1,374 research outputs found
A survey about framing the bases of Impulsive Mechanics of constrained systems into a jet-bundle geometric context
We illustrate how the different kinds of constraints acting on an impulsive
mechanical system can be clearly described in the geometric setup given by the
configuration space--time bundle and its
first jet extension in a way that ensures total
compliance with axioms and invariance requirements of Classical Mechanics. We
specify the differences between geometric and constitutive characterizations of
a constraint. We point out the relevance of the role played by the concept of
frame of reference, underlining when the frame independence is mandatorily
required and when a choice of a frame is an inescapable need. The thorough
rationalization allows the introduction of unusual but meaningful kinds of
constraints, such as unilateral kinetic constraints or breakable constraints,
and of new theoretical aspects, such as the possible dependence of the
impulsive reaction by the active forces acting on the system
How to be causal: time, spacetime, and spectra
I explain a simple definition of causality in widespread use, and indicate
how it links to the Kramers Kronig relations. The specification of causality in
terms of temporal differential eqations then shows us the way to write down
dynamical models so that their causal nature /in the sense used here/ should be
obvious to all. To extend existing treatments of causality that work only in
the frequency domain, I derive a reformulation of the long-standing Kramers
Kronig relations applicable not only to just temporal causality, but also to
spacetime "light-cone" causality based on signals carried by waves. I also
apply this causal reasoning to Maxwell's equations, which is an instructive
example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B,
cause classification/frames (not in EJP); v7 - unusual model case; v8 add
reference
Interferometric Quantum Cascade Systems
In this work we consider quantum cascade networks in which quantum systems
are connected through unidirectional channels that can mutually interact giving
rise to interference effects. In particular we show how to compute master
equations for cascade systems in an arbitrary interferometric configuration by
means of a collisional model. We apply our general theory to two specific
examples: the first consists in two systems arranged in a Mach-Zender-like
configuration; the second is a three system network where it is possible to
tune the effective chiral interactions between the nodes exploiting
interference effects.Comment: 15 pages, 5 figure
The Fermi Problem in Discrete Systems
The Fermi two-atom problem illustrates an apparent causality violation in
Quantum Field Theory which has to do with the nature of the built in
correlations in the vacuum. It has been a constant subject of theoretical
debate and discussions during the last few decades. Nevertheless, although the
issues at hand could in principle be tested experimentally, the smallness of
such apparent violations of causality in Quantum Electrodynamics prevented the
observation of the predicted effect. In the present paper we show that the
problem can be simulated within the framework of discrete systems that can be
manifested, for instance, by trapped atoms in optical lattices or trapped ions.
Unlike the original continuum case, the causal structure is no longer sharp.
Nevertheless, as we show, it is possible to distinguish between "trivial"
effects due to "direct" causality violations, and the effects associated with
Fermi's problem, even in such discrete settings. The ability to control
externally the strength of the atom-field interactions, enables us also to
study both the original Fermi problem with "bare atoms", as well as correction
in the scenario that involves "dressed" atoms. Finally, we show that in
principle, the Fermi effect can be detected using trapped ions.Comment: Second version - minor change
Global algebras of nonlinear generalized functions with applications in general relativity
We give an overview of the development of algebras of generalized functions
in the sense of Colombeau and recent advances concerning diffeomorphism
invariant global algebras of generalized functions and tensor fields. We
furthermore provide a survey on possible applications in general relativity in
light of the limitations of distribution theory
Geodesic completeness of generalized space-times
We define the notion of geodesic completeness for semi-Riemannian metrics of
low regularity in the framework of the geometric theory of generalized
functions. We then show completeness of a wide class of impulsive gravitational
wave space-times.Comment: 8 pages, v3: minor corrections, final versio
Interpreting Quantum Mechanics in Terms of Random Discontinuous Motion of Particles
This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity
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