341 research outputs found
Imaging geometry through dynamics: the observable representation
For many stochastic processes there is an underlying coordinate space, ,
with the process moving from point to point in or on variables (such as
spin configurations) defined with respect to . There is a matrix of
transition probabilities (whether between points in or between variables
defined on ) and we focus on its ``slow'' eigenvectors, those with
eigenvalues closest to that of the stationary eigenvector. These eigenvectors
are the ``observables,'' and they can be used to recover geometrical features
of
Theoretical study of the finite temperature spectroscopy in van der Waals clusters. III Solvated Chromophore as an effective diatomics
The absorption spectroscopy of calcium-doped argon clusters is described in
terms of an effective diatomics molecule Ca-(Ar_n), in the framework of
semiclassical vertical transitions. We show how, upon choosing a suitable
reaction coordinate, the effective finite-temperature equilibrium properties
can be obtained for the ground- and excited-surfaces from the potential of mean
force (PMF). An extension of the recent multiple range random-walk method is
used to calculate the PMF over continuous intervals of distances. The
absorption spectra calculated using this single-coordinate description are
found to be in good agreement with the spectra obtained from high-statistics
Monte Carlo data, in various situations. For CaAr, we compare the
performances of two different choices of the reaction coordinate. For CaAr_37,
the method is seen to be accurate enough to distinguish between different
low-energy structures. Finally, the idea of casting the initial many-body
problem into a single degree of freedom problem is tested on the spectroscopy
of calcium in bulk solid argon.Comment: 8 pages, 9 figure
Theoretical study of finite temperature spectroscopy in van der Waals clusters. I. Probing phase changes in CaAr_n
The photoabsorption spectra of calcium-doped argon clusters CaAr_n are
investigated at thermal equilibrium using a variety of theoretical and
numerical tools. The influence of temperature on the absorption spectra is
estimated using the quantum superposition method for a variety of cluster sizes
in the range 6<=n<=146. At the harmonic level of approximation, the absorption
intensity is calculated through an extension of the Gaussian theory by Wadi and
Pollak [J. Chem. Phys. vol 110, 11890 (1999)]. This theory is tested on simple,
few-atom systems in both the classical and quantum regimes for which highly
accurate Monte Carlo data can be obtained. By incorporating quantum anharmonic
corrections to the partition functions and respective weights of the isomers,
we show that the superposition method can correctly describe the
finite-temperature spectroscopic properties of CaAr_n systems. The use of the
absorption spectrum as a possible probe of isomerization or phase changes in
the argon cluster is discussed at the light of finite-size effects.Comment: 17 pages, 9 figure
Theoretical study of finite temperature spectroscopy in van der Waals clusters. II Time-dependent absorption spectra
Using approximate partition functions and a master equation approach, we
investigate the statistical relaxation toward equilibrium in selected CaAr
clusters. The Gaussian theory of absorption (previous article) is employed to
calculate the average photoabsorption intensity associated with the 4s^2->
4s^14p^1 transition of calcium as a function of time during relaxation. In
CaAr_6 and CaAr_10 simple relaxation is observed with a single time scale.
CaAr_13 exhibits much slower dynamics and the relaxation occurs over two
distinct time scales. CaAr_37 shows much slower relaxation with multiple
transients, reminiscent of glassy behavior due to competition between different
low-energy structures. We interpret these results in terms of the underlying
potential energy surfaces for these clusters.Comment: 10 pages, 9 figure
Slow relaxation, confinement, and solitons
Millisecond crystal relaxation has been used to explain anomalous decay in
doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons.
Our model exhibits confinement of mechanical energy released by excitation.
Extending the model to long times is justified by its relation to solitons,
excitations previously proposed to occur in alkali halides. Soliton damping and
observation are also discussed
Metastable states in glassy systems
Truly stable metastable states are an artifact of the mean-field
approximation or the zero temperature limit. If such appealing concepts in
glass theory as configurational entropy are to have a meaning beyond these
approximations, one needs to cast them in a form involving states with finite
lifetimes.
Starting from elementary examples and using results of Gaveau and Schulman,
we propose a simple expression for the configurational entropy and revisit the
question of taking flat averages over metastable states. The construction is
applicable to finite dimensional systems, and we explicitly show that for
simple mean-field glass models it recovers, justifies and generalises the known
results. The calculation emphasises the appearance of new dynamical order
parameters.Comment: 4 fig., 20 pages, revtex; added references and minor change
Metastability and small eigenvalues in Markov chains
In this letter we announce rigorous results that elucidate the relation
between metastable states and low-lying eigenvalues in Markov chains in a much
more general setting and with considerable greater precision as was so far
available. This includes a sharp uncertainty principle relating all low-lying
eigenvalues to mean times of metastable transitions, a relation between the
support of eigenfunctions and the attractor of a metastable state, and sharp
estimates on the convergence of probability distribution of the metastable
transition times to the exponential distribution.Comment: 5pp, AMSTe
Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata
A discretized time evolution of the wave function for a Dirac particle on a
cubic lattice is represented by a very simple quantum cellular automaton. In
each evolution step the updated value of the wave function at a given site
depends only on the values at the nearest sites, the evolution is unitary and
preserves chiral symmetry. Moreover, it is shown that the relationship between
Dirac particles and cellular automata operating on two component objects on a
lattice is indeed very close. Every local and unitary automaton on a cubic
lattice, under some natural assumptions, leads in the continuum limit to the
Weyl equation. The sum over histories is evaluated and its connection with path
integrals and theories of fermions on a lattice is outlined.Comment: 6, RevTe
Transition State Spectroscopy of the Photoinduced Ca + CH3F Reaction. 2. Experimental and Ab Initio Studies of the Free Ca***FCH3 Complex
International audienceThe Ca* + CH3F CaF* + CH3 reaction was photoinduced in 1:1 Ca***CH3F complexes formed in a supersonic expansion. The transition state of the reaction was explored by monitoring the electronically excited product, CaF, while scanning the laser that turns on the reaction. Moreover, the electronic structure of the Ca***FCH3 system was studied using ab initio methods by associating a pseudopotential description of the [Ca2+] and [F7+] cores, a core polarization operator on calcium, an extensive Gaussian basis and a treatment of the electronic problem at the CCSD(T) (ground state) and RSPT2 (excited states) level. In this contribution we present experimental results for the free complex and a comparison with the results of a previous experiment where the Ca***CH3F complexes are deposited at the surface of large argon clusters. The ab initio calculations allowed an interpretation of the experimental data in terms of two reaction mechanisms, one involving a partial charge transfer state, the other involving the excitation of the C-F stretch in the CH3F moiety prior to charge transfer
Algebraic Aspects of Abelian Sandpile Models
The abelian sandpile models feature a finite abelian group G generated by the
operators corresponding to particle addition at various sites. We study the
canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X
Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G,
and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of
toppling matrix. We construct scalar functions, linear in height variables of
the pile, that are invariant toppling at any site. These invariants provide
convenient coordinates to label the recurrent configurations of the sandpile.
For an L X L square lattice, we show that g = L. In this case, we observe that
the system has nontrivial symmetries coming from the action of the cyclotomic
Galois group of the (2L+2)th roots of unity which operates on the set of
eigenvalues of the toppling matrix. These eigenvalues are algebraic integers,
whose product is the order |G|. With the help of this Galois group, we obtain
an explicit factorizaration of |G|. We also use it to define other simpler,
though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3
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