130 research outputs found
Two-particle interference in standard and Bohmian quantum mechanics
The compatibility of standard and Bohmian quantum mechanics has recently been
challenged in the context of two-particle interference, both from a theoretical
and an experimental point of view. We analyze different setups proposed and
derive corresponding exact forms for Bohmian equations of motion. The equations
are then solved numerically, and shown to reproduce standard quantum-mechanical
results.Comment: Minor corrections, 2 references added, version to appear in J. Phys.
Finite-Dimensional Bicomplex Hilbert Spaces
This paper is a detailed study of finite-dimensional modules defined on
bicomplex numbers. A number of results are proved on bicomplex square matrices,
linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces,
including the spectral decomposition theorem. Applications to concepts relevant
to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page
The bicomplex quantum Coulomb potential problem
Generalizations of the complex number system underlying the mathematical
formulation of quantum mechanics have been known for some time, but the use of
the commutative ring of bicomplex numbers for that purpose is relatively new.
This paper provides an analytical solution of the quantum Coulomb potential
problem formulated in terms of bicomplex numbers. We define the problem by
introducing a bicomplex hamiltonian operator and extending the canonical
commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi
is a bicomplex number. Following Pauli's algebraic method, we find the
eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained,
along with appropriate eigenfunctions, by solving the extension of
Schrodinger's time-independent differential equation. Examples of solutions are
displayed. There is an orthonormal system of solutions that belongs to a
bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J.
Phy
Can Everett be Interpreted Without Extravaganza?
Everett's relative states interpretation of quantum mechanics has met with
problems related to probability, the preferred basis, and multiplicity. The
third theme, I argue, is the most important one. It has led to developments of
the original approach into many-worlds, many-minds, and decoherence-based
approaches. The latter especially have been advocated in recent years, in an
effort to understand multiplicity without resorting to what is often perceived
as extravagant constructions. Drawing from and adding to arguments of others, I
show that proponents of decoherence-based approaches have not yet succeeded in
making their ontology clear.Comment: Succinct analysis forthcoming in Found. Phy
A first experimental test of de Broglie-Bohm theory against standard quantum mechanics
De Broglie - Bohm (dBB) theory is a deterministic theory, built for
reproducing almost all Quantum Mechanics (QM) predictions, where position plays
the role of a hidden variable. It was recently shown that different coincidence
patterns are predicted by QM and dBB when a double slit experiment is realised
under specific conditions and, therefore, an experiment can test the two
theories. In this letter we present the first realisation of such a double slit
experiment by using correlated photons produced in type I Parametric Down
Conversion. Our results confirm QM contradicting dBB predictions
What we learned from the Dust Bowl: lessons in science, policy, and adaptation
This article provides a review and synthesis of scholarly knowledge of Depression-era droughts on the North American Great Plains, a time and place known colloquially as the Dust Bowl era or the Dirty Thirties. Recent events, including the 2008 financial crisis, severe droughts in the US corn belt, and the release of a popular documentary film, have spawned a resurgence in public interest in the Dust Bowl. Events of the Dust Bowl era have also proven in recent years to be of considerable interest to scholars researching phenomena related to global environmental change, including atmospheric circulation, drought modeling, land management, institutional behavior, adaptation processes, and human migration. In this review, we draw out common themes in terms of not only what natural and social scientists have learned about the Dust Bowl era itself, but also how insights gained from the study of that period are helping to enhance our understanding of climate–human relations more generally
Quantum Stephani exact cosmological solutions and the selection of time variable
We study perfect fluid Stephani quantum cosmological model. In the present
work the Schutz's variational formalism which recovers the notion of time is
applied. This gives rise to Wheeler-DeWitt equation for the scale factor. We
use the eigenfunctions in order to construct wave packets for each case. We
study the time-dependent behavior of the expectation value of the scale factor,
using many-worlds and deBroglie-Bohm interpretations of quantum mechanics.Comment: 19 pages, 7 figure
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