32 research outputs found
Manifolds in random media: A variational approach to the spatial probability distribution
We develop a new variational scheme to approximate the position dependent
spatial probability distribution of a zero dimensional manifold in a random
medium. This celebrated 'toy-model' is associated via a mapping with directed
polymers in 1+1 dimension, and also describes features of the
commensurate-incommensurate phase transition. It consists of a pointlike
'interface' in one dimension subject to a combination of a harmonic potential
plus a random potential with long range spatial correlations. The variational
approach we develop gives far better results for the tail of the spatial
distribution than the hamiltonian version, developed by Mezard and Parisi, as
compared with numerical simulations for a range of temperatures. This is
because the variational parameters are determined as functions of position. The
replica method is utilized, and solutions for the variational parameters are
presented. In this paper we limit ourselves to the replica symmetric solution.Comment: 22 pages, 3 figures available on request, Revte
Localization of polymers in a finite medium with fixed random obstacles
In this paper we investigate the conformation statistics of a Gaussian chain
embedded in a medium of finite size, in the presence of quenched random
obstacles. The similarities and differences between the case of random
obstacles and the case of a Gaussian random potential are elucidated. The
connection with the density of states of electrons in a metal with random
repulsive impurities of finite range is discussed. We also interpret the
results obtained in some previous numerical simulations.Comment: 23 pages, 3 figures, revte
Polymers with self-avoiding interaction in random media: a localization-delocalization transition
In this paper we investigate the problem of a long self-avoiding polymer
chain immersed in a random medium. We find that in the limit of a very long
chain and when the self-avoiding interaction is weak, the conformation of the
chain consists of many ``blobs'' with connecting segments. The blobs are
sections of the molecule curled up in regions of low potential in the case of a
Gaussian distributed random potential or in regions of relatively low density
of obstacles in the case of randomly distributed hard obstacles. We find that
as the strength of the self-avoiding interaction is increased the chain
undergoes a delocalization transition in the sense that the appropriate free
energy per monomer is no longer negative. The chain is then no longer bound to
a particular location in the medium but can easily wander around under the
influence of a small perturbation. For a localized chain we estimate
quantitatively the expected number of monomers in the ``blobs'' and in the
connecting segments.Comment: 20 pages, 2 figures, revtex
On the melting of the nanocrystalline vortex matter in high-temperature superconductors
Multilevel Monte Carlo simulations of the vortex matter in the
highly-anisotropic high-temperature superconductor BiSrCaCuO
were performed. We introduced low concentration of columnar defects satisfying
. Both the electromagnetic and Josephson interactions among
pancake vortices were included. The nanocrystalline, nanoliquid and homogeneous
liquid phases were identified in agreement with experiments. We observed the
two-step melting process and also noted an enhancement of the structure factor
just prior to the melting transition. A proposed theoretical model is in
agreement with our findings.Comment: 4 figure
Large time dynamics and aging of a polymer chain in a random potential
We study the out-of-equilibrium large time dynamics of a gaussian polymer
chain in a quenched random potential. The dynamics studied is a simple Langevin
dynamics commonly referred to as the Rouse model. The equations for the
two-time correlation and response function are derived within the gaussian
variational approximation. In order to implement this approximation faithfully,
we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical
action. For a short ranged correlated random potential the equations are solved
analytically in the limit of large times using certain assumptions concerning
the asymptotic behavior. Two possible dynamical behaviors are identified
depending upon the time separation- a stationary regime and an aging regime. In
the stationary regime time translation invariance holds and so is the
fluctuation dissipation theorem. The aging regime which occurs for large time
separations of the two-time correlation functions is characterized by history
dependence and the breakdown of certain equilibrium relations. The large time
limit of the equations yields equations among the order parameters that are
similar to the equations obtained in the statics using replicas. In particular
the aging solution corresponds to the broken replica solution. But there is a
difference in one equation that leads to important consequences for the
solution. The stationary regime corresponds to the motion of the polymer inside
a local minimum of the random potential, whereas in the aging regime the
polymer hops between different minima. As a byproduct we also solve exactly the
dynamics of a chain in a random potential with quadratic correlations.Comment: 21 pages, RevTeX
Interpolation of the Josephson interaction in highly anisotropic superconductors from a solution of the two dimensional sine-Gordon equation
In this paper we solve numerically the two dimensional elliptic sine-Gordon
equation with appropriate boundary conditions. These boundary conditions are
chosen to correspond to the Josephson interaction between two adjacent pancakes
belonging to the same flux-line in a highly anisotropic superconductor. An
extrapolation is obtained between the regimes of low and high separation of the
pancakes. The resulting formula is a better candidate for use in numerical
simulations than previously derived formulas.Comment: 18 pages, 9 figure
Quantum Monte Carlo simulations of a particle in a random potential
In this paper we carry out Quantum Monte Carlo simulations of a quantum
particle in a one-dimensional random potential (plus a fixed harmonic
potential) at a finite temperature. This is the simplest model of an interface
in a disordered medium and may also pertain to an electron in a dirty metal. We
compare with previous analytical results, and also derive an expression for the
sample to sample fluctuations of the mean square displacement from the origin
which is a measure of the glassiness of the system. This quantity as well as
the mean square displacement of the particle are measured in the simulation.
The similarity to the quantum spin glass in a transverse field is noted. The
effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for
publication in J. of Physics A: Mathematical and Genera
Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential
In this paper we expand our previous investigation of a quantum particle
subject to the action of a random potential plus a fixed harmonic potential at
a finite temperature T. In the classical limit the system reduces to a
well-known ``toy'' model for an interface in a random medium. It also applies
to a single quantum particle like an an electron subject to random
interactions, where the harmonic potential can be tuned to mimic the effect of
a finite box. Using the variational approximation, or alternatively, the limit
of large spatial dimensions, together with the use the replica method, and are
able to solve the model and obtain its phase diagram in the
plane, where is the particle's mass. The phase diagram is similar to that
of a quantum spin-glass in a transverse field, where the variable
plays the role of the transverse field. The glassy phase is characterized by
replica-symmetry-breaking. The quantum transition at zero temperature is also
discussed.Comment: revised version, 23 pages, revtex, 5 postscript figures in a separate
file figures.u