1,422 research outputs found
Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to a many body quantum boson system with
attractive interactions. Performing the summation over the entire spectrum of
excited states the problem is reduced to the Fredholm determinant with the Airy
kernel which is known to yield the Tracy-Widom distributionComment: 5 page
A Combined System for Update Logic and Belief Revision
Revised Selected PapersInternational audienceIn this paper we propose a logical system combining the update logic of A. Baltag, L. Moss and S. Solecki (to which we will refer to by the generic term BMS, [BMS04]) with the belief revision theory as conceived by C. Alchourron, P. Gardenfors and D. Mackinson (that we will call the AGM theory, [GardRott95]) viewed from the point of view of W. Spohn ( [Spohn90], [Spohn88]). We also give a proof system and a comparison with the AGM postulates
Early Thermal Evolution of Planetesimals and its Impact on Processing and Dating of Meteoritic Material
Radioisotopic ages for meteorites and their components provide constraints on
the evolution of small bodies: timescales of accretion, thermal and aqueous
metamorphism, differentiation, cooling and impact metamorphism. Realising that
the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat
source driving differentiation and metamorphism, thermal modeling of small
bodies is of utmost importance to set individual meteorite age data into the
general context of the thermal evolution of their parent bodies, and to derive
general conclusions about the nature of planetary building blocks in the early
solar system. As a general result, modelling easily explains that iron
meteorites are older than chondrites, as early formed planetesimals experienced
a higher concentration of short-lived nuclides and more severe heating.
However, core formation processes may also extend to 10 Ma after formation of
Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature
of the starting material is that relatively small bodies (< few km) will also
differentiate if they form within 2 Ma after CAIs. A particular interesting
feature to be explored is the possibility that some chondrites may derive from
the outer undifferentiated layers of asteroids that are differentiated in their
interiors. This could explain the presence of remnant magnetization in some
chondrites due to a planetary magnetic field.Comment: 24 pages, 9 figures, Accepted for publication as a chapter in
Protostars and Planets VI, University of Arizona Press (2014), eds. H.
Beuther, R. Klessen, C. Dullemond, Th. Hennin
Spatial structures and dynamics of kinetically constrained models for glasses
Kob and Andersen's simple lattice models for the dynamics of structural
glasses are analyzed. Although the particles have only hard core interactions,
the imposed constraint that they cannot move if surrounded by too many others
causes slow dynamics. On Bethe lattices a dynamical transition to a partially
frozen phase occurs. In finite dimensions there exist rare mobile elements that
destroy the transition. At low vacancy density, , the spacing, ,
between mobile elements diverges exponentially or faster in . Within the
mobile elements, the dynamics is intrinsically cooperative and the
characteristic time scale diverges faster than any power of (although
slower than ). The tagged-particle diffusion coefficient vanishes roughly
as .Comment: 4 pages. Accepted for pub. in Phys. Rev. Let
Complementarity relation for irreversible process derived from stochastic energetics
When the process of a system in contact with a heat bath is described by
classical Langevin equation, the method of stochastic energetics [K. Sekimoto,
J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of
Helmholtz free energy and the dissipation function of the system. We prove that
the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal
process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min,
where S_min depends on the initial and the final values of the control
parameters, but it does not depend on the pathway between these values.Comment: 3 pages. LaTeX with 6 style macro
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to the -particle quantum boson system with
attractive interactions. We find the full set of eigenfunctions and eigenvalues
of this many-body system and perform the summation over the entire spectrum of
excited states. It is shown that in the thermodynamic limit the problem is
reduced to the Fredholm determinant with the Airy kernel yielding the universal
Tracy-Widom distribution, which is known to describe the statistical properties
of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page
Non-Markovian generalization of the Lindblad theory of open quantum systems
A systematic approach to the non-Markovian quantum dynamics of open systems
is given by the projection operator techniques of nonequilibrium statistical
mechanics. Combining these methods with concepts from quantum information
theory and from the theory of positive maps, we derive a class of correlated
projection superoperators that take into account in an efficient way
statistical correlations between the open system and its environment. The
result is used to develop a generalization of the Lindblad theory to the regime
of highly non-Markovian quantum processes in structured environments.Comment: 10 pages, 1 figure, replaced by published versio
RankPL: A Qualitative Probabilistic Programming Language
In this paper we introduce RankPL, a modeling language that can be thought of
as a qualitative variant of a probabilistic programming language with a
semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used
to represent and reason about processes that exhibit uncertainty expressible by
distinguishing "normal" from" surprising" events. RankPL allows (iterated)
revision of rankings over alternative program states and supports various types
of reasoning, including abduction and causal inference. We present the
language, its denotational semantics, and a number of practical examples. We
also discuss an implementation of RankPL that is available for download
Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics
We explain the ubiquity and extremely slow evolution of non gaussian
out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means
of traditional kinetic theory. Deriving the Fokker-Planck equation for a test
particle, one also unambiguously explains and predicts striking slow algebraic
relaxation of the momenta autocorrelation, previously found in numerical
simulations. Finally, angular anomalous diffusion are predicted for a large
class of initial distributions. Non Extensive Statistical Mechanics is shown to
be unnecessary for the interpretation of these phenomena
Quantum transport through single-molecule junctions with orbital degeneracies
We consider electronic transport through a single-molecule junction where the
molecule has a degenerate spectrum. Unlike previous transport models, and
theories a rate-equations description is no longer possible, and the quantum
coherences between degenerate states have to be taken into account. We present
the derivation and application of a master equation that describes the system
in the weak-coupling limit and give an in-depth discussion of the parameter
regimes and the new phenomena due to coherent on-site dynamics
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