8,494 research outputs found
A Monte Carlo Method for Fermion Systems Coupled with Classical Degrees of Freedom
A new Monte Carlo method is proposed for fermion systems interacting with
classical degrees of freedom. To obtain a weight for each Monte Carlo sample
with a fixed configuration of classical variables, the moment expansion of the
density of states by Chebyshev polynomials is applied instead of the direct
diagonalization of the fermion Hamiltonian. This reduces a cpu time to scale as
compared to for the
diagonalization in the conventional technique; is the dimension
of the Hamiltonian. Another advantage of this method is that parallel
computation with high efficiency is possible. These significantly save total
cpu times of Monte Carlo calculations because the calculation of a Monte Carlo
weight is the bottleneck part. The method is applied to the double-exchange
model as an example. The benchmark results show that it is possible to make a
systematic investigation using a system-size scaling even in three dimensions
within a realistic cpu timescale.Comment: 6 pages including 4 figure
Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields
An improved algorithm is proposed for Monte Carlo methods to study fermion
systems interacting with adiabatical fields. To obtain a weight for each Monte
Carlo sample with a fixed configuration of adiabatical fields, a series
expansion using Chebyshev polynomials is applied. By introducing truncations of
matrix operations in a systematic and controlled way, it is shown that the cpu
time is reduced from O(N^3) to O(N) where N is the system size. Benchmark
results show that the implementation of the algorithm makes it possible to
perform systematic investigations of critical phenomena using system-size
scalings even for an electronic model in three dimensions, within a realistic
cpu timescale.Comment: 9 pages with 4 fig
Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy
We present an efficient algorithm for calculating spectral properties of
large sparse Hamiltonian matrices such as densities of states and spectral
functions. The combination of Chebyshev recursion and maximum entropy achieves
high energy resolution without significant roundoff error, machine precision or
numerical instability limitations. If controlled statistical or systematic
errors are acceptable, cpu and memory requirements scale linearly in the number
of states. The inference of spectral properties from moments is much better
conditioned for Chebyshev moments than for power moments. We adapt concepts
from the kernel polynomial approximation, a linear Chebyshev approximation with
optimized Gibbs damping, to control the accuracy of Fourier integrals of
positive non-analytic functions. We compare the performance of kernel
polynomial and maximum entropy algorithms for an electronic structure example.Comment: 8 pages RevTex, 3 postscript figure
Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians
We explore the Mott insulating state of single-band bosonic pairing
Hamiltonians using analytical approaches and large scale density matrix
renormalization group calculations. We focus on the second Mott lobe which
exhibits a magnetic quantum phase transition in the Ising universality class.
We use this feature to discuss the behavior of a range of physical observables
within the framework of the 1D quantum Ising model and the strongly anisotropic
Heisenberg model. This includes the properties of local expectation values and
correlation functions both at and away from criticality. Depending on the
microscopic interactions it is possible to achieve either antiferromagnetic or
ferromagnetic exchange interactions and we highlight the possibility of
observing the E8 mass spectrum for the critical Ising model in a longitudinal
magnetic field.Comment: 14 pages, 15 figure
Self-Modification of Policy and Utility Function in Rational Agents
Any agent that is part of the environment it interacts with and has versatile
actuators (such as arms and fingers), will in principle have the ability to
self-modify -- for example by changing its own source code. As we continue to
create more and more intelligent agents, chances increase that they will learn
about this ability. The question is: will they want to use it? For example,
highly intelligent systems may find ways to change their goals to something
more easily achievable, thereby `escaping' the control of their designers. In
an important paper, Omohundro (2008) argued that goal preservation is a
fundamental drive of any intelligent system, since a goal is more likely to be
achieved if future versions of the agent strive towards the same goal. In this
paper, we formalise this argument in general reinforcement learning, and
explore situations where it fails. Our conclusion is that the self-modification
possibility is harmless if and only if the value function of the agent
anticipates the consequences of self-modifications and use the current utility
function when evaluating the future.Comment: Artificial General Intelligence (AGI) 201
Tumor antigen(s) in cells productively infected by wild-type polyoma virus and mutant NG-18
Bose--Hubbard Models Coupled to Cavity Light Fields
Recent experiments on strongly coupled cavity quantum electrodynamics present
new directions in "matter-light" systems. Following on from our previous work
[Phys. Rev. Lett. 102, 135301 (2009)] we investigate Bose-Hubbard models
coupled to a cavity light field. We discuss the emergence of photoexcitations
or "polaritons" within the Mott phase, and obtain the complete variational
phase diagram. Exploiting connections to the super-radiance transition in the
Dicke model we discuss the nature of polariton condensation within this novel
state. Incorporating the effects of carrier superfluidity, we identify a
first-order transition between the superradiant Mott phase and the single
component atomic superfluid. The overall predictions of mean field theory are
in excellent agreement with exact diagonalization and we provide details of
superfluid fractions, density fluctuations, and finite size effects. We
highlight connections to recent work on coupled cavity arrays.Comment: 16 pages, 17 figure
Calculating response functions in time domain with non-orthonormal basis sets
We extend the recently proposed order-N algorithms (cond-mat/9703224) for
calculating linear- and nonlinear-response functions in time domain to the
systems described by nonorthonormal basis sets.Comment: 4 pages, no figure
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