207 research outputs found
Diffusion Limited Aggregation on a Cylinder
We consider the DLA process on a cylinder G x N. It is shown that this
process "grows arms", provided that the base graph G has small enough mixing
time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the
time it takes the cluster to reach the m-th layer of the cylinder is at most of
order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs
of degree 5, for which the DLA cluster on these graphs has arbitrarily small
density.
In addition, we provide an upper bound on the rate at which the "arms" grow.
This bound is valid for a large class of base graphs G, including discrete tori
of dimension at least 3.
It is also shown that for any base graph G, the density of the DLA process on
a G-cylinder is related to the rate at which the arms of the cluster grow. This
implies, that for any vertex transitive G, the density of DLA on a G-cylinder
is bounded by 2/3.Comment: 1 figur
Flux melting in BSCCO: Incorporating both electromagnetic and Josephson couplings
Multilevel Monte Carlo simulations of a BSCCO system are carried out
including both Josephson as well as electromagnetic couplings for a range of
anisotropies. A first order melting transition of the flux lattice is seen on
increasing the temperature and/or the magnetic field. The phase diagram for
BSCCO is obtained for different values of the anisotropy parameter .
The best fit to the experimental results of D. Majer {\it et al.} [Phys. Rev.
Lett. {\bf 75}, 1166 (1995)] is obtained for provided one
assumes a temperature dependence of the
penetration depth with . Assuming a dependence
the best fit is obtained for . For finite anisotropy the data is shown to collapse on a straight line
when plotted in dimensionless units which shows that the melting transition can
be satisfied with a single Lindemann parameter whose value is about 0.3. A
different scaling applies to the case. The energy jump is
measured across the transition and for large values of it is found to
increase with increasing anisotropy and to decrease with increasing magnetic
field. For infinite anisotropy we see a 2D behavior of flux droplets with a
transition taking place at a temperature independent of the magnetic field. We
also show that for smaller values of anisotropy it is reasonable to replace the
electromagnetic coupling with an in-plane interaction represented by a Bessel
function of the second kind (), thus justifying our claim in a previous
paper.Comment: 12 figures, revtex
Directed polymers on a Cayley tree with spatially correlated disorder
In this paper we consider directed walks on a tree with a fixed branching
ratio K at a finite temperature T. We consider the case where each site (or
link) is assigned a random energy uncorrelated in time, but correlated in the
transverse direction i.e. within the shell. In this paper we take the
transverse distance to be the hierarchical ultrametric distance, but other
possibilities are discussed. We compute the free energy for the case of
quenched disorder and show that there is a fundamental difference between the
case of short range spatial correlations of the disorder which behaves
similarly to the non-correlated case considered previously by Derrida and Spohn
and the case of long range correlations which has a totally different overlap
distribution which approaches a single delta function about q=1 for large L,
where L is the length of the walk. In the latter case the free energy is not
extensive in L for the intermediate and also relevant range of L values,
although in the true thermodynamic limit extensivity is restored. We identify a
crossover temperature which grows with L, and whenever T<T_c(L) the system is
always in the low temperature phase. Thus in the case of long-ranged
correlation as opposed to the short-ranged case a phase transition is absent.Comment: 23 pages, 1 figure, standard latex. J. Phys. A, accepted for
publicatio
Solvable model of a polymer in random media with long ranged disorder correlations
We present an exactly solvable model of a Gaussian (flexible) polymer chain
in a quenched random medium. This is the case when the random medium obeys very
long range quadratic correlations. The model is solved in spatial
dimensions using the replica method, and practically all the physical
properties of the chain can be found. In particular the difference between the
behavior of a chain that is free to move and a chain with one end fixed is
elucidated. The interesting finding is that a chain that is free to move in a
quadratically correlated random potential behaves like a free chain with , where is the end to end distance and is the length of the
chain, whereas for a chain anchored at one end . The exact
results are found to agree with an alternative numerical solution in
dimensions. The crossover from long ranged to short ranged correlations of the
disorder is also explored.Comment: REVTeX, 28 pages, 12 figures in eps forma
ClockâWork Trade-Off Relation for Coherence in Quantum Thermodynamics
In thermodynamics, quantum coherencesâsuperpositions between energy eigenstatesâbehave in distinctly nonclassical ways. Here we describe how thermodynamic coherence splits into two kindsââinternalâ coherence that admits an energetic value in terms of thermodynamic work, and âexternalâ coherence that does not have energetic value, but instead corresponds to the functioning of the system as a quantum clock. For the latter form of coherence, we provide dynamical constraints that relate to quantum metrology and macroscopicity, while for the former, we show that quantum states exist that have finite internal coherence yet with zero deterministic work value. Finally, under minimal thermodynamic assumptions, we establish a clockâwork trade-off relation between these two types of coherences. This can be viewed as a form of time-energy conjugate relation within quantum thermodynamics that bounds the total maximum of clock and work resources for a given system
Phase Transitions of the Flux Line Lattice in High-Temperature Superconductors with Weak Columnar and Point Disorder
We study the effects of weak columnar and point disorder on the
vortex-lattice phase transitions in high temperature superconductors. The
combined effect of thermal fluctuations and of quenched disorder is
investigated using a simplified cage model. For columnar disorder the problem
maps into a quantum particle in a harmonic + random potential. We use the
variational approximation to show that columnar and point disorder have
opposite effect on the position of the melting line as observed experimentally.
Replica symmetry breaking plays a role at the transition into a vortex glass at
low temperatures.Comment: 4 pages in 2 columns format + 2 eps figs included, uses RevTeX and
multicol.st
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
Detecting metrologically useful asymmetry and entanglement by a few local measurements
Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. Here we show how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. We show that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. We implement the detection scheme in an all-optical experiment
Replica field theory for a polymer in random media
In this paper we revisit the problem of a (non self-avoiding) polymer chain
in a random medium which was previously investigated by Edwards and Muthukumar
(EM). As noticed by Cates and Ball (CB) there is a discrepancy between the
predictions of the replica calculation of EM and the expectation that in an
infinite medium the quenched and annealed results should coincide (for a chain
that is free to move) and a long polymer should always collapse. CB argued that
only in a finite volume one might see a ``localization transition'' (or
crossover) from a stretched to a collapsed chain in three spatial dimensions.
Here we carry out the replica calculation in the presence of an additional
confining harmonic potential that mimics the effect of a finite volume. Using a
variational scheme with five variational parameters we derive analytically for
d<4 the result R~(g |ln \mu|)^{-1/(4-d)} ~(g lnV)^{-1/(4-d)}, where R is the
radius of gyration, g is the strength of the disorder, \mu is the spring
constant associated with the confining potential and V is the associated
effective volume of the system. Thus the EM result is recovered with their
constant replaced by ln(V) as argued by CB. We see that in the strict infinite
volume limit the polymer always collapses, but for finite volume a transition
from a stretched to a collapsed form might be observed as a function of the
strength of the disorder. For d<2 and for large
V>V'~exp[g^(2/(2-d))L^((4-d)/(2-d))] the annealed results are recovered and
R~(Lg)^(1/(d-2)), where L is the length of the polymer. Hence the polymer also
collapses in the large L limit. The 1-step replica symmetry breaking solution
is crucial for obtaining the above results.Comment: Revtex, 32 page
Witnessing quantum resource conversion within deterministic quantum computation using one pure superconducting qubit
Deterministic quantum computation with one qubit (DQC1) is iconic in
highlighting that exponential quantum speedup may be achieved with negligible
entanglement. Its discovery catalyzed heated study of general quantum
resources, and various conjectures regarding their role in DQC1's performance
advantage. Coherence and discord are prominent candidates, respectively
characterizing non-classicality within localized and correlated systems. Here
we realize DQC1 within a superconducting system, engineered such that the
dynamics of coherence and discord can be tracked throughout its execution. We
experimentally confirm that DQC1 acts as a resource converter, consuming
coherence to generate discord during its operation. Our results highlight
superconducting circuits as a promising platform for both realizing DQC1 and
related algorithms, and experimentally characterizing resource dynamics within
quantum protocols.Comment: 6 pages, 4 figure
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