40 research outputs found
The interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory
Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open
quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A
66, 012108 (2002)] we investigated this question using the orthodox
interpretation of quantum mechanics. We found that the solution of a
non-Markovian SSE represents the state the system would be in at that time if a
measurement was performed on the environment at that time, and yielded a
particular result. However, the linking of solutions at different times to make
a trajectory is, we concluded, a fiction. In this paper we investigate this
question using the modal (hidden variable) interpretation of quantum mechanics.
We find that the noise function appearing in the non-Markovian SSE can
be interpreted as a hidden variable for the environment. That is, some chosen
property (beable) of the environment has a definite value even in the
absence of measurement on the environment. The non-Markovian SSE gives the
evolution of the state of the system ``conditioned'' on this environment hidden
variable. We present the theory for diffusive non-Markovian SSEs that have as
their Markovian limit SSEs corresponding to homodyne and heterodyne detection,
as well as one which has no Markovian limit.Comment: 9 page
Scaling and self-averaging in the three-dimensional random-field Ising model
We investigate, by means of extensive Monte Carlo simulations, the magnetic
critical behavior of the three-dimensional bimodal random-field Ising model at
the strong disorder regime. We present results in favor of the two-exponent
scaling scenario, , where and are the
critical exponents describing the power-law decay of the connected and
disconnected correlation functions and we illustrate, using various finite-size
measures and properly defined noise to signal ratios, the strong violation of
self-averaging of the model in the ordered phase.Comment: 8 pages, 6 figures, to be published in Eur. Phys. J.
The three-dimensional randomly dilute Ising model: Monte Carlo results
We perform a high-statistics simulation of the three-dimensional randomly
dilute Ising model on cubic lattices with . We choose a
particular value of the density, x=0.8, for which the leading scaling
corrections are suppressed. We determine the critical exponents, obtaining , , , and ,
in agreement with previous numerical simulations. We also estimate numerically
the fixed-point values of the four-point zero-momentum couplings that are used
in field-theoretical fixed-dimension studies. Although these results somewhat
differ from those obtained using perturbative field theory, the
field-theoretical estimates of the critical exponents do not change
significantly if the Monte Carlo result for the fixed point is used. Finally,
we determine the six-point zero-momentum couplings, relevant for the
small-magnetization expansion of the equation of state, and the invariant
amplitude ratio that expresses the universality of the free-energy
density per correlation volume. We find .Comment: 34 pages, 7 figs, few correction
Atom-optics hologram in the time domain
The temporal evolution of an atomic wave packet interacting with object and
reference electromagnetic waves is investigated beyond the weak perturbation of
the initial state. It is shown that the diffraction of an ultracold atomic beam
by the inhomogeneous laser field can be interpreted as if the beam passes
through a three-dimensional hologram, whose thickness is proportional to the
interaction time. It is found that the diffraction efficiency of such a
hologram may reach 100% and is determined by the duration of laser pulses. On
this basis a method for reconstruction of the object image with matter waves is
offered.Comment: RevTeX, 13 pages, 8 figures; minor grammatical change
Ising model on 3D random lattices: A Monte Carlo study
We report single-cluster Monte Carlo simulations of the Ising model on
three-dimensional Poissonian random lattices with up to 128,000 approx. 503
sites which are linked together according to the Voronoi/Delaunay prescription.
For each lattice size quenched averages are performed over 96 realizations. By
using reweighting techniques and finite-size scaling analyses we investigate
the critical properties of the model in the close vicinity of the phase
transition point. Our random lattice data provide strong evidence that, for the
available system sizes, the resulting effective critical exponents are
indistinguishable from recent high-precision estimates obtained in Monte Carlo
studies of the Ising model and \phi^4 field theory on three-dimensional regular
cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure
Wang-Landau study of the 3D Ising model with bond disorder
We implement a two-stage approach of the Wang-Landau algorithm to investigate
the critical properties of the 3D Ising model with quenched bond randomness. In
particular, we consider the case where disorder couples to the nearest-neighbor
ferromagnetic interaction, in terms of a bimodal distribution of strong versus
weak bonds. Our simulations are carried out for large ensembles of disorder
realizations and lattices with linear sizes in the range . We apply
well-established finite-size scaling techniques and concepts from the scaling
theory of disordered systems to describe the nature of the phase transition of
the disordered model, departing gradually from the fixed point of the pure
system. Our analysis (based on the determination of the critical exponents)
shows that the 3D random-bond Ising model belongs to the same universality
class with the site- and bond-dilution models, providing a single universality
class for the 3D Ising model with these three types of quenched uncorrelated
disorder.Comment: 7 pages, 7 figures, to be published in Eur. Phys. J.
Spinor condensates and light scattering from Bose-Einstein condensates
These notes discuss two aspects of the physics of atomic Bose-Einstein
condensates: optical properties and spinor condensates. The first topic
includes light scattering experiments which probe the excitations of a
condensate in both the free-particle and phonon regime. At higher light
intensity, a new form of superradiance and phase-coherent matter wave
amplification were observed. We also discuss properties of spinor condensates
and describe studies of ground--state spin domain structures and dynamical
studies which revealed metastable excited states and quantum tunneling.Comment: 58 pages, 33 figures, to appear in Proceedings of Les Houches 1999
Summer School, Session LXXI
Critical aspects of the random-field Ising model
We investigate the critical behavior of the three-dimensional random-field Ising model
(RFIM) with a Gaussian field distribution at zero temperature. By implementing a
computational approach that maps the ground-state of the RFIM to the maximum-flow
optimization problem of a network, we simulate large ensembles of disorder realizations of
the model for a broad range of values of the disorder strength h and
system sizes = L3, with L ≤ 156. Our averaging procedure
outcomes previous studies of the model, increasing the sampling of ground states by a
factor of 103. Using well-established finite-size scaling schemes, the
fourth-order’s Binder cumulant, and the sample-to-sample fluctuations of various
thermodynamic quantities, we provide high-accuracy estimates for the critical field
hc, as well as the critical exponents ν,
β/ν, and γ̅/ν of the correlation length, order parameter, and
disconnected susceptibility, respectively. Moreover, using properly defined noise to
signal ratios, we depict the variation of the self-averaging property of the model, by
crossing the phase boundary into the ordered phase. Finally, we discuss the controversial
issue of the specific heat based on a scaling analysis of the bond energy, providing
evidence that its critical exponent α ≈ 0−
Resolving uncertainties in predictive equations for urban tree crown characteristics of the southeastern United States: Local and general equations for common and widespread species
Urban forest research and management requires improved methods for quantifying ecosystem structure and function. Regional equations for urban tree crown width and height can accordingly improve predictions of urban tree structure. Using a large regional dataset with 12 locations in the southeastern US, we developed diameter-based equations for 97 urban tree species. Whereas previously published urban equations have almost exclusively been developed with one location on public or commercial land, our data included both public and private land uses. For 5 widespread, common urban tree species (Acer rubrum, Cornus florida, Pinus taeda, Quercus nigra and Lagerstroemia spp.), we also assessed the inclusion of additional variables such as crown light exposure, land cover, basal area, and location. Overall, height and crown width models were improved when including additional predictors, although competition and location effects varied by species. Study city was a significant predictor of tree height in all species except C. florida, and a significant predictor of crown width for all species except C. florida and Q. nigra. This indicates that anthropogenically-influenced variation among cities can lead to significant differences in both tree form and structure and that future model development should utilize data encompassing multiple cities. Our predictive equations for urban tree crown characteristics provide an improved method for planning, management, and estimating the provision of ecosystem services to improve quality of life in cities. © 2016 Elsevier Gmb
Resolving uncertainties in predictive equations for urban tree crown characteristics of the southeastern United States: Local and general equations for common and widespread species
Urban forest research and management requires improved methods for quantifying ecosystem structure and function. Regional equations for urban tree crown width and height can accordingly improve predictions of urban tree structure. Using a large regional dataset with 12 locations in the southeastern US, we developed diameter-based equations for 97 urban tree species. Whereas previously published urban equations have almost exclusively been developed with one location on public or commercial land, our data included both public and private land uses. For 5 widespread, common urban tree species (Acer rubrum, Cornus florida, Pinus taeda, Quercus nigra and Lagerstroemia spp.), we also assessed the inclusion of additional variables such as crown light exposure, land cover, basal area, and location. Overall, height and crown width models were improved when including additional predictors, although competition and location effects varied by species. Study city was a significant predictor of tree height in all species except C. florida, and a significant predictor of crown width for all species except C. florida and Q. nigra. This indicates that anthropogenically-influenced variation among cities can lead to significant differences in both tree form and structure and that future model development should utilize data encompassing multiple cities. Our predictive equations for urban tree crown characteristics provide an improved method for planning, management, and estimating the provision of ecosystem services to improve quality of life in cities. © 2016 Elsevier Gmb