237 research outputs found
Classical statistical distributions can violate Bell-type inequalities
We investigate two-particle phase-space distributions in classical mechanics
characterized by a well-defined value of the total angular momentum. We
construct phase-space averages of observables related to the projection of the
particles' angular momenta along axes with different orientations. It is shown
that for certain observables, the correlation function violates Bell's
inequality. The key to the violation resides in choosing observables impeding
the realization of the counterfactual event that plays a prominent role in the
derivation of the inequalities. This situation can have statistical (detection
related) or dynamical (interaction related) underpinnings, but non-locality
does not play any role.Comment: v3: Extended version. To be published in J. Phys.
Individually-rational collective choice
There is a collection of exogenously given socially-feasible sets, and, for each one of them, each individual in a group chooses from an individually-feasible set. The fact that the product of the individually-feasible sets is larger than the socially-feasible set notwithstanding, there arises no conflict between individual choices. Assuming that individual preferences are random, I characterize rationalizable collective choices
Entanglement and chaos in the kicked top
The standard kicked top involves a periodically kicked angular momentum. By
considering this angular momentum as a collection of entangled spins, we
compute the bipartite entanglement dynamics as a function of the dynamics of
the classical counterpart. Our numerical results indicate that the entanglement
of the quantum top depends on the specific details of the dynamics of the
classical top rather than depending universally on the global properties of the
classical regime. These results are grounded on linking the entanglement rate
to averages involving the classical angular momentum, thereby explaining why
regular dynamics can entangle as efficiently as the classically chaotic regime.
The findings are in line with previous results obtained with a 2-particle top
model, and we show here that the standard kicked top can be obtained as a
limiting case of the 2-particle top
Nonparametric instrumental regression with non-convex constraints
This paper considers the nonparametric regression model with an additive
error that is dependent on the explanatory variables. As is common in empirical
studies in epidemiology and economics, it also supposes that valid instrumental
variables are observed. A classical example in microeconomics considers the
consumer demand function as a function of the price of goods and the income,
both variables often considered as endogenous. In this framework, the economic
theory also imposes shape restrictions on the demand function, like
integrability conditions. Motivated by this illustration in microeconomics, we
study an estimator of a nonparametric constrained regression function using
instrumental variables by means of Tikhonov regularization. We derive rates of
convergence for the regularized model both in a deterministic and stochastic
setting under the assumption that the true regression function satisfies a
projected source condition including, because of the non-convexity of the
imposed constraints, an additional smallness condition
Realism and the wave-function
Realism -- the idea that the concepts in physical theories refer to 'things'
existing in the real world -- is introduced as a tool to analyze the status of
the wave-function. Although the physical entities are recognized by the
existence of invariant quantities, examples from classical and quantum physics
suggest that not all the theoretical terms refer to the entities: some terms
refer to properties of the entities, and some terms have only an epistemic
function. In particular, it is argued that the wave-function may be written in
terms of classical non-referring and epistemic terms. The implications for
realist interpretations of quantum mechanics and on the teaching of quantum
physics are examined.Comment: No figure
Non-Hermitian quantum mechanics: the case of bound state scattering theory
Excited bound states are often understood within scattering based theories as
resulting from the collision of a particle on a target via a short-range
potential. We show that the resulting formalism is non-Hermitian and describe
the Hilbert spaces and metric operator relevant to a correct formulation of
such theories. The structure and tools employed are the same that have been
introduced in current works dealing with PT-symmetric and quasi-Hermitian
problems. The relevance of the non-Hermitian formulation to practical
computations is assessed by introducing a non-Hermiticity index. We give a
numerical example involving scattering by a short-range potential in a Coulomb
field for which it is seen that even for a small but non-negligible
non-Hermiticity index the non-Hermitian character of the problem must be taken
into account. The computation of physical quantities in the relevant Hilbert
spaces is also discussed
Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
We survey some of the main conceptual developments in the study of
PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place
during the past ten years or so. We offer a precise mathematical description of
a quantum system and its representations that allows us to describe the idea of
unitarization of a quantum system by modifying the inner product of the Hilbert
space. We discuss the role and importance of the quantum-to-classical
correspondence principle that provides the physical interpretation of the
observables in quantum mechanics. Finally, we address the problem of
constructing an underlying classical Hamiltonian for a unitary quantum system
defined by an a priori non-Hermitian Hamiltonian.Comment: 11 page
Generalized Hamiltonian structures for Ermakov systems
We construct Poisson structures for Ermakov systems, using the Ermakov
invariant as the Hamiltonian. Two classes of Poisson structures are obtained,
one of them degenerate, in which case we derive the Casimir functions. In some
situations, the existence of Casimir functions can give rise to superintegrable
Ermakov systems. Finally, we characterize the cases where linearization of the
equations of motion is possible
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