Relativity of arithmetic as a fundamental symmetry of physicsQuantum Studies: Mathematics and Foundations - Tập 3 - Trang 123-133 - 2015
Marek Czachor
Arithmetic operations can be defined in various ways, even if one assumes
commutativity and associativity of addition and multiplication, and
distributivity of multiplication with respect to addition. In consequence,
whenever one encounters ‘plus’ or ‘times’ one has certain freedom of
interpreting this operation. This leads to some freedom in definitions of
derivatives, integrals and, thus, practi... hiện toàn bộ
A new class of superoscillatory functions based on a generalized polar coordinate systemQuantum Studies: Mathematics and Foundations - Tập 7 - Trang 307-313 - 2020
Yakir Aharonov, Tomer Shushi
Is it possible for a band-limited signal to possess oscillation that is
arbitrarily higher than its highest Fourier component? Common knowledge assumed
that the answer is ‘No.’ Counterintuitively, it turns out that there are
band-limited functions that are able to oscillate arbitrarily faster than their
fastest Fourier components. These are the superoscillatory functions. Since
their discovery, su... hiện toàn bộ
Theoretic impetuses and lengths of Feinberg–Horodecki equationQuantum Studies: Mathematics and Foundations - Tập 9 - Trang 141-153 - 2021
C. A. Onate, D. T. Bankole, A. S. Olayinka, O. E. Odeyemi
The exact solution of the Feinberg–Horodecki equation for time-dependent
harmonic vector potential has been investigated under a one-dimensional system.
The quantized momentum and its corresponding un-normalized wave functions were
explicitly obtained. The Fisher information (for time and momentum) and variance
(for time and momentum) were calculated using expectation values of time and
momentum v... hiện toàn bộ
Noise suppression in inverse weak value-based phase detectionQuantum Studies: Mathematics and Foundations - Tập 5 - Trang 579-588 - 2017
Kevin Lyons, John C. Howell, Andrew N. Jordan
We examine the effect of different sources of technical noise on inverse weak
value-based precision phase measurements. We find that this type of measurement
is similarly robust to technical noise as related experiments in the weak value
regime. In particular, the measurements considered here are robust to additive
Gaussian white noise and angular jitter noise commonly encountered in optical
exper... hiện toàn bộ
A scheme for performing strong and weak sequential measurements of non-commuting observablesQuantum Studies: Mathematics and Foundations - Tập 4 - Trang 13-27 - 2016
Aharon Brodutch, Eliahu Cohen
Quantum systems usually travel a multitude of different paths when evolving
through time from an initial to a final state. In general, the possible paths
will depend on the future and past boundary conditions, as well as the system’s
dynamics. We present a gedanken experiment where a single system apparently
follows mutually exclusive paths simultaneously, each with probability one,
depending on w... hiện toàn bộ
A conjecture concerning determinism, reduction, and measurement in quantum mechanicsQuantum Studies: Mathematics and Foundations - Tập 3 - Trang 279-292 - 2016
Arthur Jabs
It is shown that it is possible to introduce determinism into quantum mechanics
by tracing the probabilities in the Born rules back to pseudorandomness in the
absolute phase constants of the wave functions. Each wave function is conceived
to contain an individual phase factor $$\exp (\mathrm {i}\alpha )$$ . In an
ensemble of systems, the phase constants $$\alpha $$ are taken to be
pseudorandom num... hiện toàn bộ
Loops, projective invariants, and the realization of the Borromean topological link in quantum mechanicsQuantum Studies: Mathematics and Foundations - Tập 3 - Trang 337-359 - 2016
Elias Zafiris
All the typical global quantum mechanical observables are complex relative
phases obtained by interference phenomena. They are described by means of some
global geometric phase factor, which is thought of as the “memory” of a quantum
system undergoing a “cyclic evolution” after coming back to its original
physical state. The origin of a geometric phase factor can be traced to the
local phase invar... hiện toàn bộ
Reconstructing quantum theory from its possibilistic operational formalismQuantum Studies: Mathematics and Foundations - Tập 10 - Trang 115-159 - 2022
Eric Buffenoir
We develop a possibilistic semantic formalism for quantum phenomena from an
operational perspective. This semantic system is based on a Chu duality between
preparation processes and yes/no tests, the target space being a three-valued
set equipped with an informational interpretation. A basic set of axioms is
introduced for the space of states. This basic set of axioms suffices to
constrain the spa... hiện toàn bộ