169,124 research outputs found
Localization and Pattern Formation in Quantum Physics. I. Phenomena of Localization
In these two related parts we present a set of methods, analytical and
numerical, which can illuminate the behaviour of quantum system, especially in
the complex systems. The key points demonstrating advantages of this approach
are: (i) effects of localization of possible quantum states, more proper than
"gaussian-like states"; (ii) effects of non-perturbative multiscales which
cannot be calculated by means of perturbation approaches; (iii) effects of
formation of complex quantum patterns from localized modes or classification
and possible control of the full zoo of quantum states, including (meta) stable
localized patterns (waveletons). We'll consider calculations of Wigner
functions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding
to polynomial Hamiltonians. Modeling demonstrates the appearance of (meta)
stable patterns generated by high-localized (coherent) structures or
entangled/chaotic behaviour. We can control the type of behaviour on the level
of reduced algebraical variational system. At the end we presented the
qualitative definition of the Quantum Objects in comparison with their
Classical Counterparts, which natural domain of definition is the category of
multiscale/multiresolution decompositions according to the action of
internal/hidden symmetry of the proper realization of scales of functional
spaces. It gives rational natural explanation of such pure quantum effects as
``self-interaction''(self-interference) and instantaneous quantum interaction.Comment: LaTeX2e, spie.cls, 13 pages, 15 figures, submitted to Proc. of SPIE
Meeting, The Nature of Light: What is a Photon? Optics & Photonics, SP200,
San Diego, CA, July-August, 200
Localization phenomena in models of ion-conducting glass formers
The mass transport in soft-sphere mixtures of small and big particles as well
as in the disordered Lorentz gas (LG) model is studied using molecular dynamics
(MD) computer simulations. The soft-sphere mixture shows anomalous
small-particle diffusion signifying a localization transition separate from the
big-particle glass transition. Switching off small-particle excluded volume
constraints slows down the small-particle dynamics, as indicated by incoherent
intermediate scattering functions. A comparison of logarithmic time derivatives
of the mean-squared displacements reveals qualitative similarities between the
localization transition in the soft-sphere mixture and its counterpart in the
LG. Nevertheless, qualitative differences emphasize the need for further
research elucidating the connection between both models.Comment: to appear in Eur. Phys. J. Special Topic
Ehrenfest time in the weak dynamical localization
The quantum kicked rotor (QKR) is known to exhibit dynamical localization in
the space of its angular momentum. The present paper is devoted to the
systematic first--principal (without a regularizer) diagrammatic calculations
of the weak--localization corrections for QKR. Our particular emphasis is on
the Ehrenfest time regime -- the phenomena characteristic for the
classical--to--quantum crossover of classically chaotic systems.Comment: 27 pages, 9 figure
Abelian categories from triangulated categories via Nakaoka-Palu's localization
The aim of this paper is to provide an expansion to Abe-Nakaoka's heart
construction of the following two different realizations of the module category
over the endomorphism ring of a rigid object in a triangulated category:
Buan-Marsh's localization and Iyama-Yoshino's subfactor. Our method depends on
a modification of Nakaoka-Palu's HTCP localization, a Gabriel-Zisman
localization of extriangulated categories which is also realized as a subfactor
of the original ones. Besides of the heart construction, our generalized HTCP
localization involves the following phenomena: (1) stable category with respect
to a class of objects; (2) recollement of triangulated categories; (3)
recollement of abelian categories under a mild assumption.Comment: 28 page
Islands in the Gap: Intertwined Transport and Localization in Structurally Complex Materials
Localized waves in disordered one-dimensional materials have been studied for
decades, including white-noise and correlated disorder, as well as
quasi-periodic disorder. How these wave phenomena relate to those in
crystalline (periodic ordered) materials---arguably the better understood
setting---has been a mystery ever since Anderson discovered disorder-induced
localization. Nonetheless, together these revolutionized materials science and
technology and led to new physics far beyond the solid state. We introduce a
broad family of structurally complex materials---chaotic crystals---that
interpolate between these organizational extremes---systematically spanning
periodic structures and random disorder. Within the family one can tune the
degree of disorder to sweep through an intermediate structurally disordered
region between two periodic lattices. This reveals new transport and
localization phenomena reflected in a rich array of energy-dependent
localization degree and density of states. In particular, strong localization
is observed even with a very low degree of disorder. Moreover, markedly
enhanced localization and delocalization coexist in a very narrow range of
energies. Most notably, beyond the simply smoothed bands found in previous
disorder studies, islands of transport emerge in band gaps and sharp band
boundaries persist in the presence of substantial disorder. Finally, the family
of materials comes with rather direct specifications of how to assemble the
requisite material organizations.Comment: 7 pages, 3 figures, supplementary material;
http://csc.ucdavis.edu/~cmg/compmech/pubs/talisdm.ht
Analysis of Localization Phenomena in Weakly Interacting Disordered Lattice Gases
Disorder plays a crucial role in many systems particularly in solid state
physics. However, the disorder in a particular system can usually not be chosen
or controlled. We show that the unique control available for ultracold atomic
gases may be used for the production and observation of disordered quantum
degenerate gases. A detailed analysis of localization effects for two possible
realizations of a disordered potential is presented. In a theoretical analysis
clear localization effects are observed when a superlattice is used to provide
a quasiperiodic disorder. The effects of localization are analyzed by
investigating the superfluid fraction and the localization length within the
system. The theoretical analysis in this paper paves a clear path for the
future observation of Anderson-like localization in disordered quantum gases.Comment: 9 pages, 13 figure
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