146 research outputs found
Efficient Diagonalization of Kicked Quantum Systems
We show that the time evolution operator of kicked quantum systems, although
a full matrix of size NxN, can be diagonalized with the help of a new method
based on a suitable combination of fast Fourier transform and Lanczos algorithm
in just N^2 ln(N) operations. It allows the diagonalization of matrizes of
sizes up to N\approx 10^6 going far beyond the possibilities of standard
diagonalization techniques which need O(N^3) operations. We have applied this
method to the kicked Harper model revealing its intricate spectral properties.Comment: Text reorganized; part on the kicked Harper model extended. 13 pages
RevTex, 1 figur
Un théorème no-go pour les théories supersymétriques pleinement unifiées brisées par un vide métastable
Le modèle standard, bien qu’étant la théorie la plus complète et précise jamais conçue, mène toutefois à plusieurs problèmes et questions non résolues, tels le problème de la hiérarchie ou de l’origine de la masse des neutrinos. Parmi les solutions avancées, les plus populaires sont sans doute les théories de grande unification et l’ajout de la supersymétrie. L’inclusion simultanée de ces deux extensions du modèle standard semble d’ailleurs encouragée par l’unification des constantes de couplage. Toutefois, briser la supersymétrie constitue un obstacle de taille à la réalisation de modèles réalistes et nécessite donc l’introduction d’un secteur caché, découplé du modèle standard. Le présent mémoire a pour objectif de tester une unification totale du secteur caché et du modèle standard supersymétrique minimal unifié sous la bannière des théories supersymétriques pleinement unifiées. Pour délimiter l’étude de tels modèles, deux hypothèses sont posées : le mécanisme de brisure de supersymétrie du secteur caché est le mécanisme Intriligator-Seiberg-Shih et les brisures de symétrie jaugée surviennent par un mécanisme de Higgs avec un potentiel quartique. Un théorème no-go est par la suite démontré, stipulant qu’il est impossible d’avoir une théorie supersymétrique pleinement unifiée soumise à ces deux conditions.The Standard Model, while being the most complete and precise theory ever built, possesses many flaws for which several solutions exist. Among the most popular are the Grand Unified Theories and supersymmetry. The introduction of both extensions simultaneously yields an even more elegant solution, since the coupling constants of the Minimal Supersymmetric Standard Model seems to converge into one unique point. However, the challenge that supersymmetry breaking represents is an obstacle to realistic model building and forces the need to break supersymmetry in a new sector, decoupled from the Minimal Supersymmetric Standard Model. This memoir aims to resolve this problem by suggesting the complete unification of the decoupled sector with the Minimal Supersymmetric Standard Model under the denomination Fully Supersymmetric Grand Unified Theories. To begin the study of such models, two assumptions are made: the supersymmetry breaking mechanism is the Intriligator-Seiberg-Shih mechanism, and the symmetry breaking mechanism is the Higgs mechanism with a quartic potential. Then, a no-go theorem is proved, showing that it is impossible to have a Fully Supersymmetric Grand Unified Theory for which these two conditions are satisfied
Tunneling and the Band Structure of Chaotic Systems
We compute the dispersion laws of chaotic periodic systems using the
semiclassical periodic orbit theory to approximate the trace of the powers of
the evolution operator. Aside from the usual real trajectories, we also include
complex orbits. These turn out to be fundamental for a proper description of
the band structure since they incorporate conduction processes through
tunneling mechanisms. The results obtained, illustrated with the kicked-Harper
model, are in excellent agreement with numerical simulations, even in the
extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax
Semi-classical study of the Quantum Hall conductivity
The semi-classical study of the integer Quantum Hall conductivity is
investigated for electrons in a bi-periodic potential .
The Hall conductivity is due to the tunnelling effect and we concentrate our
study to potentials having three wells in a periodic cell. A non-zero
topological conductivity requires special conditions for the positions, and
shapes of the wells. The results are derived analytically and well confirmed by
numerical calculations.Comment: 23 pages, 13 figure
Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics
We consider a quasi one-dimensional chain of N chaotic scattering elements
with periodic boundary conditions. The classical dynamics of this system is
dominated by diffusion. The quantum theory, on the other hand, depends
crucially on whether the chain is disordered or invariant under lattice
translations. In the disordered case, the spectrum is dominated by Anderson
localization whereas in the periodic case, the spectrum is arranged in bands.
We investigate the special features in the spectral statistics for a periodic
chain. For finite N, we define spectral form factors involving correlations
both for identical and non-identical Bloch numbers. The short-time regime is
treated within the semiclassical approximation, where the spectral form factor
can be expressed in terms of a coarse-grained classical propagator which obeys
a diffusion equation with periodic boundary conditions. In the long-time
regime, the form factor decays algebraically towards an asymptotic constant. In
the limit , we derive a universal scaling function for the form
factor. The theory is supported by numerical results for quasi one-dimensional
periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps
Assessing Doha's Street Network from the Perspective of 'Complete Streets' Concept
Streets are considered dynamic spaces in cities, and their design should be safe, comfortable and efficient for all users. Well-functioning streets can create a healthy lifestyle for a city and its users. Many cities are suffering from transportation issues because of their poorly designed street networks that do not integrate the different modes of transportation, or establish safe environments in which pedestrian and cyclists are treated as kings. In this manner, Doha as a city is experiencing the same kind of problem, creating corridors that do not take into consideration different travel modes, which causes severe congestion, delay and shortage in street capacity and, most importantly, users’ dissatisfaction. Therefore, there is a need to investigate and explore some methods that aim to improve cities’ street networks. “Complete Streets” is a roadway design concept initiated with the intention of integrating numerous modes of transportation and their variety of users. Complete Streets are also envisioned to provide traffic, safety and public health benefits, and integrate a healthy lifestyle into built environments worldwide. The newly-emerging concept can be adapted in contexts that fail to combine the different street elements that a street should have. Considering the low quality of the current street network, this thesis aims to evaluate the current streets in Doha city based on the degree of users’ satisfaction, and provide approaches to enhance them from the perspective of the ‘Complete Streets’ concept. The study analyzes two international case studies that have successfully implemented the concept and improved their current street network and enhanced users’ built environment. The analysis will help in extracting criteria that are used to assess the current performance of the street network and recommending ways to improve them. The methodological approach of this research will focus on the selection of two neighborhoods in Doha based on their contextual location and types of land use: a downtown area or urban center exemplified in Fereej bin Mahmoud, and a suburban area or residential district of Al Waab. Three nominated streets of the existing network within the two areas will be selected based on an evaluation matrix, and assessed according to the users’ perspectives and future preferences and aspirations. This approach is supported by two major data collection tools: a visual questionnaire survey and semi-structured interviews with local authorities. A total of 100 questionnaires were collected for the two selected areas from different types of users. Results showed that users are completely unsatisfied with the current conditions of the selected streets in the two areas, which lack the major components of Complete Street variables: pedestrian, bicycle, green and transit improvements, which has resulted in the absence of safety. The produced results along with the evaluation criteria have helped in improving the current streets’ designs and have created a new enhanced cross-section that meets the concept of Complete Streets
Localization of Eigenstates & Mean Wehrl Entropy
Dynamics of a periodically time dependent quantum system is reflected in the
features of the eigenstates of the Floquet operator. Of the special importance
are their localization properties quantitatively characterized by the
eigenvector entropy, the inverse participation ratio or the eigenvector
statistics. Since these quantities depend on the choice of the eigenbasis, we
suggest to use the overcomplete basis of coherent states, uniquely determined
by the classical phase space. In this way we define the mean Wehrl entropy of
eigenvectors of the Floquet operator and demonstrate that this quantity is
useful to describe quantum chaotic systems.Comment: 7 pages in Latex with 4 pictures in .ps (included), submitted to
Physica
Adiabatically coupled systems and fractional monodromy
We present a 1-parameter family of systems with fractional monodromy and
adiabatic separation of motion. We relate the presence of monodromy to a
redistribution of states both in the quantum and semi-quantum spectrum. We show
how the fractional monodromy arises from the non diagonal action of the
dynamical symmetry of the system and manifests itself as a generic property of
an important subclass of adiabatically coupled systems
Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?
We find that a 2D periodic potential with different modulation amplitudes in
x- and y-direction and a perpendicular magnetic field may lead to a transition
to electron transport along the direction of stronger modulation and to
localization in the direction of weaker modulation. In the experimentally
accessible regime we relate this new quantum transport phenomenon to avoided
band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea
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