1,120 research outputs found
Exact solution of the nuclear pairing problem
In many applications to finite Fermi-systems, the pairing problem has to be
treated exactly. We suggest a numerical method of exact solution based on SU(2)
quasispin algebras and demonstrate its simplicity and practicality. We show
that the treatment of binding energies with the use of the exact pairing and
uncorrelated monopole contribution of other residual interactions can serve as
an effective alternative to the full shell-model diagonalization in spherical
nuclei. A self-consistent combination of the exactly treated pairing and
Hartree-Fock method is discussed. Results for Sn isotopes indicate a good
agreement with experimental data.Comment: 10 pages, 2 figure
Applying Mean-field Approximation to Continuous Time Markov Chains
The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent
deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications
of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique,
moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and
uid model checking analysis techniques
Polynomial Triangles Revisited
A polynomial triangle is an array whose inputs are the coefficients in
integral powers of a polynomial. Although polynomial coefficients have appeared
in several works, there is no systematic treatise on this topic. In this paper
we plan to fill this gap. We describe some aspects of these arrays, which
generalize similar properties of the binomial coefficients. Some combinatorial
models enumerated by polynomial coefficients, including lattice paths model,
spin chain model and scores in a drawing game, are introduced. Several known
binomial identities are then extended. In addition, we calculate recursively
generating functions of column sequences. Interesting corollaries follow from
these recurrence relations such as new formulae for the Fibonacci numbers and
Hermite polynomials in terms of trinomial coefficients. Finally, properties of
the entropy density function that characterizes polynomial coefficients in the
thermodynamical limit are studied in details.Comment: 24 pages with 1 figure eps include
Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other
things) biological transport and traffic flow. We begin with a broad overview
of this class of driven diffusive systems - which includes exclusion processes
- focusing on interesting physical properties, such as shocks and phase
transitions. We then turn our attention specifically to those models for which
the exact distribution of microstates in the steady state can be expressed in a
matrix product form. In addition to a gentle introduction to this matrix
product approach, how it works and how it relates to similar constructions that
arise in other physical contexts, we present a unified, pedagogical account of
the various means by which the statistical mechanical calculations of
macroscopic physical quantities are actually performed. We also review a number
of more advanced topics, including nonequilibrium free energy functionals, the
classification of exclusion processes involving multiple particle species,
existence proofs of a matrix product state for a given model and more
complicated variants of the matrix product state that allow various types of
parallel dynamics to be handled. We conclude with a brief discussion of open
problems for future research.Comment: 127 pages, 31 figures, invited topical review for J. Phys. A (uses
IOP class file
Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions
We present a general derivation of semi-fermionic representation for spin
operators in terms of a bilinear combination of fermions in real and imaginary
time formalisms. The constraint on fermionic occupation numbers is fulfilled by
means of imaginary Lagrange multipliers resulting in special shape of
quasiparticle distribution functions. We show how Schwinger-Keldysh technique
for spin operators is constructed with the help of semi-fermions. We
demonstrate how the idea of semi-fermionic representation might be extended to
the groups possessing dynamic symmetries (e.g. singlet/triplet transitions in
quantum dots). We illustrate the application of semi-fermionic representations
for various problems of strongly correlated and mesoscopic physics.Comment: Review article, 40 pages, 11 figure
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