70,706 research outputs found
Destruction of Anderson localization in quantum nonlinear Schr\"odinger lattices
The four-wave interaction in quantum nonlinear Schr\"odinger lattices with
disorder is shown to destroy the Anderson localization of waves, giving rise to
unlimited spreading of the nonlinear field to large distances. Moreover, the
process is not thresholded in the quantum domain, contrary to its "classical"
counterpart, and leads to an accelerated spreading of the subdiffusive type,
with the dispersion for
. The results, presented here, shed new light on the
origin of subdiffusion in systems with a broad distribution of relaxation
times.Comment: 4 pages, no figure
A topological approximation of the nonlinear Anderson model
We study the phenomena of Anderson localization in the presence of nonlinear
interaction on a lattice. A class of nonlinear Schrodinger models with
arbitrary power nonlinearity is analyzed. We conceive the various regimes of
behavior, depending on the topology of resonance-overlap in phase space,
ranging from a fully developed chaos involving Levy flights to pseudochaotic
dynamics at the onset of delocalization. It is demonstrated that quadratic
nonlinearity plays a dynamically very distinguished role in that it is the only
type of power nonlinearity permitting an abrupt localization-delocalization
transition with unlimited spreading already at the delocalization border. We
describe this localization-delocalization transition as a percolation
transition on a Cayley tree. It is found in vicinity of the criticality that
the spreading of the wave field is subdiffusive in the limit
t\rightarrow+\infty. The second moment grows with time as a powerlaw t^\alpha,
with \alpha = 1/3. Also we find for superquadratic nonlinearity that the analog
pseudochaotic regime at the edge of chaos is self-controlling in that it has
feedback on the topology of the structure on which the transport processes
concentrate. Then the system automatically (without tuning of parameters)
develops its percolation point. We classify this type of behavior in terms of
self-organized criticality dynamics in Hilbert space. For subquadratic
nonlinearities, the behavior is shown to be sensitive to details of definition
of the nonlinear term. A transport model is proposed based on modified
nonlinearity, using the idea of stripes propagating the wave process to large
distances. Theoretical investigations, presented here, are the basis for
consistency analysis of the different localization-delocalization patterns in
systems with many coupled degrees of freedom in association with the asymptotic
properties of the transport.Comment: 20 pages, 2 figures; improved text with revisions; accepted for
publication in Physical Review
Shostakovich, old believers and new minimalists
The chapter discusses ‘minimalist’ elements of Dmitri Shostakovich's style as embodiments/ expressions of traditional Russian expressive modes rooted in the idioms of old folk music and the music of the ‘old believers’
The collection volume comprises a selection of articles that, as a group, marks an important new stage in our understanding of Shostakovich and his working environment. The papers have in common a perspective that we believe offers the most fruitful route forward for Shostakovich studies today. All address aspects of the composer’s output in the context of his life and cultural milieu. They are thus illuminating from two directions: the uncovering of ‘outside’ stimuli allows us to perceive the motivations behind Shostakovich’s artistic choices, while at the same time the nature of those choices offers insights into the workings of the larger world—cultural, social, political—that he inhabited. Thus his often ostensibly quirky choices are revealed as responses—by turns sentimental, moving, sardonic and angry—to the particular conditions, with all their absurdities and contradictions, that he had to negotiate.
The composer emerging from the role of tortured loner of older narratives into that of the gregarious and engaged member of his society that, for better and worse, characterized the everyday reality of his life
On the Schatten-von Neumann properties of some pseudo-differential operators
We obtain a number of explicit estimates for quasi-norms of
pseudo-differential operators in the Schatten-von Neumann classes with
. The estimates are applied to derive semi-classical bounds for
operators with smooth or non-smooth symbols.Comment: 22 page
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