3,787 research outputs found
Real time evolution using the density matrix renormalization group
We describe an extension to the density matrix renormalization group method
incorporating real time evolution into the algorithm. Its application to
transport problems in systems out of equilibrium and frequency dependent
correlation functions is discussed and illustrated in several examples. We
simulate a scattering process in a spin chain which generates a spatially
non-local entangled wavefunction.Comment: 4 pages, 4 eps figures, some minor corrections in text and Eq.(3
Bio-inspired swing leg control for spring-mass robots running on ground with unexpected height disturbance
We proposed three swing leg control policies for spring-mass running robots, inspired by experimental data from our recent collaborative work on ground running birds. Previous investigations suggest that animals may prioritize injury avoidance and/or efficiency as their objective function during running rather than maintaining limit-cycle stability. Therefore, in this study we targeted structural capacity (maximum leg force to avoid damage) and efficiency as the main goals for our control policies, since these objective functions are crucial to reduce motor size and structure weight. Each proposed policy controls the leg angle as a function of time during flight phase such that its objective function during the subsequent stance phase is regulated. The three objective functions that are regulated in the control policies are (i) the leg peak force, (ii) the axial impulse, and (iii) the leg actuator work. It should be noted that each control policy regulates one single objective function. Surprisingly, all three swing leg control policies result in nearly identical subsequent stance phase dynamics. This implies that the implementation of any of the proposed control policies would satisfy both goals (damage avoidance and efficiency) at once. Furthermore, all three control policies require a surprisingly simple leg angle adjustment: leg retraction with constant angular acceleration
Quantum data compression, quantum information generation, and the density-matrix renormalization group method
We have studied quantum data compression for finite quantum systems where the
site density matrices are not independent, i.e., the density matrix cannot be
given as direct product of site density matrices and the von Neumann entropy is
not equal to the sum of site entropies. Using the density-matrix
renormalization group (DMRG) method for the 1-d Hubbard model, we have shown
that a simple relationship exists between the entropy of the left or right
block and dimension of the Hilbert space of that block as well as of the
superblock for any fixed accuracy. The information loss during the RG procedure
has been investigated and a more rigorous control of the relative error has
been proposed based on Kholevo's theory. Our results are also supported by the
quantum chemistry version of DMRG applied to various molecules with system
lengths up to 60 lattice sites. A sum rule which relates site entropies and the
total information generated by the renormalization procedure has also been
given which serves as an alternative test of convergence of the DMRG method.Comment: 8 pages, 7 figure
Dynamics of Rumor Spreading in Complex Networks
We derive the mean-field equations characterizing the dynamics of a rumor
process that takes place on top of complex heterogeneous networks. These
equations are solved numerically by means of a stochastic approach. First, we
present analytical and Monte Carlo calculations for homogeneous networks and
compare the results with those obtained by the numerical method. Then, we study
the spreading process in detail for random scale-free networks. The time
profiles for several quantities are numerically computed, which allow us to
distinguish among different variants of rumor spreading algorithms. Our
conclusions are directed to possible applications in replicated database
maintenance, peer to peer communication networks and social spreading
phenomena.Comment: Final version to appear in PR
Dissipative dynamics and cooling rates of trapped impurity atoms immersed in a reservoir gas
We study the dissipative dynamics of neutral atoms in anisotropic harmonic potentials, immersed in a reservoir species that is not trapped by the harmonic potential. Considering initial motional excitation of the atoms along one direction, we explore the resulting spontaneous emission of reservoir excitations, across a range of trap parameters from strong to weak radial confinement. In different limits these processes are useful as a basis for analogies to laser cooling, or as a means to introduce controlled dissipation to many-body dynamics. For realistic experimental parameters, we analyze the distribution of the atoms during the decay and determine the effects of heating arising from a finite temperature reservoir
Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
The Lieb-Robinson bound implies that the unitary time evolution of an
operator can be restricted to an effective light cone for any Hamiltonian with
short-range interactions. Here we present a very efficient renormalization
group algorithm based on this light cone structure to study the time evolution
of prepared initial states in the thermodynamic limit in one-dimensional
quantum systems. The algorithm does not require translational invariance and
allows for an easy implementation of local conservation laws. We use the
algorithm to investigate the relaxation dynamics of double occupancies in
fermionic Hubbard models as well as a possible thermalization. For the
integrable Hubbard model we find a pure power-law decay of the number of doubly
occupied sites towards the value in the long-time limit while the decay becomes
exponential when adding a nearest neighbor interaction. In accordance with the
eigenstate thermalization hypothesis, the long-time limit is reasonably well
described by a thermal average. We point out though that such a description
naturally requires the use of negative temperatures. Finally, we study a
doublon impurity in a N\'eel background and find that the excess charge and
spin spread at different velocities, providing an example of spin-charge
separation in a highly excited state.Comment: published versio
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
We report a way of obtaining a spin configuration snapshot, which is one of
the representative spin configurations in canonical ensemble, in a finite area
of infinite size two-dimensional (2D) classical lattice models. The corner
transfer matrix renormalization group (CTMRG), a variant of the density matrix
renormalization group (DMRG), is used for the numerical calculation. The matrix
product structure of the variational state in CTMRG makes it possible to
stochastically fix spins each by each according to the conditional probability
with respect to its environment.Comment: 4 pages, 8figure
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The error of representation: basic understanding
Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model
The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
We give a generalization to an infinite tree geometry of Vidal's infinite
time-evolving block decimation (iTEBD) algorithm for simulating an infinite
line of quantum spins. We numerically investigate the quantum Ising model in a
transverse field on the Bethe lattice using the Matrix Product State ansatz. We
observe a second order phase transition, with certain key differences from the
transverse field Ising model on an infinite spin chain. We also investigate a
transverse field Ising model with a specific longitudinal field. When the
transverse field is turned off, this model has a highly degenerate ground state
as opposed to the pure Ising model whose ground state is only doubly
degenerate.Comment: 28 pages, 23 figures, PDFlate
Large Area Crop Inventory Experiment (LACIE). Intensive test site assessment report
There are no author-identified significant results in this report
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