102 research outputs found
Action principle for cellular automata and the linearity of quantum mechanics
We introduce an action principle for a class of integer valued cellular
automata and obtain Hamiltonian equations of motion. Employing sampling theory,
these discrete deterministic equations are invertibly mapped on continuum
equations for a set of bandwidth limited harmonic oscillators, which encode the
Schr\"odinger equation. Thus, the linearity of quantum mechanics is related to
the action principle of such cellular automata and its conservation laws to
discrete ones.Comment: 6 pages; presented in part in invited talks at "Wigner 111 Scientific
Symposium" (11-13 Nov 2013, Budapest) and "EmQM13 - Emergent Quantum
Mechanics" (3-6 Oct 2013, Vienna
Open Quantum Systems, Entropy and Chaos
Entropy generation in quantum sytems is tied to the existence of a
nonclassical environment (heat bath or other) with which the system interacts.
The continuous `measuring' of the open system by its environment induces
decoherence of its wave function and entropy increase. Examples of
nonrelativistic quantum Brownian motion and of interacting scalar fields
illustrate these general concepts. It is shown that the Hartree-Fock
approximation around the bare classical limit can lead to spurious semiquantum
chaos, which may affect the determination of entropy production and
thermalization also in other cases.Comment: 22 pages including 4 figures; LaTex uses epsf and sprocl.sty file. -
Invited talk, 5th Rio de Janeiro International Workshop on Relativistic
Aspects of Nuclear Physics, August 1997; proceedings to be publ., T. Kodama
et al., eds. (World Scientific
On configuration space, Born's rule and ontological states
It is shown how configuration space, possibly encompassing ordinary spatial
structures, Born's rule, and ontological states aiming to address an underlying
reality beyond Quantum Mechanics relate to each other in models of Hamiltonian
cellular automata.Comment: 12 pages; to appear in the FIAS Interdisciplinary Science Series
volume dedicated to the memory of Walter Greiner. arXiv admin note: text
overlap with arXiv:1711.0032
Are nonlinear discrete cellular automata compatible with quantum mechanics?
We consider discrete and integer-valued cellular automata (CA). A particular
class of which comprises "Hamiltonian CA" with equations of motion that bear
similarities to Hamilton's equations, while they present discrete updating
rules. The dynamics is linear, quite similar to unitary evolution described by
the Schroedinger equation. This has been essential in our construction of an
invertible map between such CA and continuous quantum mechanical models, which
incorporate a fundamental discreteness scale. Based on Shannon's sampling
theory, it leads, for example, to a one-to-one relation between quantum
mechanical and CA conservation laws. The important issue of linearity of the
theory is examined here by incorporating higher-order nonlinearities into the
underlying action. These produce inconsistent nonlocal (in time) effects when
trying to describe continuously such nonlinear CA. Therefore, in the present
framework, only linear CA and local quantum mechanical dynamics are compatible.Comment: 11 pages. Talk presented at the DISCRETE 2014 international
conference, King's College, London, 2-6 December 201
Spacetime and Matter - a duality of partial orders
A new kind of duality between the deep structures of spacetime and matter is
proposed here, considering two partial orders which incorporate causality,
extensity, and discreteness. This may have surprising consequences for the
emergence of quantum mechanics, which are discussed.Comment: Fourth prize in the 2009 FQXi essay contest "What is Ultimately
Possible in Physics?
Gauge Symmetry of the Third Kind and Quantum Mechanics as an Infrared Phenomenon
We introduce functional degrees of freedom by a new gauge principle related
to the phase of the wave functional. Thereby, quantum mechanical systems are
seen as dissipatively embedded part of a nonlinear classical structure
producing universal correlations. There are a fundamental length and an
entropy/area parameter, besides standard couplings. For states that are
sufficiently spread over configuration space, quantum field theory is
recovered.Comment: 12 pages. To appear in the Festschrift "A Sense of Beauty in Physics"
dedicated to Adriano Di Giacomo on occasion of his 70th birthda
Four questions for quantum-classical hybrid theory
Four questions are discussed which may be addressed to any proposal of a
quantum-classical hybrid theory which concerns the direct coupling of classical
and quantum mechanical degrees of freedom. In particular, we consider the
formulation of hybrid dynamics presented recently in Ref.[1]. This linear
theory differs from the nonlinear ensemble theory of Hall and Reginatto, but
shares with it to fulfil all consistency requirements discussed in the
literature, while earlier attempts failed. - Here, we additionally ask: Does
the theory allow for superposition, separable, and entangled states originating
in the quantum mechanical sector? Does it allow for "Free Will", as introduced,
in this context, by Diosi [2]. Is it local? Does it provide hints for the
emergence of quantum mechanics from dynamics beneath?Comment: 16 pages - based on talk at the Conference on Emergent Quantum
Mechanics / Heinz von Foerster Congress (Vienna University, Nov. 11-13, 2011
Quantum-classical hybrid dynamics - a summary
A summary of a recently proposed description of quantum-classical hybrids is
presented, which concerns quantum and classical degrees of freedom of a
composite object that interact directly with each other. This is based on
notions of classical Hamiltonian mechanics suitably extended to quantum
mechanics.Comment: 7 pages; summarizing invited talks at 6th International Workshop
DICE2012, Castello Pasquini/Castiglioncello (Tuscany), September 17-21, 2012
and at Marcus Wallenberg Symposium "Quantum Theory: Advances and Problems -
QTAP", Linnaeus University, Vaxjoe (Sweden) June 10-13, 201
The Gauge Symmetry of the Third Kind and Quantum Mechanics as an Infrared Limit
We introduce functional degrees of freedom by a new gauge principle related
to the phase of the wave functional. Thus, quantum mechanical systems are
dissipatively embedded into a nonlinear classical dynamical structure. There is
a necessary fundamental length, besides an entropy/area parameter, and standard
couplings. For states that are sufficiently spread over configuration space,
quantum field theory is recovered.Comment: 7 pages. To appear in International Journal of Quantum Information.
Talk at "Advances in Foundations of Quantum Mechanics and Quantum Information
with Atoms and Photons", Torino, May 2-5, 200
Multipartite Cellular Automata and the Superposition Principle
Cellular automata can show well known features of quantum mechanics, such as
a linear updating rule that resembles a discretized form of the Schr\"odinger
equation together with its conservation laws. Surprisingly, a whole class of
"natural" Hamiltonian cellular automata, which are based entirely on
integer-valued variables and couplings and derived from an Action Principle,
can be mapped reversibly to continuum models with the help of Sampling Theory.
This results in "deformed" quantum mechanical models with a finite discreteness
scale , which for reproduce the familiar continuum limit.
Presently, we show, in particular, how such automata can form "multipartite"
systems consistently with the tensor product structures of nonrelativistic
many-body quantum mechanics, while maintaining the linearity of dynamics.
Consequently, the Superposition Principle is fully operative already on the
level of these primordial discrete deterministic automata, including the
essential quantum effects of interference and entanglement.Comment: 12 pages; accepted for publication - Int. J. Qu. Inf
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