2,537 research outputs found
Negative Interactions in Irreversible Self-Assembly
This paper explores the use of negative (i.e., repulsive) interaction the
abstract Tile Assembly Model defined by Winfree. Winfree postulated negative
interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu,
and Yin explored their power in the context of reversible attachment
operations. We explore the power of negative interactions with irreversible
attachments, and we achieve two main results. Our first result is an
impossibility theorem: after t steps of assembly, Omega(t) tiles will be
forever bound to an assembly, unable to detach. Thus negative glue strengths do
not afford unlimited power to reuse tiles. Our second result is a positive one:
we construct a set of tiles that can simulate a Turing machine with space bound
s and time bound t, while ensuring that no intermediate assembly grows larger
than O(s), rather than O(s * t) as required by the standard Turing machine
simulation with tiles
Noninteracting Fermions in infinite dimensions
Usually, we study the statistical behaviours of noninteracting Fermions in
finite (mainly two and three) dimensions. For a fixed number of fermions, the
average energy per fermion is calculated in two and in three dimensions and it
becomes equal to 50 and 60 per cent of the fermi energy respectively. However,
in the higher dimensions this percentage increases as the dimensionality
increases and in infinite dimensions it becomes 100 per cent. This is an
intersting result, at least pedagogically. Which implies all fermions are
moving with Fermi momentum. This result is not yet discussed in standard text
books of quantum statistics. In this paper, this fact is discussed and
explained. I hope, this article will be helpful for graduate students to study
the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010
Discontinuous percolation transitions in real physical systems
We study discontinuous percolation transitions (PT) in the diffusion-limited
cluster aggregation model of the sol-gel transition as an example of real
physical systems, in which the number of aggregation events is regarded as the
number of bonds occupied in the system. When particles are Brownian, in which
cluster velocity depends on cluster size as with
, a larger cluster has less probability to collide with other
clusters because of its smaller mobility. Thus, the cluster is effectively more
suppressed in growth of its size. Then the giant cluster size increases
drastically by merging those suppressed clusters near the percolation
threshold, exhibiting a discontinuous PT. We also study the tricritical
behavior by controlling the parameter , and the tricritical point is
determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure
BLITZEN: A highly integrated massively parallel machine
The architecture and VLSI design of a new massively parallel processing array chip are described. The BLITZEN processing element array chip, which contains 1.1 million transistors, serves as the basis for a highly integrated, miniaturized, high-performance, massively parallel machine that is currently under development. Each processing element has 1K bits of static RAM and performs bit-serial processing with functional elements for arithmetic, logic, and shifting
Phase transition from quark-meson coupling hyperonic matter to deconfined quark matter
We investigate the possibility and consequences of phase transitions from an
equation of state (EOS) describing nucleons and hyperons interacting via mean
fields of sigma, omega, and rho mesons in the recently improved quark-meson
coupling (QMC) model to an EOS describing a Fermi gas of quarks in an MIT bag.
The transition to a mixed phase of baryons and deconfined quarks, and
subsequently to a pure deconfined quark phase, is described using the method of
Glendenning. The overall EOS for the three phases is calculated for various
scenarios and used to calculate stellar solutions using the
Tolman-Oppenheimer-Volkoff equations. The results are compared with recent
experimental data, and the validity of each case is discussed with consequences
for determining the species content of the interior of neutron stars.Comment: 12 pages, 14 figures; minor typos correcte
Nonzero orbital angular momentum superfluidity in ultracold Fermi gases
We analyze the evolution of superfluidity for nonzero orbital angular
momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein
condensation (BEC) limit in three dimensions. First, we analyze the low energy
scattering properties of finite range interactions for all possible angular
momentum channels. Second, we discuss ground state () superfluid
properties including the order parameter, chemical potential, quasiparticle
excitation spectrum, momentum distribution, atomic compressibility, ground
state energy and low energy collective excitations. We show that a quantum
phase transition occurs for nonzero angular momentum pairing, unlike the s-wave
case where the BCS to BEC evolution is just a crossover. Third, we present a
gaussian fluctuation theory near the critical temperature (),
and we analyze the number of bound, scattering and unbound fermions as well as
the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau
functional near , and compare the Ginzburg-Landau coherence length
with the zero temperature average Cooper pair size.Comment: 28 pages and 24 figure
Energy distribution and cooling of a single atom in an optical tweezer
We investigate experimentally the energy distribution of a single rubidium
atom trapped in a strongly focused dipole trap under various cooling regimes.
Using two different methods to measure the mean energy of the atom, we show
that the energy distribution of the radiatively cooled atom is close to
thermal. We then demonstrate how to reduce the energy of the single atom, first
by adiabatic cooling, and then by truncating the Boltzmann distribution of the
single atom. This provides a non-deterministic way to prepare atoms at low
microKelvin temperatures, close to the ground state of the trapping potential.Comment: 9 pages, 6 figures, published in PR
Analog approach for the eigen-decomposition of positive definite matrices
AbstractThis paper proposes an analog approach for performing the eigen-decomposition of positive definite matrices. We show analytically and by simulations that the proposed circuit is guaranteed to converge to the desired eigenvectors and eigenvalues of positive definite matrices
Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach
We study the effects of dissipation and decoherence induced on a harmonic
oscillator by the coupling to a chaotic system with two degrees of freedom.
Using the Feynman-Vernon approach and treating the chaotic system
semiclassically we show that the effects of the low dimensional chaotic
environment are in many ways similar to those produced by thermal baths. The
classical correlation and response functions play important roles in both
classical and quantum formulations. Our results are qualitatively similar to
the high temperature regime of the Caldeira-Leggett model.Comment: 31 pages, 4 figure
Complete analysis of phase transitions and ensemble equivalence for the Curie-Weiss-Potts model
Using the theory of large deviations, we analyze the phase transition structure of the Curie–Weiss–Potts spin model, which is a mean-field approximation to the nearest-neighbor Potts model. It is equivalent to the Potts model on the complete graph on n vertices. The analysis is carried out both for the canonical ensemble and the microcanonical ensemble. Besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles, we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates, relating these to concavity and support properties of the microcanonical entropy. The Curie–Weiss–Potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out
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