465 research outputs found
Traffic by multiple species of molecular motors
We study the traffic of two types of molecular motors using the two-species
symmetric simple exclusion process (ASEP) with periodic boundary conditions and
with attachment and detachment of particles. We determine characteristic
properties such as motor densities and currents by simulations and analytical
calculations. For motors with different unbinding probabilities, mean field
theory gives the correct bound density and total current of the motors, as
shown by numerical simulations. For motors differing in their stepping
probabilities, the particle-hole symmetry of the current-density relationship
is broken and mean field theory fails drastically. The total motor current
exhibits exponential finite-size scaling, which we use to extrapolate the total
current to the thermodynamic limit. Finally, we also study the motion of a
single motor in the background of many non-moving motors.Comment: 23 pages, 6 figures, late
Entanglement in Valence-Bond-Solid States
This article reviews the quantum entanglement in Valence-Bond-Solid (VBS)
states defined on a lattice or a graph. The subject is presented in a
self-contained and pedagogical way. The VBS state was first introduced in the
celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki
(abbreviation AKLT is widely used). It became essential in condensed matter
physics and quantum information (measurement-based quantum computation). Many
publications have been devoted to the subject. Recently entanglement was
studied in the VBS state. In this review we start with the definition of a
general AKLT spin chain and the construction of VBS ground state. In order to
study entanglement, a block subsystem is introduced and described by the
density matrix. Density matrices of 1-dimensional models are diagonalized and
the entanglement entropies (the von Neumann entropy and Renyi entropy) are
calculated. In the large block limit, the entropies also approach finite
limits. Study of the spectrum of the density matrix led to the discovery that
the density matrix is proportional to a projector.Comment: Published version, 80 pages, 8 figures; references update
A transition from river networks to scale-free networks
A spatial network is constructed on a two dimensional space where the nodes
are geometrical points located at randomly distributed positions which are
labeled sequentially in increasing order of one of their co-ordinates. Starting
with such points the network is grown by including them one by one
according to the serial number into the growing network. The -th point is
attached to the -th node of the network using the probability: where is the degree of the -th node
and is the Euclidean distance between the points and . Here
is a continuously tunable parameter and while for one gets
the simple Barab\'asi-Albert network, the case for
corresponds to the spatially continuous version of the well known Scheidegger's
river network problem. The modulating parameter is tuned to study the
transition between the two different critical behaviors at a specific value
which we numerically estimate to be -2.Comment: 5 pages, 5 figur
Theory of resistor networks: The two-point resistance
The resistance between arbitrary two nodes in a resistor network is obtained
in terms of the eigenvalues and eigenfunctions of the Laplacian matrix
associated with the network. Explicit formulas for two-point resistances are
deduced for regular lattices in one, two, and three dimensions under various
boundary conditions including that of a Moebius strip and a Klein bottle. The
emphasis is on lattices of finite sizes. We also deduce summation and product
identities which can be used to analyze large-size expansions of two-and-higher
dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte
Correlation Functions of Dense Polymers and c=-2 Conformal Field Theory
The model of dense lattice polymers is studied as an example of non-unitary
Conformal Field Theory (CFT) with . ``Antisymmetric'' correlation
functions of the model are proved to be given by the generalized Kirchhoff
theorem. Continuous limit of the model is described by the free complex
Grassmann field with null vacuum vector. The fundamental property of the
Grassmann field and its twist field (both having non-positive conformal
weights) is that they themselves suppress zero mode so that their correlation
functions become non-trivial. The correlation functions of the fields with
positive conformal weights are non-zero only in the presence of the Dirichlet
operator that suppresses zero mode and imposes proper boundary conditions.Comment: 5 pages, REVTeX, remark is adde
Inhomogeneous Superconductivity in Comb-Shaped Josephson Junction Networks
We show that some of the Josephson couplings of junctions arranged to form an
inhomogeneous network undergo a non-perturbative renormalization provided that
the network's connectivity is pertinently chosen. As a result, the zero-voltage
Josephson critical currents turn out to be enhanced along directions
selected by the network's topology. This renormalization effect is possible
only on graphs whose adjacency matrix admits an hidden spectrum (i.e. a set of
localized states disappearing in the thermodynamic limit). We provide a
theoretical and experimental study of this effect by comparing the
superconducting behavior of a comb-shaped Josephson junction network and a
linear chain made with the same junctions: we show that the Josephson critical
currents of the junctions located on the comb's backbone are bigger than the
ones of the junctions located on the chain. Our theoretical analysis, based on
a discrete version of the Bogoliubov-de Gennes equation, leads to results which
are in good quantitative agreement with experimental results.Comment: 4 pages, 2 figures, revte
Parameterized Edge Hamiltonicity
We study the parameterized complexity of the classical Edge Hamiltonian Path
problem and give several fixed-parameter tractability results. First, we settle
an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT
parameterized by vertex cover, and that it also admits a cubic kernel. We then
show fixed-parameter tractability even for a generalization of the problem to
arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set.
We also consider the problem parameterized by treewidth or clique-width.
Surprisingly, we show that the problem is FPT for both of these standard
parameters, in contrast to its vertex version, which is W-hard for
clique-width. Our technique, which may be of independent interest, relies on a
structural characterization of clique-width in terms of treewidth and complete
bipartite subgraphs due to Gurski and Wanke
Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients
In this paper we give a method for constructing systematically all simple
2-connected graphs with n vertices from the set of simple 2-connected graphs
with n-1 vertices, by means of two operations: subdivision of an edge and
addition of a vertex. The motivation of our study comes from the theory of
non-ideal gases and, more specifically, from the virial equation of state. It
is a known result of Statistical Mechanics that the coefficients in the virial
equation of state are sums over labelled 2-connected graphs. These graphs
correspond to clusters of particles. Thus, theoretically, the virial
coefficients of any order can be calculated by means of 2-connected graphs used
in the virial coefficient of the previous order. Our main result gives a method
for constructing inductively all simple 2-connected graphs, by induction on the
number of vertices. Moreover, the two operations we are using maintain the
correspondence between graphs and clusters of particles.Comment: 23 pages, 5 figures, 3 table
A rigorous implementation of the Jeans--Landau--Teller approximation
Rigorous bounds on the rate of energy exchanges between vibrational and
translational degrees of freedom are established in simple classical models of
diatomic molecules. The results are in agreement with an elementary
approximation introduced by Landau and Teller. The method is perturbative
theory ``beyond all orders'', with diagrammatic techniques (tree expansions) to
organize and manipulate terms, and look for compensations, like in recent
studies on KAM theorem homoclinic splitting.Comment: 23 pages, postscrip
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