1,458 research outputs found
Localization in one-dimensional incommensurate lattices beyond the Aubry-Andr\'e model
Localization properties of particles in one-dimensional incommensurate
lattices without interaction are investigated with models beyond the
tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2
model with finite next-nearest-neighbor hopping t_2, we find the localization
properties qualitatively different from those of the AA model, signaled by the
appearance of mobility edges. We then further go beyond the tight-binding
assumption and directly study the system based on the more fundamental
single-particle Schr\"odinger equation. With this approach, we also observe the
presence of mobility edges and localization properties dependent on
incommensuration.Comment: 5 pages, 6 figure
Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-Andr\'e models
We study the quantum localization phenomena of noninteracting particles in
one-dimensional lattices based on tight-binding models with various forms of
hopping terms beyond the nearest neighbor, which are generalizations of the
famous Aubry-Andr\'e and noninteracting Anderson model. For the case with
deterministic disordered potential induced by a secondary incommensurate
lattice (i.e. the Aubry-Andr\'e model), we identify a class of self dual
models, for which the boundary between localized and extended eigenstates are
determined analytically by employing a generalized Aubry-Andr\'e
transformation. We also numerically investigate the localization properties of
non-dual models with next-nearest-neighbor hopping, Gaussian, and power-law
decay hopping terms. We find that even for these non-dual models, the
numerically obtained mobility edges can be well approximated by the
analytically obtained condition for localization transition in the self dual
models, as long as the decay of the hopping rate with respect to distance is
sufficiently fast. For the disordered potential with genuinely random
character, we examine scenarios with next-nearest-neighbor hopping,
exponential, Gaussian, and power-law decay hopping terms numerically. We find
that the higher order hopping terms can remove the symmetry in the localization
length about the energy band center compared to the Anderson model.
Furthermore, our results demonstrate that for the power-law decay case, there
exists a critical exponent below which mobility edges can be found. Our
theoretical results could, in principle, be directly tested in shallow atomic
optical lattice systems enabling non-nearest-neighbor hopping.Comment: 18 pages, 24 figures updated with additional reference
Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting
Cylindrical algebraic decomposition (CAD) is an important tool, both for
quantifier elimination over the reals and a range of other applications.
Traditionally, a CAD is built through a process of projection and lifting to
move the problem within Euclidean spaces of changing dimension. Recently, an
alternative approach which first decomposes complex space using triangular
decomposition before refining to real space has been introduced and implemented
within the RegularChains Library of Maple. We here describe a freely available
package ProjectionCAD which utilises the routines within the RegularChains
Library to build CADs by projection and lifting. We detail how the projection
and lifting algorithms were modified to allow this, discuss the motivation and
survey the functionality of the package
Density Matrix Renormalization Group study on incommensurate quantum Frenkel-Kontorova model
By using the density matrix renormalization group (DMRG) technique, the
incommensurate quantum Frenkel-Kontorova model is investigated numerically. It
is found that when the quantum fluctuation is strong enough, the
\emph{g}-function featured by a saw-tooth map in the depinned state will show a
different kind of behavior, similar to a standard map, but with reduced
magnitude. The related position correlations are studied in details, which
leads to a potentially interesting application to the recently well-explored
phase transitions in cold atoms loaded in optical lattices.Comment: 11 figures, submitted to Phys. Rev.
Surface spin-flop and discommensuration transitions in antiferromagnets
Phase diagrams as a function of anisotropy and magnetic field are
obtained for discommensurations and surface states for an antiferromagnet in
which is parallel to the easy axis, by modeling it using the ground states
of a one-dimensional chain of classical XY spins. A surface spin-flop phase
exists for all , but the interval in over which it is stable becomes
extremely small as goes to zero. First-order transitions, separating
different surface states and ending in critical points, exist inside the
surface spin-flop region. They accumulate at a field (depending on )
significantly less than the value for a bulk spin-flop transition. For
there is no surface spin-flop phase in the strict sense;
instead, the surface restructures by, in effect, producing a discommensuration
infinitely far away in the bulk. The results are used to explain in detail the
phase transitions occurring in systems consisting of a finite, even number of
layers.Comment: Revtex 17 pages, 15 figure
Breathers on lattices with long range interaction
We analyze the properties of breathers (time periodic spatially localized
solutions) on chains in the presence of algebraically decaying interactions
. We find that the spatial decay of a breather shows a crossover from
exponential (short distances) to algebraic (large distances) decay. We
calculate the crossover distance as a function of and the energy of the
breather. Next we show that the results on energy thresholds obtained for short
range interactions remain valid for and that for (anomalous
dispersion at the band edge) nonzero thresholds occur for cases where the short
range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199
Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation
Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (âČ1ââHz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from âwakeâ to âcoma.â In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complementsâand contrasts withâconventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning
General Properties of Two-dimensional Conformal Transformation in Electrostatics
Electrostatic properties of two-dimensional nanosystems can be described by
their geometry resonances. In this paper we prove that these modes as well as
the corresponding eigenvalues are invariant under any conformal transformation.
This invariance further leads to a new way to studying the transformed
structures. Namely, transforming a geometry is equivalent to modifying the
strengths of these invariant eigenmodes excited by the external excitations
On quantization of weakly nonlinear lattices. Envelope solitons
A way of quantizing weakly nonlinear lattices is proposed. It is based on
introducing "pseudo-field" operators. In the new formalism quantum envelope
solitons together with phonons are regarded as elementary quasi-particles
making up boson gas. In the classical limit the excitations corresponding to
frequencies above linear cut-off frequency are reduced to conventional envelope
solitons. The approach allows one to identify the quantum soliton which is
localized in space and understand existence of a narrow soliton frequency band.Comment: 5 pages. Phys. Rev. E (to appear
Examining the prevalence of chronic homelessness among single adults according to national definitions in Canada
This article examines the prevalence of chronic homelessness when applying definitions used in Canada to a sample of homeless and vulnerably housed single adults enrolled in a multi-city longitudinal study. The federal governmentâs current definition, Reaching Home, identified the highest proportion of homeless single adults (31 percent; 95% CI = 27.2 â 34.1) as âchronically homeless.â Our findings suggest that the federal definitions of chronic homelessness, which are based on both shelter stays and periods of homelessness outside the shelter system, are double the size of this sub-population when compared to definitions based on shelter stays alone. Participants who were male, identified as Indigenous, and reported problematic drug use, were more likely to be chronically homeless for definitions based on any-kind of homelessness. The findings highlight the importance of counting unsheltered and hidden homelessness to estimate the number of single adults who are chronically homeless.Cet article examine la prĂ©valence de lâitinĂ©rance chronique lors de lâapplication de dĂ©finitions utilisĂ©es au Canada Ă un Ă©chantillon dâadultes cĂ©libataires sans abri et logĂ©s de façon vulnĂ©rable, inscrits dans une Ă©tude longitudinale multi-villes. La dĂ©finition actuelle du gouvernement fĂ©dĂ©ral, Reaching Home, a identifiĂ© la plus grande proportion dâadultes cĂ©libataires sans abri (31 pour cent ; 95 % CI = 27,2 - 34,1) comme «sans abri chronique». Nos rĂ©sultats suggĂšrent que les dĂ©finitions de lâitinĂ©rance chronique, qui sont basĂ©es Ă la fois sur les sĂ©jours en refuge et les pĂ©riodes dâitinĂ©rance en dehors du systĂšme de refuge, reprĂ©sentent le double de la taille de cette sous-population par rapport aux dĂ©finitions basĂ©es uniquement sur les sĂ©jours en refuge. Les participants qui Ă©taient de sexe masculin, sâidentifiaient comme indigĂšnes et dĂ©claraient avoir fait un usage problĂ©matique de drogues, Ă©taient plus susceptibles dâĂȘtre associĂ©s Ă lâitinĂ©rance chronique pour les dĂ©finitions basĂ©es sur tout type dâitinĂ©rance. Les rĂ©sultats soulignent lâimportance de compter lâitinĂ©rance non abritĂ©e et cachĂ©e pour estimer le nombre dâadultes cĂ©libataires qui sont chroniquement sans abri
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