5,427 research outputs found
Particle number conservation in quantum many-body simulations with matrix product operators
Incorporating conservation laws explicitly into matrix product states (MPS)
has proven to make numerical simulations of quantum many-body systems much less
resources consuming. We will discuss here, to what extent this concept can be
used in simulation where the dynamically evolving entities are matrix product
operators (MPO). Quite counter-intuitively the expectation of gaining in speed
by sacrificing information about all but a single symmetry sector is not in all
cases fulfilled. It turns out that in this case often the entanglement imposed
by the global constraint of fixed particle number is the limiting factor.Comment: minor changes, 18 pages, 5 figure
Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit
We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the
Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the
thermodynamic limit. The BMPS is built on a dual series of reduced
biorthonormal bases for the left and right Perron states of a non-Hermitian
matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG)
algorithms and compare their numerical performance in both finite and infinite
systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which
are translationally invariant in the thermodynamic limit. We also develop an
efficient wave function transformation of the iBTMRG, an analogy of McCulloch
in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as
the lattice size is increased. The resulting iBMPS allows for probing bulk
properties of the system in the thermodynamic limit without boundary effects
and allows for reducing the computational cost to be independent of the lattice
size, which are illustrated by calculating the magnetization as a function of
the temperature and the critical spin-spin correlation in the thermodynamic
limit for a 2D classical Ising model.Comment: 14 pages, 9 figure
Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group
A useful concept for finding numerically the dominant correlations of a given
ground state in an interacting quantum lattice system in an unbiased way is the
correlation density matrix. For two disjoint, separated clusters, it is defined
to be the density matrix of their union minus the direct product of their
individual density matrices and contains all correlations between the two
clusters. We show how to extract from the correlation density matrix a general
overview of the correlations as well as detailed information on the operators
carrying long-range correlations and the spatial dependence of their
correlation functions. To determine the correlation density matrix, we
calculate the ground state for a class of spinless extended Hubbard models
using the density matrix renormalization group. This numerical method is based
on matrix product states for which the correlation density matrix can be
obtained straightforwardly. In an appendix, we give a detailed tutorial
introduction to our variational matrix product state approach for ground state
calculations for 1- dimensional quantum chain models. We show in detail how
matrix product states overcome the problem of large Hilbert space dimensions in
these models and describe all techniques which are needed for handling them in
practice.Comment: 50 pages, 34 figures, to be published in New Journal of Physic
Genome-wide mapping reveals single-origin chromosome replication in Leishmania, a eukaryotic microbe
Background
DNA replication initiates on defined genome sites, termed origins. Origin usage appears to follow common rules in the eukaryotic organisms examined to date: all chromosomes are replicated from multiple origins, which display variations in firing efficiency and are selected from a larger pool of potential origins. To ask if these features of DNA replication are true of all eukaryotes, we describe genome-wide origin mapping in the parasite Leishmania.
Results
Origin mapping in Leishmania suggests a striking divergence in origin usage relative to characterized eukaryotes, since each chromosome appears to be replicated from a single origin. By comparing two species of Leishmania, we find evidence that such origin singularity is maintained in the face of chromosome fusion or fission events during evolution. Mapping Leishmania origins suggests that all origins fire with equal efficiency, and that the genomic sites occupied by origins differ from related non-origins sites. Finally, we provide evidence that origin location in Leishmania displays striking conservation with Trypanosoma brucei, despite the latter parasite replicating its chromosomes from multiple, variable strength origins.
Conclusions
The demonstration of chromosome replication for a single origin in Leishmania, a microbial eukaryote, has implications for the evolution of origin multiplicity and associated controls, and may explain the pervasive aneuploidy that characterizes Leishmania chromosome architecture
Exploring local quantum many-body relaxation by atoms in optical superlattices
We establish a setting - atoms in optical superlattices with period 2 - in
which one can experimentally probe signatures of the process of local
relaxation and apparent thermalization in non-equilibrium dynamics without the
need of addressing single sites. This opens up a way to explore the convergence
of subsystems to maximum entropy states in quenched quantum many-body systems
with present technology. Remarkably, the emergence of thermal states does not
follow from a coupling to an environment, but is a result of the complex
non-equilibrium dynamics in closed systems. We explore ways of measuring the
relevant signatures of thermalization in this analogue quantum simulation of a
relaxation process, exploiting the possibilities offered by optical
superlattices.Comment: 4 pages, 3 figures, version to published in Physical Review Letter
Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime
Power-law tail behavior and the summation scheme of Levy-stable distributions
is the basis for their frequent use as models when fat tails above a Gaussian
distribution are observed. However, recent studies suggest that financial asset
returns exhibit tail exponents well above the Levy-stable regime (). In this paper we illustrate that widely used tail index estimates (log-log
linear regression and Hill) can give exponents well above the asymptotic limit
for close to 2, resulting in overestimation of the tail exponent in
finite samples. The reported value of the tail exponent around 3 may
very well indicate a Levy-stable distribution with .Comment: To be published in Int. J. Modern Physics C (2001) vol. 12 no.
From density-matrix renormalization group to matrix product states
In this paper we give an introduction to the numerical density matrix
renormalization group (DMRG) algorithm, from the perspective of the more
general matrix product state (MPS) formulation. We cover in detail the
differences between the original DMRG formulation and the MPS approach,
demonstrating the additional flexibility that arises from constructing both the
wavefunction and the Hamiltonian in MPS form. We also show how to make use of
global symmetries, for both the Abelian and non-Abelian cases.Comment: Numerous small changes and clarifications, added a figur
Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 2: Appendices
There are no author-identified significant results in this report
Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 1: Text
The author has identified the following significant results. Image interpretation and computer-assisted techniques were developed to analyze LANDSAT scenes in support of resource inventory and monitoring requirements for the Texas coastal region. Land cover and land use maps, at a scale of 1:125,000 for the image interpretation product and 1:24,000 for the computer-assisted product, were generated covering four Texas coastal test sites. Classification schemes which parallel national systems were developed for each procedure, including 23 classes for image interpretation technique and 13 classes for the computer-assisted technique. Results indicate that LANDSAT-derived land cover and land use maps can be successfully applied to a variety of planning and management activities on the Texas coast. Computer-derived land/water maps can be used with tide gage data to assess shoreline boundaries for management purposes
- …