464,539 research outputs found
Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard
Square billiards are quantum systems complying with the dynamical
quantum-classical correspondence. Hence an initially localized wavefunction
launched along a classical periodic orbit evolves along that orbit, the
spreading of the quantum amplitude being controlled by the spread of the
corresponding classical statistical distribution. We investigate wavepacket
dynamics and compute the corresponding de Broglie-Bohm trajectories in the
quantum square billiard. We also determine the trajectories and statistical
distribution dynamics for the equivalent classical billiard. Individual Bohmian
trajectories follow the streamlines of the probability flow and are generically
non-classical. This can also hold even for short times, when the wavepacket is
still localized along a classical trajectory. This generic feature of Bohmian
trajectories is expected to hold in the classical limit. We further argue that
in this context decoherence cannot constitute a viable solution in order to
recover classicality.Comment: Figures downgraded to low resolution; To be published in Found. Phys.
(2009)
Transfer Learning for Speech and Language Processing
Transfer learning is a vital technique that generalizes models trained for
one setting or task to other settings or tasks. For example in speech
recognition, an acoustic model trained for one language can be used to
recognize speech in another language, with little or no re-training data.
Transfer learning is closely related to multi-task learning (cross-lingual vs.
multilingual), and is traditionally studied in the name of `model adaptation'.
Recent advance in deep learning shows that transfer learning becomes much
easier and more effective with high-level abstract features learned by deep
models, and the `transfer' can be conducted not only between data distributions
and data types, but also between model structures (e.g., shallow nets and deep
nets) or even model types (e.g., Bayesian models and neural models). This
review paper summarizes some recent prominent research towards this direction,
particularly for speech and language processing. We also report some results
from our group and highlight the potential of this very interesting research
field.Comment: 13 pages, APSIPA 201
Finite element surface registration incorporating curvature, volume preservation, and statistical model information
We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models
Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors
It was recently conjectured that, in SU(3) gauge theories with fundamental
quarks, valence spontaneous chiral symmetry breaking is equivalent to
condensation of local dynamical chirality and appearance of chiral polarization
scale . Here we consider more general association involving the
low-energy layer of chirally polarized modes which, in addition to its width
(), is also characterized by volume density of participating
modes () and the volume density of total chirality (). Few
possible forms of the correspondence are discussed, paying particular attention
to singular cases where emerges as the most versatile characteristic.
The notion of finite-volume "order parameter", capturing the nature of these
connections, is proposed. We study the effects of temperature (in N=0 QCD)
and light quarks (in N=12), both in the regime of possible symmetry
restoration, and find agreement with these ideas. In N=0 QCD, results from
several volumes indicate that, at the lattice cutoff studied, the deconfinement
temperature is strictly smaller than the overlap-valence chiral
transition temperature in real Polyakov line vacuum. Somewhat similar
intermediate phase (in quark mass) is also seen in N=12. It is suggested
that deconfinement in N=0 is related to indefinite convexity of absolute
X-distributions.Comment: 45 pages, 20 figures; v2: reduced the size of submission and fixed
references to appendices; v3: minor changes - published for
Grassmann Variables and the Jaynes-Cummings Model
This paper shows that phase space methods using a positive P type
distribution function involving both c-number variables (for the cavity mode)
and Grassmann variables (for the two level atom) can be used to treat the
Jaynes-Cummings model. Although it is a Grassmann function, the distribution
function is equivalent to six c-number functions of the two bosonic variables.
Experimental quantities are given as bosonic phase space integrals involving
the six functions. A Fokker-Planck equation involving both left and right
Grassmann differentiation can be obtained for the distribution function, and is
equivalent to six coupled equations for the six c-number functions.
The approach used involves choosing the canonical form of the (non-unique)
positive P distribution function, where the correspondence rules for bosonic
operators are non-standard and hence the Fokker-Planck equation is also
unusual. Initial conditions, such as for initially uncorrelated states, are
used to determine the initial distribution function. Transformations to new
bosonic variables rotating at the cavity frequency enables the six coupled
equations for the new c-number functions (also equivalent to the canonical
Grassmann distribution function) to be solved analytically, based on an ansatz
from a 1980 paper by Stenholm. It is then shown that the distribution function
is the same as that determined from the well-known solution based on coupled
equations for state vector amplitudes of atomic and n-photon product states.
The treatment of the simple two fermion mode Jaynes-Cummings model is a
useful test case for the future development of phase space Grassmann
distribution functional methods for multi-mode fermionic applications in
quantum-atom optics.Comment: 57 pages, 0 figures. Version
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