2,220 research outputs found
Quantization with Action-Angle Coherent States
For a single degree of freedom confined mechanical system with given energy,
we know that the motion is always periodic and action-angle variables are
convenient choice as conjugate phase-space variables. We construct action-angle
coherent states in view to provide a quantization scheme that yields precisely
a given observed energy spectrum for such a system. This construction
is based on a Bayesian approach: each family corresponds to a choice of
probability distributions such that the classical energy averaged with respect
to this probability distribution is precisely up to a constant shift. The
formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an
alternative to the canonical quantization. In particular, it also yields a
satisfactory angle operator as a bounded self-adjoint operator
POVM Quantization
We present a general formalism for giving a measure space paired with a
separable Hilbert space a quantum version based on normalized positive
operator-valued measure. The latter are built from families of density
operators labelled by points of the measure space. We specially focus on
various probabilistic aspects of these constructions. Simple or more elaborate
examples illustrate the procedure: circle, 2-sphere, plane, half-plane. Links
with POVM quantum measurement and quantum statistical inference are sketched
Types for Location and Data Security in Cloud Environments
Cloud service providers are often trusted to be genuine, the damage caused by
being discovered to be attacking their own customers outweighs any benefits
such attacks could reap. On the other hand, it is expected that some cloud
service users may be actively malicious. In such an open system, each location
may run code which has been developed independently of other locations (and
which may be secret). In this paper, we present a typed language which ensures
that the access restrictions put on data on a particular device will be
observed by all other devices running typed code. Untyped, compromised devices
can still interact with typed devices without being able to violate the
policies, except in the case when a policy directly places trust in untyped
locations. Importantly, our type system does not need a middleware layer or all
users to register with a preexisting PKI, and it allows for devices to
dynamically create new identities. The confidentiality property guaranteed by
the language is defined for any kind of intruder: we consider labeled
bisimilarity i.e. an attacker cannot distinguish two scenarios that differ by
the change of a protected value. This shows our main result that, for a device
that runs well typed code and only places trust in other well typed devices,
programming errors cannot cause a data leakage.Comment: Short version to appear in Computer Security Foundations Symposium
(CSF'17), August 201
Three paths toward the quantum angle operator
We examine mathematical questions around angle (or phase) operator associated
with a number operator through a short list of basic requirements. We implement
three methods of construction of quantum angle. The first one is based on
operator theory and parallels the definition of angle for the upper half-circle
through its cosine and completed by a sign inversion. The two other methods are
integral quantization generalizing in a certain sense the Berezin-Klauder
approaches. One method pertains to Weyl-Heisenberg integral quantization of the
plane viewed as the phase space of the motion on the line. It depends on a
family of "weight" functions on the plane. The third method rests upon coherent
state quantization of the cylinder viewed as the phase space of the motion on
the circle. The construction of these coherent states depends on a family of
probability distributions on the line.Comment: 20 page
Quantum states of the bouncing universe
In this paper we study quantum dynamics of the bouncing cosmological model.
We focus on the model of the flat Friedman-Robertson-Walker universe with a
free scalar field. The bouncing behavior, which replaces classical singularity,
appears due to the modification of general relativity along the methods of loop
quantum cosmology. We show that there exist a unitary transformation that
enables to describe the system as a free particle with Hamiltonian equal to
canonical momentum. We examine properties of the various quantum states of the
Universe: boxcar state, standard coherent state, and soliton-like state, as
well as Schr{\"o}dinger's cat states constructed from these states.
Characteristics of the states such as quantum moments and Wigner functions are
investigated. We show that each of these states have, for some range of
parameters, a proper semiclassical limit fulfilling the correspondence
principle. Decoherence of the superposition of two universes is described and
possible interpretations in terms of triad orientation and
Belinsky-Khalatnikov-Lifshitz conjecture are given. Some interesting features
regarding the area of the negative part of the Wigner function have emerged.Comment: 18 pages, 19 figure
Krein Spaces in de Sitter Quantum Theories
Experimental evidences and theoretical motivations lead to consider the
curved space-time relativity based on the de Sitter group or
as an appealing substitute to the flat space-time Poincare
relativity. Quantum elementary systems are then associated to unitary
irreducible representations of that simple Lie group. At the lowest limit of
the discrete series lies a remarkable family of scalar representations
involving Krein structures and related undecomposable representation cohomology
which deserves to be thoroughly studied in view of quantization of the
corresponding carrier fields. The purpose of this note is to present the
mathematical material needed to examine the problem and to indicate possible
extensions of an exemplary case, namely the so-called de Sitterian massless
minimally coupled field, i.e. a scalar field in de Sitter space-time which does
not couple to the Ricci curvature
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