5,826 research outputs found
Foundations for a theory of emergent quantum mechanics and emergent classical gravity
Quantum systems are viewed as emergent systems from the fundamental degrees
of freedom. The laws and rules of quantum mechanics are understood as an
effective description, valid for the emergent systems and specially useful to
handle probabilistic predictions of observables. After introducing the
geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert
space theory, a Hilbert space structure is constructed from the Hilbert space
formulation of the underlying Hamilton-Randers model and associated with the
space of wave functions of quantum mechanical systems. We can prove the
emergence of the Born rule from ergodic considerations. A geometric mechanism
for a natural spontaneous collapse of the quantum states based on the
concentration of measure phenomena as it appears in metric geometry is
discussed.We show the existence of stable vacua states for the quantized matter
Hamiltonian. Another consequence of the concentration of measure is the
emergence of a weak equivalence principle for one of the dynamics of the
fundamental degrees of freedom. We suggest that the reduction of the quantum
state is driven by a gravitational type interaction.
Such interaction appears only in the dynamical domain when localization of
quantum observables happens, it must be a classical interaction. We discuss the
double slit experiment in the context of the framework proposed, the
interference phenomena associated with a quantum system in an external
gravitational potential, a mechanism explaining non-quantum locality and also
provide an argument in favour of an emergent interpretation of every
macroscopic time parameter. Entanglement is partially described in the context
of Hamilton-Randers theory and how naturally Bell's inequalities should be
violated.Comment: Extensive changes in chapter 1 and chapter 2; minor changes in other
chapters; several refereces added and others update; 192 pages including
index of contents and reference
Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers
Quantum computers are important examples of processes whose evolution can be
described in terms of iterations of single step operators or their adjoints.
Based on this, Hamiltonian evolution of processes with associated step
operators is investigated here. The main limitation of this paper is to
processes which evolve quantum ballistically, i.e. motion restricted to a
collection of nonintersecting or distinct paths on an arbitrary basis. The main
goal of this paper is proof of a theorem which gives necessary and sufficient
conditions that T must satisfy so that there exists a Hamiltonian description
of quantum ballistic evolution for the process, namely, that T is a partial
isometry and is orthogonality preserving and stable on some basis. Simple
examples of quantum ballistic evolution for quantum Turing machines with one
and with more than one type of elementary step are discussed. It is seen that
for nondeterministic machines the basis set can be quite complex with much
entanglement present. It is also proved that, given a step operator T for an
arbitrary deterministic quantum Turing machine, it is decidable if T is stable
and orthogonality preserving, and if quantum ballistic evolution is possible.
The proof fails if T is a step operator for a nondeterministic machine. It is
an open question if such a decision procedure exists for nondeterministic
machines. This problem does not occur in classical mechanics.Comment: 37 pages Latexwith 2 postscript figures tar+gzip+uuencoded, to be
published in Phys. Rev.
Gibbs distributions for random partitions generated by a fragmentation process
In this paper we study random partitions of 1,...n, where every cluster of
size j can be in any of w\_j possible internal states. The Gibbs (n,k,w)
distribution is obtained by sampling uniformly among such partitions with k
clusters. We provide conditions on the weight sequence w allowing construction
of a partition valued random process where at step k the state has the Gibbs
(n,k,w) distribution, so the partition is subject to irreversible fragmentation
as time evolves. For a particular one-parameter family of weight sequences
w\_j, the time-reversed process is the discrete Marcus-Lushnikov coalescent
process with affine collision rate K\_{i,j}=a+b(i+j) for some real numbers a
and b. Under further restrictions on a and b, the fragmentation process can be
realized by conditioning a Galton-Watson tree with suitable offspring
distribution to have n nodes, and cutting the edges of this tree by random
sampling of edges without replacement, to partition the tree into a collection
of subtrees. Suitable offspring distributions include the binomial, negative
binomial and Poisson distributions.Comment: 38 pages, 2 figures, version considerably modified. To appear in the
Journal of Statistical Physic
The Nonequilibrium Thermodynamics of Small Systems
The interactions of tiny objects with their environment are dominated by
thermal fluctuations. Guided by theory and assisted by micromanipulation tools,
scientists have begun to study such interactions in detail.Comment: PDF file, 13 pages. Long version of the paper published in Physics
Toda
Computational universes
Suspicions that the world might be some sort of a machine or algorithm
existing ``in the mind'' of some symbolic number cruncher have lingered from
antiquity. Although popular at times, the most radical forms of this idea never
reached mainstream. Modern developments in physics and computer science have
lent support to the thesis, but empirical evidence is needed before it can
begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio
Computation and construction universality of reversible cellular automata
An arbitrary d-dimensional cellular automaton can be constructively embedded in areversible one having d+1 dimensions. In particular, there exist computation- and construction-universal reversible cellular automata. Thus, we explicitly show a way of implementing nontrivial irreversible processes in a reversible medium. Finally, we derive new results for the bounding problem for configurations, both in general and for reversible cellular automata
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