3,566 research outputs found
From dispersionless to soliton systems via Weyl-Moyal like deformations
The formalism of quantization deformation is reviewed and the Weyl-Moyal like
deformation is applied to systematic construction of the field and lattice
integrable soliton systems from Poisson algebras of dispersionless systems.Comment: 26 page
Generalized Weyl-Wigner map and Vey quantum mechanics
The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics
directly from the standard operator formulation. The covariant generalization
of Moyal theory, also known as Vey quantum mechanics, was presented in the
literature many years ago. However, a derivation of the formalism directly from
standard operator quantum mechanics, clarifying the relation between the two
formulations is still missing. In this paper we present a covariant
generalization of the Weyl order prescription and of the Weyl-Wigner map and
use them to derive Vey quantum mechanics directly from the standard operator
formulation. The procedure displays some interesting features: it yields all
the key ingredients and provides a more straightforward interpretation of the
Vey theory including a direct implementation of unitary operator
transformations as phase space coordinate transformations in the Vey idiom.
These features are illustrated through a simple example.Comment: 15 pages, LaTe
Direct Detection of Electroweak-Interacting Dark Matter
Assuming that the lightest neutral component in an SU(2)L gauge multiplet is
the main ingredient of dark matter in the universe, we calculate the elastic
scattering cross section of the dark matter with nucleon, which is an important
quantity for the direct detection experiments. When the dark matter is a real
scalar or a Majorana fermion which has only electroweak gauge interactions, the
scattering with quarks and gluon are induced through one- and two-loop quantum
processes, respectively, and both of them give rise to comparable contributions
to the elastic scattering cross section. We evaluate all of the contributions
at the leading order and find that there is an accidental cancellation among
them. As a result, the spin-independent cross section is found to be
O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio
Time dependent transformations in deformation quantization
We study the action of time dependent canonical and coordinate
transformations in phase space quantum mechanics. We extend the covariant
formulation of the theory by providing a formalism that is fully invariant
under both standard and time dependent coordinate transformations. This result
considerably enlarges the set of possible phase space representations of
quantum mechanics and makes it possible to construct a causal representation
for the distributional sector of Wigner quantum mechanics.Comment: 16 pages, to appear in the J. Math. Phy
Quantum Convolutional Coding with Shared Entanglement: General Structure
We present a general theory of entanglement-assisted quantum convolutional
coding. The codes have a convolutional or memory structure, they assume that
the sender and receiver share noiseless entanglement prior to quantum
communication, and they are not restricted to possess the
Calderbank-Shor-Steane structure as in previous work. We provide two
significant advances for quantum convolutional coding theory. We first show how
to "expand" a given set of quantum convolutional generators. This expansion
step acts as a preprocessor for a polynomial symplectic Gram-Schmidt
orthogonalization procedure that simplifies the commutation relations of the
expanded generators to be the same as those of entangled Bell states (ebits)
and ancilla qubits. The above two steps produce a set of generators with
equivalent error-correcting properties to those of the original generators. We
then demonstrate how to perform online encoding and decoding for a stream of
information qubits, halves of ebits, and ancilla qubits. The upshot of our
theory is that the quantum code designer can engineer quantum convolutional
codes with desirable error-correcting properties without having to worry about
the commutation relations of these generators.Comment: 23 pages, replaced with final published versio
The quantum dynamic capacity formula of a quantum channel
The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections;
v3 has correction regarding the optimizatio
The ethical challenge of Touraine's 'living together'
In Can We Live Together? Alain Touraine combines a consummate analysis of crucial social tensions in contemporary societies with a strong normative appeal for a new emancipatory 'Subject' capable of overcoming the twin threats of atomisation or authoritarianism. He calls for a move from 'politics to ethics' and then from ethics back to politics to enable the new Subject to make a reality out of the goals of democracy and solidarity. However, he has little to say about the nature of such an ethics. This article argues that this lacuna could usefully be filled by adopting a form of radical humanism found in the work of Erich Fromm. It defies convention in the social sciences by operating from an explicit view of the 'is' and the 'ought' of common human nature, specifying reason, love and productive work as the qualities to be realised if we are to move closer to human solidarity. Although there remain significant philosophical and political differences between the two positions, particularly on the role to be played by 'the nation', their juxtaposition opens new lines of inquiry in the field of cosmopolitan ethics
In-medium meson properties and field transformations
Since the existing calculations of the effective meson mass in nuclear medium
involve approximations, it is important to examine whether they satisfy the
general requirement of the equivalence theorem that the physical observables
should be independent of the choice of field variables. We study here
consequences of nucleon field transformations. As an illustrative case we
consider the in-medium effective pion mass calculated for the s-wave
pion-nucleon interaction in the linear density approximation. We demonstrate
that it is necessary to include the Born term explicitly in order that the
effective pion mass should obey the equivalence theorem.Comment: 10 pages, using RevTeX4. More detailed discussion, references added.
To be published in Phys. Rev.
Nature of 45 degree vortex lattice reorientation in tetragonal superconductors
The transformation of the vortex lattice in a tetragonal superconductor which
consists of its 45 degree reorientation relative to the crystal axes is studied
using the nonlocal London model. It is shown that the reorientation occurs as
two successive second order (continuous) phase transitions. The transition
magnetic fields are calculated for a range of parameters relevant for
borocarbide superconductors in which the reorientation has been observed
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