54 research outputs found
Definition and evolution of quantum cellular automata with two qubits per cell
Studies of quantum computer implementations suggest cellular quantum computer
architectures. These architectures can simulate the evolution of quantum
cellular automata, which can possibly simulate both quantum and classical
physical systems and processes. It is however known that except for the trivial
case, unitary evolution of one-dimensional homogeneous quantum cellular
automata with one qubit per cell is not possible. Quantum cellular automata
that comprise two qubits per cell are defined and their evolution is studied
using a quantum computer simulator. The evolution is unitary and its linearity
manifests itself as a periodic structure in the probability distribution
patterns.Comment: 13 pages, 4 figure
A classical explanation of quantization
In the context of our recently developed emergent quantum mechanics, and, in
particular, based on an assumed sub-quantum thermodynamics, the necessity of
energy quantization as originally postulated by Max Planck is explained by
means of purely classical physics. Moreover, under the same premises, also the
energy spectrum of the quantum mechanical harmonic oscillator is derived.
Essentially, Planck's constant h is shown to be indicative of a particle's
"zitterbewegung" and thus of a fundamental angular momentum. The latter is
identified with quantum mechanical spin, a residue of which is thus present
even in the non-relativistic Schroedinger theory.Comment: 20 pages; version accepted for publication in Foundations of Physic
An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations
A classical explanation of interference effects in the double slit experiment
is proposed. We claim that for every single "particle" a thermal context can be
defined, which reflects its embedding within boundary conditions as given by
the totality of arrangements in an experimental apparatus. To account for this
context, we introduce a "path excitation field", which derives from the
thermodynamics of the zero-point vacuum and which represents all possible paths
a "particle" can take via thermal path fluctuations. The intensity distribution
on a screen behind a double slit is calculated, as well as the corresponding
trajectories and the probability density current. The trajectories are shown to
obey a "no crossing" rule with respect to the central line, i.e., between the
two slits and orthogonal to their connecting line. This agrees with the Bohmian
interpretation, but appears here without the necessity of invoking the quantum
potential.Comment: 26 pages, 6 figures; accepted version to be published in Annals of
Physics (2012
The Quantum as an Emergent System
Double slit interference is explained with the aid of what we call
"21stcentury classical physics". We model a particle as an oscillator
("bouncer") in a thermal context, which is given by some assumed "zero-point"
field of the vacuum. In this way, the quantum is understood as an emergent
system, i.e., a steady-state system maintained by a constant throughput of
(vacuum) energy. To account for the particle's thermal environment, we
introduce a "path excitation field", which derives from the thermodynamics of
the zero-point vacuum and which represents all possible paths a particle can
take via thermal path fluctuations. The intensity distribution on a screen
behind a double slit is calculated, as well as the corresponding trajectories
and the probability density current. Further, particular features of the
relative phase are shown to be responsible for nonlocal effects not only in
ordinary quantum theory, but also in our classical approach.Comment: 24 pages, 2 figures, based on a talk given at "Emergent Quantum
Mechanics (Heinz von Foerster Conference 2011)",
http://www.univie.ac.at/hvf11/congress/EmerQuM.htm
Quantum dynamics, dissipation, and asymmetry effects in quantum dot arrays
We study the role of dissipation and structural defects on the time evolution
of quantum dot arrays with mobile charges under external driving fields. These
structures, proposed as quantum dot cellular automata, exhibit interesting
quantum dynamics which we describe in terms of equations of motion for the
density matrix. Using an open system approach, we study the role of asymmetries
and the microscopic electron-phonon interaction on the general dynamical
behavior of the charge distribution (polarization) of such systems. We find
that the system response to the driving field is improved at low temperatures
(and/or weak phonon coupling), before deteriorating as temperature and
asymmetry increase. In addition to the study of the time evolution of
polarization, we explore the linear entropy of the system in order to gain
further insights into the competition between coherent evolution and
dissipative processes.Comment: 11pages,9 figures(eps), submitted to PR
Thermodynamic Gravity and the Schrodinger Equation
We adopt a 'thermodynamical' formulation of Mach's principle that the rest
mass of a particle in the Universe is a measure of its long-range collective
interactions with all other particles inside the horizon. We consider all
particles in the Universe as a 'gravitationally entangled' statistical ensemble
and apply the approach of classical statistical mechanics to it. It is shown
that both the Schrodinger equation and the Planck constant can be derived
within this Machian model of the universe. The appearance of probabilities,
complex wave functions, and quantization conditions is related to the
discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy
Quantum mechanics of lattice gas automata. I. One particle plane waves and potentials
Classical lattice gas automata effectively simulate physical processes such
as diffusion and fluid flow (in certain parameter regimes) despite their
simplicity at the microscale. Motivated by current interest in quantum
computation we recently defined quantum lattice gas automata; in this paper we
initiate a project to analyze which physical processes these models can
effectively simulate. Studying the single particle sector of a one dimensional
quantum lattice gas we find discrete analogues of plane waves and wave packets,
and then investigate their behaviour in the presence of inhomogeneous
potentials.Comment: 19 pages, plain TeX, 14 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages), two additional large
figures available upon reques
Single atom quantum walk with 1D optical superlattices
A proposal for the implementation of quantum walks using cold atom technology
is presented. It consists of one atom trapped in time varying optical
superlattices. The required elements are presented in detail including the
preparation procedure, the manipulation required for the quantum walk evolution
and the final measurement. These procedures can be, in principle, implemented
with present technology.Comment: 6 pages, 7 figure
From quantum cellular automata to quantum lattice gases
A natural architecture for nanoscale quantum computation is that of a quantum
cellular automaton. Motivated by this observation, in this paper we begin an
investigation of exactly unitary cellular automata. After proving that there
can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in
one dimension, we weaken the homogeneity condition and show that there are
nontrivial, exactly unitary, partitioning cellular automata. We find a one
parameter family of evolution rules which are best interpreted as those for a
one particle quantum automaton. This model is naturally reformulated as a two
component cellular automaton which we demonstrate to limit to the Dirac
equation. We describe two generalizations of this automaton, the second of
which, to multiple interacting particles, is the correct definition of a
quantum lattice gas.Comment: 22 pages, plain TeX, 9 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages); minor typographical
corrections and journal reference adde
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