Topological Invariants in Fermi Systems with Time-Reversal Invariance
We discuss topological invariants for Fermi systems that have time-reversal invariance. The TKN^2 integers (first Chern numbers) are replaced by second Chern numbers, and Berry's phase becomes a unit quaternion, or equivalently an element of SU(2). The canonical example playing much the same role as spin ½ in a magnetic field is spin ½ in a quadrupole electric field. In particular, the associated bundles are nontrivial and have ± 1 second Chern number. The connection that governs the adiabatic evolution coincides with the symmetric SU(2) Yang-Mills instanton
2+1 Dimensional Georgi-Glashow Instantons in Weyl Gauge
Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are
transformed into the Weyl gauge. This illustrates the tunneling interpretation
of these instantons and provides a smooth regularization of the singular
unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron
solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D
Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak
theory which has a sphaleron but no instantons. We also discuss the spectral
flow picture of fundamental fermions in a Georgi-Glashow instanton background.Comment: 22 pages, 8 figures, revtex4; v2 - references and comments adde
How does working from home during Covid-19 affect what managers do? Evidence from time-use studies
We assess how the sudden and widespread shift to working from home during the pandemic impacted how managers allocate time throughout their working day. We analyze the results from an online time-use survey with data on 1,192 knowledge workers (out of which 973 are managers) in two waves, a pre-pandemic wave collected in August/2019 (615 participants, out of which 506 are managers) and a post-pandemic wave collected in August/2020 (577 participants, out of which 464 are managers). Our findings indicate that the forced transition to WFH created by the COVID pandemic was associated with a drastic reduction in commuting time for managers, but also an increase in time spent in work rather than on personal activities. This included reallocating time gained from commuting into more time spent in meetings, possibly to recoup some of the extemporaneous interactions that typically happen in the office. This change is particularly pronounced for managers employed in larger organizations. We use the results from the time-use studies to discuss implications for the development of new technologies
Multitasking while driving: a time use study of commuting knowledge workers to access current and future uses
Commuting has enormous impact on individuals, families, organizations, and society. Advances in vehicle automation may help workers employ the time spent commuting in productive work-tasks or wellbeing activities. To achieve this goal, however, we need to develop a deeper understanding of which work and personal activities are of value for commuting workers. In this paper we present results from an online time-use study of 400 knowledge workers who commute-by-driving. The data allow us to study multitasking-while-driving behavior of com-muting knowledge workers, identify which non-driving tasks knowledge workers currently engage in while driving, and the non-driving tasks individuals would like to engage in when using a safe highly automated vehicle in the future. We discuss the implications of our findings for the design of technology that supports work and wellbeing activities in automated cars
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