11,723 research outputs found
Entanglement and nonclassicality for multi-mode radiation field states
Nonclassicality in the sense of quantum optics is a prerequisite for
entanglement in multi-mode radiation states. In this work we bring out the
possibilities of passing from the former to the latter, via action of
classicality preserving systems like beamsplitters, in a transparent manner.
For single mode states, a complete description of nonclassicality is available
via the classical theory of moments, as a set of necessary and sufficient
conditions on the photon number distribution. We show that when the mode is
coupled to an ancilla in any coherent state, and the system is then acted upon
by a beamsplitter, these conditions turn exactly into signatures of NPT
entanglement of the output state. Since the classical moment problem does not
generalize to two or more modes, we turn in these cases to other familiar
sufficient but not necessary conditions for nonclassicality, namely the Mandel
parameter criterion and its extensions. We generalize the Mandel matrix from
one-mode states to the two-mode situation, leading to a natural classification
of states with varying levels of nonclassicality. For two--mode states we
present a single test that can, if successful, simultaneously show
nonclassicality as well as NPT entanglement. We also develop a test for NPT
entanglement after beamsplitter action on a nonclassical state, tracing
carefully the way in which it goes beyond the Mandel nonclassicality test. The
result of three--mode beamsplitter action after coupling to an ancilla in the
ground state is treated in the same spirit. The concept of genuine tripartite
entanglement, and scalar measures of nonclassicality at the Mandel level for
two-mode systems, are discussed. Numerous examples illustrating all these
concepts are presented.Comment: Latex, 46 page
Magellan: Preliminary description of Venus surface geologic units
Observations from approximately one-half of the Magellan nominal eight-month mission to map Venus are summarized. Preliminary compilation of initial geologic observations of the planet reveals a surface dominated by plains that are characterized by extensive and intensive volcanism and tectonic deformation. Four broad categories of units have been identified: plains units, linear belts, surficial units, and terrain units
Dobinski-type relations: Some properties and physical applications
We introduce a generalization of the Dobinski relation through which we
define a family of Bell-type numbers and polynomials. For all these sequences
we find the weight function of the moment problem and give their generating
functions. We provide a physical motivation of this extension in the context of
the boson normal ordering problem and its relation to an extension of the Kerr
Hamiltonian.Comment: 7 pages, 1 figur
Some useful combinatorial formulae for bosonic operators
We give a general expression for the normally ordered form of a function
F(w(a,a*)) where w is a function of boson annihilation and creation operators
satisfying [a,a*]=1. The expectation value of this expression in a coherent
state becomes an exact generating function of Feynman-type graphs associated
with the zero-dimensional Quantum Field Theory defined by F(w). This enables
one to enumerate explicitly the graphs of given order in the realm of
combinatorially defined sequences. We give several examples of the use of this
technique, including the applications to Kerr-type and superfluidity-type
hamiltonians.Comment: 8 pages, 3 figures, 17 reference
A generic Hopf algebra for quantum statistical mechanics
In this paper, we present a Hopf algebra description of a bosonic quantum
model, using the elementary combinatorial elements of Bell and Stirling
numbers. Our objective in doing this is as follows. Recent studies have
revealed that perturbative quantum field theory (pQFT) displays an astonishing
interplay between analysis (Riemann zeta functions), topology (Knot theory),
combinatorial graph theory (Feynman diagrams) and algebra (Hopf structure).
Since pQFT is an inherently complicated study, so far not exactly solvable and
replete with divergences, the essential simplicity of the relationships between
these areas can be somewhat obscured. The intention here is to display some of
the above-mentioned structures in the context of a simple bosonic quantum
theory, i.e. a quantum theory of non-commuting operators that do not depend on
space-time. The combinatorial properties of these boson creation and
annihilation operators, which is our chosen example, may be described by
graphs, analogous to the Feynman diagrams of pQFT, which we show possess a Hopf
algebra structure. Our approach is based on the quantum canonical partition
function for a boson gas.Comment: 8 pages/(4 pages published version), 1 Figure. arXiv admin note: text
overlap with arXiv:1011.052
From Quantum Mechanics to Quantum Field Theory: The Hopf route
We show that the combinatorial numbers known as {\em Bell numbers} are
generic in quantum physics. This is because they arise in the procedure known
as {\em Normal ordering} of bosons, a procedure which is involved in the
evaluation of quantum functions such as the canonical partition function of
quantum statistical physics, {\it inter alia}. In fact, we shall show that an
evaluation of the non-interacting partition function for a single boson system
is identical to integrating the {\em exponential generating function} of the
Bell numbers, which is a device for encapsulating a combinatorial sequence in a
single function. We then introduce a remarkable equality, the Dobinski
relation, and use it to indicate why renormalisation is necessary in even the
simplest of perturbation expansions for a partition function. Finally we
introduce a global algebraic description of this simple model, giving a Hopf
algebra, which provides a starting point for extensions to more complex
physical systems
Hierarchical Dobinski-type relations via substitution and the moment problem
We consider the transformation properties of integer sequences arising from
the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form
exp(x (a*)^r a), r=1,2,..., under the composition of their exponential
generating functions (egf). They turn out to be of Sheffer-type. We demonstrate
that two key properties of these sequences remain preserved under
substitutional composition: (a)the property of being the solution of the
Stieltjes moment problem; and (b) the representation of these sequences through
infinite series (Dobinski-type relations). We present a number of examples of
such composition satisfying properties (a) and (b). We obtain new Dobinski-type
formulas and solve the associated moment problem for several hierarchically
defined combinatorial families of sequences.Comment: 14 pages, 31 reference
What determines auditory similarity? The effect of stimulus group and methodology.
Two experiments on the internal representation of auditory stimuli compared the pairwise and grouping methodologies as means of deriving similarity judgements. A total of 45 undergraduate students participated in each experiment, judging the similarity of short auditory stimuli, using one of the methodologies. The experiments support and extend Bonebright's (1996) findings, using a further 60 stimuli. Results from both methodologies highlight the importance of category information and acoustic features, such as root mean square (RMS) power and pitch, in similarity judgements. Results showed that the grouping task is a viable alternative to the pairwise task with N > 20 sounds whilst highlighting subtle differences, such as cluster tightness, between the different task results. The grouping task is more likely to yield category information as underlying similarity judgements
Spatio-Temporal Scaling of Solar Surface Flows
The Sun provides an excellent natural laboratory for nonlinear phenomena. We
use motions of magnetic bright points on the solar surface, at the smallest
scales yet observed, to study the small scale dynamics of the photospheric
plasma. The paths of the bright points are analyzed within a continuous time
random walk framework. Their spatial and temporal scaling suggest that the
observed motions are the walks of imperfectly correlated tracers on a turbulent
fluid flow in the lanes between granular convection cells.Comment: Now Accepted by Physical Review Letter
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