24,343 research outputs found
(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum
mechanics," Pascual Jordan (1927b,g) presented his version of what came to be
known as the Dirac-Jordan statistical transformation theory. As an alternative
that avoids the mathematical difficulties facing the approach of Jordan and
Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert
space formalism of quantum mechanics. In this paper, we focus on Jordan and von
Neumann. Central to the formalisms of both are expressions for conditional
probabilities of finding some value for one quantity given the value of
another. Beyond that Jordan and von Neumann had very different views about the
appropriate formulation of problems in quantum mechanics. For Jordan, unable to
let go of the analogy to classical mechanics, the solution of such problems
required the identication of sets of canonically conjugate variables, i.e., p's
and q's. For von Neumann, not constrained by the analogy to classical
mechanics, it required only the identication of a maximal set of commuting
operators with simultaneous eigenstates. He had no need for p's and q's. Jordan
and von Neumann also stated the characteristic new rules for probabilities in
quantum mechanics somewhat differently. Jordan (1927b) was the first to state
those rules in full generality. Von Neumann (1927a) rephrased them and, in a
subsequent paper (von Neumann, 1927b), sought to derive them from more basic
considerations. In this paper we reconstruct the central arguments of these
1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by
Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these
papers that bring out the gradual loosening of the ties between the new quantum
formalism and classical mechanics.Comment: New version. The main difference with the old version is that the
introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has
been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has
been accepted for publication in European Physical Journal
Elastocaloric response of PbTiO3 predicted from a first-principles effective Hamiltonian
A first-principles based effective Hamiltonian is used within a molecular
dynamics simulation to study the elastocaloric effect in PbTiO3. It is found
that the transition temperature is a linear function of uniaxial tensile
stress. Negative temperature change is calculated, when the uniaxial tensile
stress is switched off, as a function of initial temperature
Delta-T(T_initial). It is predicted that the formation of domain structures
under uniaxial tensile stress degrades the effectiveness of the elastocaloric
effect.Comment: 6 pages, 7 figures, published in JPS
Perturbative Gadgets at Arbitrary Orders
Adiabatic quantum algorithms are often most easily formulated using many-body
interactions. However, experimentally available interactions are generally
two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by
which arbitrary three-body effective interactions can be obtained using
Hamiltonians consisting only of two-body interactions. These three-body
effective interactions arise from the third order in perturbation theory. Since
their introduction, perturbative gadgets have become a standard tool in the
theory of quantum computation. Here we construct generalized gadgets so that
one can directly obtain arbitrary k-body effective interactions from two-body
Hamiltonians. These effective interactions arise from the kth order in
perturbation theory.Comment: Corrected an error: U dagger vs. U invers
Quantum Discord and Quantum Computing - An Appraisal
We discuss models of computing that are beyond classical. The primary
motivation is to unearth the cause of nonclassical advantages in computation.
Completeness results from computational complexity theory lead to the
identification of very disparate problems, and offer a kaleidoscopic view into
the realm of quantum enhancements in computation. Emphasis is placed on the
`power of one qubit' model, and the boundary between quantum and classical
correlations as delineated by quantum discord. A recent result by Eastin on the
role of this boundary in the efficient classical simulation of quantum
computation is discussed. Perceived drawbacks in the interpretation of quantum
discord as a relevant certificate of quantum enhancements are addressed.Comment: To be published in the Special Issue of the International Journal of
Quantum Information on "Quantum Correlations: entanglement and beyond." 11
pages, 4 figure
Thermal correlators of anyons in two dimensions
The anyon fields have trivial -commutator for not integer.
For integer the commutators become temperature-dependent operator
valued distributions. The -point functions do not factorize as for quasifree
states.Comment: 14 pages, LaTeX (misprints corrected, a reference added
Upper limit to in scalar-tensor gravity theories
In a previous paper (Serna & Alimi 1996), we have pointed out the existence
of some particular scalar-tensor gravity theories able to relax the
nucleosynthesis constraint on the cosmic baryonic density. In this paper, we
present an exhaustive study of primordial nucleosynthesis in the framework of
such theories taking into account the currently adopted observational
constraints. We show that a wide class of them allows for a baryonic density
very close to that needed for the universe closure. This class of theories
converges soon enough towards General Relativity and, hence, is compatible with
all solar-system and binary pulsar gravitational tests. In other words, we show
that primordial nucleosynthesis does not always impose a very stringent bound
on the baryon contribution to the density parameter.Comment: uuencoded tar-file containing 16 pages, latex with 5 figures,
accepted for publication in Astrophysical Journal (Part 1
An astronomical search for evidence of new physics: Limits on gravity-induced birefringence from the magnetic white dwarf RE J0317-853
The coupling of the electromagnetic field directly with gravitational gauge
fields leads to new physical effects that can be tested using astronomical
data. Here we consider a particular case for closer scrutiny, a specific
nonminimal coupling of torsion to electromagnetism, which enters into a
metric-affine geometry of space-time. We show that under the assumption of this
nonminimal coupling, spacetime is birefringent in the presence of such a
gravitational field. This leads to the depolarization of light emitted from
extended astrophysical sources. We use polarimetric data of the magnetic white
dwarf to set strong constraints on the essential coupling
constant for this effect, giving k^2 \lsim (19 {m})^2 .Comment: Statements about Moffat's NGT modified. Accepted for publication in
Phys.Rev.
Testing the equivalence principle: why and how?
Part of the theoretical motivation for improving the present level of testing
of the equivalence principle is reviewed. The general rationale for optimizing
the choice of pairs of materials to be tested is presented. One introduces a
simplified rationale based on a trichotomy of competing classes of theoretical
models.Comment: 11 pages, Latex, uses ioplppt.sty, submitted to Class. Quantum Gra
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