197 research outputs found
Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions
In this paper we prove inversion formulas for the Dunkl intertwining operator
and for its dual and we deduce the expression of the
representing distributions of the inverse operators and
, and we give some applications.Comment: This is a contribution to the Special Issue on Dunkl Operators and
Related Topics, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
The halo of the exotic nucleus 11Li: a single Cooper pair
If neutrons are progressively added to a normal nucleus, the Pauli principle
forces them into states of higher momentum. When the core becomes
neutron-saturated, the nucleus expels most of the wavefunction of the last
neutrons outside to form a halo, which because of its large size can have lower
momentum. It is an open question how nature stabilizes such a fragile system
and provides the glue needed to bind the halo neutrons to the core. Here we
show that this problem is similar to that of the instability of the normal
state of an electron system at zero temperature solved by Cooper, solution
which is at the basis of BCS theory of superconductivity. By mimicking this
approach using, aside from the bare nucleon-nucleon interaction, the long
wavelength vibrations of the nucleus Li, the paradigm of halo nuclei, as
tailored glues of the least bound neutrons, we are able to obtain a unified and
quantitative picture of the observed properties of Li.Comment: 16 pages, 1 b/w figures, 2 colour figure
Response function beyond mean field of neutron-rich nuclei
The damping of single-particle and collective motion in exotic isotopes is a
new topic and its study may shed light on basic problems of nuclear dynamics.
For instance, it is known that nuclear structure calculations are not able, as
a rule, to account completely for the empirical single-particle damping. In
this contribution, we present calculations of the single-particle self-energy
in the case of the neutron-rich light nucleus O, by taking proper care
of the continuum, and we show that there are important differences with the
case of nuclei along the valley of stability.Comment: 9 pages, 4 figures. To appear in: Proceedings of the Topical
Conference on Giant Resonances, Varenna, May 11-16, 1997 (Nucl. Phys. A, to
be published
Designability of lattice model heteropolymers
Protein folds are highly designable, in the sense that many sequences fold to
the same conformation. In the present work we derive an expression for the
designability in a 20 letter lattice model of proteins which, relying only on
the Central Limit Theorem, has a generality which goes beyond the simple model
used in its derivation. This expression displays an exponential dependence on
the energy of the optimal sequence folding on the given conformation measured
with respect to the lowest energy of the conformational dissimilar structures,
energy difference which constitutes the only parameter controlling
designability. Accordingly, the designability of a native conformation is
intimately connected to the stability of the sequences folding to them.Comment: in press on Phys. Rev.
Semiclassical Approximation to Neutron Star Superfluidity Corrected for Proximity Effects
The inner crust of a neutron star is a superfluid and inhomogeneous system,
consisting of a lattice of nuclei immersed in a sea of neutrons. We perform a
quantum calculation of the associated pairing gap and compare it to the results
one obtains in the Local Density Approximation (LDA). It is found that the LDA
overestimates the spatial dependence of the gap, and leads to a specific heat
of the system which is too large at low temperatures, as compared with the
quantal result. This is caused by the neglect of proximity effects and the
delocalized character of the single-particle wavefunctions close to the Fermi
energy. It is possible to introduce an alternative, simple semiclassical
approximation of the pairing gap which leads to a specific heat that is in good
agreement with the quantum calculation.Comment: RevteX, 8 Postscript Figure
High-Current Field Emission from an Atomic Quantum Wire
Linear chains of carbon atoms have been proposed as the electron emitting
structures of open tip carbon nanotubes subject to an electric field. To better
understand the implications of the results of Smalley and collaborators, the
electromagnetic response of linear carbon chains to both static and dynamics
fields have been studied, making use of ab-initio methods. It is found that the
associated emission currents, plotted as a function of the bias potential,
follow Fowler-Nordheim intensity-voltage curves typical of the field emission
of metallic tips. Under standard bias conditions, linear carbon chains of one
nanometer of length are expected to deliver currents of the order of one
microampere. These systems behave, furthermore, as conducting needles in
photoabsorption processes. Linear carbon chains are thus likely to constitute
the ultimate atomic-scale realization of metallic wires.Comment: 10 pages, 4 figures, RevTe
Hierarchy of folding and unfolding events of protein G, CI2, and ACBP from explicit-solvent simulations
The study of the mechanism which is at the basis of the phenomenon of protein folding requires the knowledge of multiple folding trajectories under biological conditions. Using a biasing molecular-dynamics algorithm based on the physics of the ratchet-and-pawl system, we carry out all-atom, explicit solvent simulations of the sequence of folding events which proteins G, CI2, and ACBP undergo in evolving from the denatured to the folded state. Starting from highly disordered conformations, the algorithm allows the proteins to reach, at the price of a modest computational effort, nativelike conformations, within a root mean square deviation (RMSD) of approximately 1 . A scheme is developed to extract, from the myriad of events, information concerning the sequence of native contact formation and of their eventual correlation. Such an analysis indicates that all the studied proteins fold hierarchically, through pathways which, although not deterministic, are well-defined with respect to the order of contact formation. The algorithm also allows one to study unfolding, a process which looks, to a large extent, like the reverse of the major folding pathway. This is also true in situations in which many pathways contribute to the folding process, like in the case of protein G
Parity inversion and breakdown of shell closure in Be isotopes
The coupling of single-particle motion and of vibrations in 411Be produces dressed neutrons which spend only a fraction of the time in pure single-particle states, and which weighing differently from the bare neutrons lead to parity inversion. The interaction of the two least bound neutrons in the ground state of 412Be mediated by the v14 Argonne nucleon-nucleon potential and by the exchange of surface vibrations of the core 10Be gives rise to a strongly correlated state, where the two valence neutrons are distributed over s2,p2, and d2 configurations, resulting in the breaking of the N=8 shell closure
Use of the Metropolis algorithm to simulate the dynamics of protein chains
The Metropolis implementation of the Monte Carlo algorithm has been developed
to study the equilibrium thermodynamics of many-body systems. Choosing small
trial moves, the trajectories obtained applying this algorithm agree with those
obtained by Langevin's dynamics. Applying this procedure to a simplified
protein model, it is possible to show that setting a threshold of 1 degree on
the movement of the dihedrals of the protein backbone in a single Monte Carlo
step, the mean quantities associated with the off-equilibrium dynamics (e.g.,
energy, RMSD, etc.) are well reproduced, while the good description of higher
moments requires smaller moves. An important result is that the time duration
of a Monte Carlo step depends linearly on the temperature, something which
should be accounted for when doing simulations at different temperatures.Comment: corrections to the text and to the figure
Shell Model for Warm Rotating Nuclei
In order to provide a microscopic description of levels and E2 transitions in
rapidly rotating nuclei with internal excitation energy up to a few MeV, use is
made of a shell model which combines the cranked Nilsson mean-field and the
residual surface delta two-body force. The damping of collective rotational
motion is investigated in the case of a typical rare-earth nucleus, namely \Yb.
It is found that rotational damping sets in at around 0.8 MeV above the yrast
line, and the levels which form rotational band structures are thus limited. We
predict at a given rotational frequency existence of about 30 rotational bands
of various lengths, in overall agreement with the experimental findings. The
onset of the rotational damping proceeds quite gradually as a function of the
internal excitation energy. The transition region extends up to around 2 MeV
above yrast and it is characterized by the presence of scars of discrete
rotational bands which extend over few spin values and stand out among the
damped transitions, and by a two-component profile in the
correlation. The important role played by the high-multipole components of the
two-body residual interaction is emphasized.Comment: 28 pages, LaTe
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