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Software fault-freeness and reliability predictions
Many software development practices aim at ensuring that software is correct, or fault-free. In safety critical applications, requirements are in terms of probabilities of certain behaviours, e.g. as associated to the Safety Integrity Levels of IEC 61508. The two forms of reasoning - about evidence of correctness and about probabilities of certain failures -are rarely brought together explicitly. The desirability of using claims of correctness has been argued by many authors, but not been taken up in practice. We address how to combine evidence concerning probability of failure together with evidence pertaining to likelihood of fault-freeness, in a Bayesian framework. We present novel results to make this approach practical, by guaranteeing reliability predictions that are conservative (err on the side of pessimism), despite the difficulty of stating prior probability distributions for reliability parameters. This approach seems suitable for practical application to assessment of certain classes of safety critical systems
Amplitude-mode dynamics of polariton condensates
We study the stability of collective amplitude excitations in non-equilibrium
polariton condensates. These excitations correspond to renormalized upper
polaritons and to the collective amplitude modes of atomic gases and
superconductors. They would be present following a quantum quench or could be
created directly by resonant excitation. We show that uniform amplitude
excitations are unstable to the production of excitations at finite
wavevectors, leading to the formation of density-modulated phases. The physical
processes causing the instabilities can be understood by analogy to optical
parametric oscillators and the atomic Bose supernova.Comment: 4 pages, 2 figure
Mixed Symmetry Solutions of Generalized Three-Particle Bargmann-Wigner Equations in the Strong-Coupling Limit
Starting from a nonlinear isospinor-spinor field equation, generalized
three-particle Bargmann-Wigner equations are derived. In the strong-coupling
limit, a special class of spin 1/2 bound-states are calculated. These solutions
which are antisymmetric with respect to all indices, have mixed symmetries in
isospin-superspin space and in spin orbit space. As a consequence of this mixed
symmetry, we get three solution manifolds. In appendix \ref{b}, table 2, these
solution manifolds are interpreted as the three generations of leptons and
quarks. This interpretation will be justified in a forthcoming paper.Comment: 17 page
Numerical time propagation of quantum systems in radiation fields
Atoms, molecules or excitonic quasiparticles, for which excitations are
induced by external radiation fields and energy is dissipated through radiative
decay, are examples of driven open quantum systems. We explain the use of
commutator-free exponential time-propagators for the numerical solution of the
associated Schr\"odinger or master equations with a time-dependent Hamilton
operator. These time-propagators are based on the Magnus series but avoid the
computation of commutators, which makes them suitable for the efficient
propagation of systems with a large number of degrees of freedom. We present an
optimized fourth order propagator and demonstrate its efficiency in comparison
to the direct Runge-Kutta computation. As an illustrative example we consider
the parametrically driven dissipative Dicke model, for which we calculate the
periodic steady state and the optical emission spectrum.Comment: 23 pages, 11 figure
Mixtures of fermionic atoms in an optical lattice
A mixture of light and heavy spin-polarized fermionic atoms in an optical
lattice is considered. Tunneling of the heavy atoms is neglected such that they
are only subject to thermal fluctuations. This results in a complex interplay
between light and heavy atoms caused by quantum tunneling of the light atoms.
The distribution of the heavy atoms is studied. It can be described by an
Ising-like distribution with a first-order transition from homogeneous to
staggered order. The latter is caused by an effective nonlocal interaction due
to quantum tunneling of the light atoms. A second-order transition is also
possible between an ordered and a disordered phase of the heavy atoms
Energy evolution in time-dependent harmonic oscillator
The theory of adiabatic invariants has a long history, and very important
implications and applications in many different branches of physics,
classically and quantally, but is rarely founded on rigorous results. Here we
treat the general time-dependent one-dimensional harmonic oscillator, whose
Newton equation cannot be solved in general. We
follow the time-evolution of an initial ensemble of phase points with sharply
defined energy at time and calculate rigorously the distribution of
energy after time , which is fully (all moments, including the
variance ) determined by the first moment . For example,
, and all
higher even moments are powers of , whilst the odd ones vanish
identically. This distribution function does not depend on any further details
of the function and is in this sense universal. In ideal
adiabaticity , and the variance is
zero, whilst for finite we calculate , and for the
general case using exact WKB-theory to all orders. We prove that if is of class (all derivatives up to and including the order
are continuous) , whilst for class it is known to be exponential .Comment: 26 pages, 5 figure
Distribution of roots of random real generalized polynomials
The average density of zeros for monic generalized polynomials,
, with real holomorphic and
real Gaussian coefficients is expressed in terms of correlation functions of
the values of the polynomial and its derivative. We obtain compact expressions
for both the regular component (generated by the complex roots) and the
singular one (real roots) of the average density of roots. The density of the
regular component goes to zero in the vicinity of the real axis like
. We present the low and high disorder asymptotic
behaviors. Then we particularize to the large limit of the average density
of complex roots of monic algebraic polynomials of the form with real independent, identically distributed
Gaussian coefficients having zero mean and dispersion . The average density tends to a simple, {\em universal}
function of and in the domain where nearly all the roots are located for
large .Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed
tarfile (.66MB) containing 8 Postscript figures is available by e-mail from
[email protected]
Dipolar superfluidity in electron-hole bilayer systems
Bilayer electron-hole systems, where the electrons and holes are created via
doping and confined to separate layers, undergo excitonic condensation when the
distance between the layers is smaller than typical distance between particles
within a layer. We argue that the excitonic condensate is a novel dipolar
superfluid in which the phase of the condensate couples to the {\it gradient}
of the vector potential. We predict the existence of dipolar supercurrent which
can be tuned by an in-plane magnetic field and detected by independent contacts
to the layers. Thus the dipolar superfluid offers an example of excitonic
condensate in which the {\it composite} nature of its constituent excitons is
manifest in the macroscopic superfluid state. We also discuss various
properties of this superfluid including the role of vortices.Comment: 5 pages, 1 figure, minor changes and added few references; final
published versio
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