7,797 research outputs found
The New SI and the Fundamental Constants of Nature
The launch in 2019 of the new international system of units is an opportunity
to highlight the key role that the fundamental laws of physics and chemistry
play in our lives and in all the processes of basic research, industry and
commerce. The main objective of these notes is to present the new SI in an
accessible way for a wide audience. After reviewing the fundamental constants
of nature and its universal laws, the new definitions of SI units are presented
using, as a unifying principle, the discrete nature of energy, matter and
information in these universal laws. The new SI system is here to stay:
although the experimental realizations may change due to technological
improvements, the definitions will remain unaffected. Quantum metrology is
expected to be one of the driving forces to achieve new quantum technologies of
the second generation.
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La puesta en marcha en 2019 del nuevo sistema internacional de unidades es
una oportunidad para resaltar el papel fundamental que las leyes fundamentales
de la F\'{\i}sica y la Qu\'{\i}mica juegan en nuestra vida y en todos los
procesos de la investigaci\'on fundamental, la industria y el comercio. El
principal objetivo de estas notas es presentar el nuevo SI de forma accesible
para una audiencia amplia. Tras repasar las constantes fundamentales de la
naturaleza y sus leyes universales, se presentan las nuevas definiciones de las
unidades SI utilizando como principio unificador la naturaleza discreta de la
energ\'{\i}a, la materia y la informaci\'on en esas leyes universales. El nuevo
sistema SI tiene vocaci\'on de futuro: aunque las realizaciones experimentales
cambien por mejoras tecnol\'gicas, las definiciones permanecer\'an inalteradas.
La Metrolog\'{\i}a cu\'antica est\'a llamada a ser uno de las fuerzas motrices
para conseguir nuevas tecnolog\'{\i}as cu\'anticas de segunda generaci\'on.Comment: Revtex file, color figures. English version y en espa\~no
Topological Heat Transport and Symmetry-Protected Boson Currents
The study of non-equilibrium properties in topological systems is of
practical and fundamental importance. Here, we analyze the stationary
properties of a two-dimensional bosonic Hofstadter lattice coupled to two
thermal baths in the quantum open-system formalism. Novel phenomena appear like
chiral edge heat currents that are the out-of-equilibrium counterparts of the
zero-temperature edge currents. They support a new concept of dissipative
symmetry-protection, where a set of discrete symmetries protects topological
heat currents, differing from the symmetry-protection devised in closed systems
and zero-temperature. Remarkably, one of these currents flows opposite to the
decreasing external temperature gradient. As the starting point, we consider
the case of a single external reservoir already showing prominent results like
thermal erasure effects and topological thermal currents. Our results are
experimentally accessible with platforms like photonics systems and optical
lattices.Comment: RevTeX4 file, color figure
The Renormalization Group Method and Quantum Groups: the postman always rings twice
We review some of our recent results concerning the relationship between the
Real-Space Renormalization Group method and Quantum Groups. We show this
relation by applying real-space RG methods to study two quantum group invariant
Hamiltonians, that of the XXZ model and the Ising model in a transverse field
(ITF) defined in an open chain with appropriate boundary terms. The quantum
group symmetry is preserved under the RG transformation except for the
appearence of a quantum group anomalous term which vanishes in the classical
case. This is called {\em the quantum group anomaly}. We derive the new qRG
equations for the XXZ model and show that the RG-flow diagram obtained in this
fashion exhibits the correct line of critical points that the exact model has.
In the ITF model the qRG-flow equations coincide with the tensor product
decomposition of cyclic irreps of with .Comment: LATEX file, 21 pages, no figures. To appear in "From Field Theory to
Quantum Groups", World Scientific. Proceedings to honor J.Lukierski in his
60th birthda
Analytic Formulations of the Density Matrix Renormalization Group
We present two new analytic formulations of the Density Matrix
Renormalization Group Method. In these formulations we combine the block
renormalization group (BRG) procedure with Variational and Fokker-Planck
methods. The BRG method is used to reduce the lattice size while the latter are
used to construct approximate target states to compute the block density
matrix. We apply our DMRG methods to the Ising Model in a transverse field (ITF
model) and compute several of its critical properties which are then compared
with the old BRG results.Comment: LATEX file, 25 pages, 8 figures available upon reques
Insertion Sort is O(n log n)
Traditional Insertion Sort runs in O(n^2) time because each insertion takes
O(n) time. When people run Insertion Sort in the physical world, they leave
gaps between items to accelerate insertions. Gaps help in computers as well.
This paper shows that Gapped Insertion Sort has insertion times of O(log n)
with high probability, yielding a total running time of O(n log n) with high
probability.Comment: 6 pages, Latex. In Proceedings of the Third International Conference
on Fun With Algorithms, FUN 200
Systematic Analysis of Majorization in Quantum Algorithms
Motivated by the need to uncover some underlying mathematical structure of
optimal quantum computation, we carry out a systematic analysis of a wide
variety of quantum algorithms from the majorization theory point of view. We
conclude that step-by-step majorization is found in the known instances of fast
and efficient algorithms, namely in the quantum Fourier transform, in Grover's
algorithm, in the hidden affine function problem, in searching by quantum
adiabatic evolution and in deterministic quantum walks in continuous time
solving a classically hard problem. On the other hand, the optimal quantum
algorithm for parity determination, which does not provide any computational
speed-up, does not show step-by-step majorization. Lack of both speed-up and
step-by-step majorization is also a feature of the adiabatic quantum algorithm
solving the 2-SAT ``ring of agrees'' problem. Furthermore, the quantum
algorithm for the hidden affine function problem does not make use of any
entanglement while it does obey majorization. All the above results give
support to a step-by-step Majorization Principle necessary for optimal quantum
computation.Comment: 15 pages, 14 figures, final versio
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