9,128 research outputs found
Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions
We study few-body problems in mixed dimensions with heavy atoms
trapped individually in parallel one-dimensional tubes or two-dimensional
disks, and a single light atom travels freely in three dimensions. By using the
Born-Oppenheimer approximation, we find three- and four-body bound states for a
broad region of heavy-light atom scattering length combinations. Specifically,
the existence of trimer and tetramer states persist to negative scattering
lengths regime, where no two-body bound state is present. These few-body bound
states are analogous to the Efimov states in three dimensions, but are stable
against three-body recombination due to geometric separation. In addition, we
find that the binding energy of the ground trimer and tetramer state reaches
its maximum value when the scattering lengths are comparable to the separation
between the low-dimensional traps. This resonant behavior is a unique feature
for the few-body bound states in mixed dimensions.Comment: Extended version with 14 pages and 14 figure
Magneto-optical evidence of the percolation nature of the metal-insulator transition in the 2D electron system
We compare the results of the transport and time-resolved
magneto-luminescence measurements in disordered 2D electron systems in
GaAs-AlGaAs heterostructures in the extreme quantum limit, in particular, in
the vicinity of the metal-insulator transition (MIT). At filling factors , the optical signal has two components: the single-rate exponentially
decaying part attributed to a uniform liquid and a power-law long-living tail
specific to a microscopically inhomogeneous state of electrons. We interprete
this result as a separation of the 2D electron system into a liquid and
localized phases, especially because the MIT occurs strikingly close to those
filling factors where the liquid occupies of the sample area (the
percollation threshold condition in two-component media).Comment: 5 pages RevTex + 4 fig., to appear in PRB, Rapid Com
Equivariant pretheories and invariants of torsors
In the present paper we introduce and study the notion of an equivariant
pretheory: basic examples include equivariant Chow groups, equivariant K-theory
and equivariant algebraic cobordism. To extend this set of examples we define
an equivariant (co)homology theory with coefficients in a Rost cycle module and
provide a version of Merkurjev's (equivariant K-theory) spectral sequence for
such a theory. As an application we generalize the theorem of
Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a
G-equivariant pretheory we associate a graded ring which serves as an invariant
of E. In the case of Chow groups this ring encodes the information concerning
the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes
of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous
preprint: the construction of an equivariant cycle (co)homology and the
spectral sequence (generalizing the long exact localization sequence) are
adde
Weak Charge Quantization as an Instanton of Interacting sigma-model
Coulomb blockade in a quantum dot attached to a diffusive conductor is
considered in the framework of the non-linear sigma-model. It is shown that the
weak charge quantization on the dot is associated with instanton configurations
of the Q-field in the conductor. The instantons have a finite action and are
replica non--symmetric. It is argued that such instantons may play a role in
the transition regime to the interacting insulator.Comment: 4 pages. The 2D case substantially modifie
Identifying and Indexing Icosahedral Quasicrystals from Powder Diffraction Patterns
We present a scheme to identify quasicrystals based on powder diffraction
data and to provide a standardized indexing. We apply our scheme to a large
catalog of powder diffraction patterns, including natural minerals, to look for
new quasicrystals. Based on our tests, we have found promising candidates
worthy of further exploration.Comment: 4 pages, 1 figur
A note about the ground state of the hydrogen molecular ion
Three simple parametric trial functions for the molecular ion are presented. Each of them provides subsequently the
most accurate approximation for the Born-Oppenheimer ground state energy among
several-parametric trial functions. These trial functions are chosen following
a criterion of physical adequacy and includes the electronic correlation in the
exponential form , where is a variational
parameter. The Born-Oppenheimer energy is found to be \,a.u., respectively, for optimal equilateral triangular
configuration of protons with the equilibrium interproton distance
\,a.u. The variational energy agrees in three significant digits (s.d.)
with most accurate results available at present as well as for major
expectation values.Comment: 12 pages, 1 figure, 3 table
Structural Properties and Relative Stability of (Meta)Stable Ordered, Partially-ordered and Disordered Al-Li Alloy Phases
We resolve issues that have plagued reliable prediction of relative phase
stability for solid-solutions and compounds. Due to its commercially important
phase diagram, we showcase Al-Li system because historically density-functional
theory (DFT) results show large scatter and limited success in predicting the
structural properties and stability of solid-solutions relative to ordered
compounds. Using recent advances in an optimal basis-set representation of the
topology of electronic charge density (and, hence, atomic size), we present DFT
results that agree reasonably well with all known experimental data for the
structural properties and formation energies of ordered, off-stoichiometric
partially-ordered and disordered alloys, opening the way for reliable study in
complex alloys.Comment: 7 pages, 2 figures, 2 Table
Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
Fractional generalization of an exterior derivative for calculus of
variations is defined. The Hamilton and Lagrange approaches are considered.
Fractional Hamilton and Euler-Lagrange equations are derived. Fractional
equations of motion are obtained by fractional variation of Lagrangian and
Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe
Schematic Models for Active Nonlinear Microrheology
We analyze the nonlinear active microrheology of dense colloidal suspensions
using a schematic model of mode-coupling theory. The model describes the
strongly nonlinear behavior of the microscopic friction coefficient as a
function of applied external force in terms of a delocalization transition. To
probe this regime, we have performed Brownian dynamics simulations of a system
of quasi-hard spheres. We also analyze experimental data on hard-sphere-like
colloidal suspensions [Habdas et al., Europhys. Lett., 2004, 67, 477]. The
behavior at very large forces is addressed specifically
Analysis of Collectivism and Egoism Phenomena within the Context of Social Welfare
Comparative benefits provided by the basic social strategies including
collectivism and egoism are investigated within the framework of democratic
decision-making. In particular, we study the mechanism of growing "snowball" of
cooperation.Comment: 12 pages, 5 figures. Translated from Russian. Original Russian Text
published in Problemy Upravleniya, 2008, No. 4, pp. 30-3
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