182,670 research outputs found
Effective Theory for Trapped Few-Fermion Systems
We apply the general principles of effective field theories to the
construction of effective interactions suitable for few- and many-body
calculations in a no-core shell model framework. We calculate the spectrum of
systems with three and four two-component fermions in a harmonic trap. In the
unitary limit, we find that three-particle results are within 10% of known
semi-analytical values even in small model spaces. The method is very general,
and can be readily extended to other regimes, more particles, different species
(e.g., protons and neutrons in nuclear physics), or more-component fermions (as
well as bosons). As an illustration, we present calculations of the
lowest-energy three-fermion states away from the unitary limit and find a
possible inversion of parity in the ground state in the limit of trap size
large compared to the scattering length. Furthermore, we investigate the lowest
positive-parity states for four fermions, although we are limited by the
dimensions we can currently handle in this case.Comment: 8 pages, 5 figure
First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space
We investigate the quantum many-body dynamics of dissociation of a
Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic
atoms and analyze the resulting atom-atom correlations. The quantum fields of
both the molecules and atoms are simulated from first principles in three
dimensions using the positive-P representation method. This allows us to
provide an exact treatment of the molecular field depletion and s-wave
scattering interactions between the particles, as well as to extend the
analysis to nonuniform systems. In the simplest uniform case, we find that the
major source of atom-atom decorrelation is atom-atom recombination which
produces molecules outside the initially occupied condensate mode. The unwanted
molecules are formed from dissociated atom pairs with non-opposite momenta. The
net effect of this process -- which becomes increasingly significant for
dissociation durations corresponding to more than about 40% conversion -- is to
reduce the atom-atom correlations. In addition, for nonuniform systems we find
that mode-mixing due to inhomogeneity can result in further degradation of the
correlation signal. We characterize the correlation strength via the degree of
squeezing of particle number-difference fluctuations in a certain
momentum-space volume and show that the correlation strength can be increased
if the signals are binned into larger counting volumes.Comment: Final published version, with updated references and minor
modification
The potential of effective field theory in NN scattering
We study an effective field theory of interacting nucleons at distances much
greater than the pion's Compton wavelength. In this regime the NN potential is
conjectured to be the sum of a delta function and its derivatives. The question
we address is whether this sum can be consistently truncated at a given order
in the derivative expansion, and systematically improved by going to higher
orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find
that the cutoff can be taken to infinity only if the effective range is
negative. A positive effective range---which occurs in nature---requires that
the cutoff be kept finite and below the scale of the physics which has been
integrated out, i.e. O(m_\pi). Comparison of cutoff schemes and dimensional
regularization reveals that the physical scattering amplitude is sensitive to
the choice of regulator. Moreover, we show that the presence of some regulator
scale, a feature absent in dimensional regularization, is essential if the
effective field theory of NN scattering is to be useful. We also show that one
can define a procedure where finite cutoff dependence in the scattering
amplitude is removed order by order in the effective potential. However, the
characteristic momentum in the problem is given by the cutoff, and not by the
external momentum. It follows that in the presence of a finite cutoff there is
no small parameter in the effective potential, and consequently no systematic
truncation of the derivative expansion can be made. We conclude that there is
no effective field theory of NN scattering with nucleons alone.Comment: 25 pages LaTeX, 3 figures (uses epsf
Universal Properties of Cuprate Superconductors: T_c Phase Diagram, Room-Temperature Thermopower, Neutron Spin Resonance, and STM Incommensurability Explained in Terms of Chiral Plaquette Pairing
We report that four properties of cuprates and their evolution with
doping are consequences of simply counting four-site plaquettes arising from
doping, (1) the universal T_c phase diagram (superconductivity between ~0.05 and
~0.27 doping per CuO_2 plane and optimal T_c at ~0.16), (2) the universal doping
dependence of the room-temperature thermopower, (3) the superconducting
neutron spin resonance peak (the â41 meV peakâ), and (4) the dispersionless
scanning tunneling conductance incommensurability. Properties (1), (3), and (4)
are explained with no adjustable parameters, and (2) is explained with exactly one.
The successful quantitative interpretation of four very distinct aspects of cuprate
phenomenology by a simple counting rule provides strong evidence for four-site
plaquette percolation in these materials. This suggests that inhomogeneity, percolation,
and plaquettes play an essential role in cuprates. This geometric analysis
may provide a useful guide to search for new compositions and structures with
improved superconducting properties
Neural Mechanisms for Information Compression by Multiple Alignment, Unification and Search
This article describes how an abstract framework for perception and cognition may be realised in terms of neural mechanisms and neural processing.
This framework â called information compression by multiple alignment, unification and search (ICMAUS) â has been developed in previous research as a generalized model of any system for processing information, either natural or
artificial. It has a range of applications including the analysis and production of natural language, unsupervised inductive learning, recognition of objects and patterns, probabilistic reasoning, and others. The proposals in this article may be seen as an extension and development of
Hebbâs (1949) concept of a âcell assemblyâ.
The article describes how the concept of âpatternâ in the ICMAUS framework may be mapped onto a version of the cell
assembly concept and the way in which neural mechanisms may achieve the effect of âmultiple alignmentâ in the ICMAUS framework.
By contrast with the Hebbian concept of a cell assembly, it is proposed here that any one neuron can belong in one assembly and only one assembly. A key feature of present proposals, which is not part of the Hebbian concept, is that any cell assembly may contain âreferencesâ or âcodesâ that serve to identify one or more other cell assemblies. This mechanism allows information to be stored in a compressed form, it provides a robust mechanism by which assemblies may be connected to form hierarchies and other kinds of structure, it means that assemblies can express
abstract concepts, and it provides solutions to some of the other problems associated with cell assemblies.
Drawing on insights derived from the ICMAUS framework, the article also describes how learning may be achieved with neural mechanisms. This concept of learning is significantly different from the Hebbian concept and appears to provide a better account of what we know about human learning
- âŠ