2,508 research outputs found

### Communication Complexity Protocol for Q-trits

Consider a function where its entries are distributed among many parties.
Suppose each party is allowed to transmit only a limited amount of information
to a net. One can use a classical protocol to guess the value of the global
function. Is there a quantum protocol improving the results of all classical
protocols? Brukner et. al. showed the deep connection between such problems and
the theory of Bell's inequalities. Here we generalize the theory to trits.
There the best classical protocol fails whereas the quantum protocol yields the
correct answer.Comment: 8 page

### Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning

We show that linear congruential pseudo-random-number generators can cause
systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm,
if the lattice size is a multiple of a very large power of 2 and one random
number is used per bond. These systematic errors arise from correlations within
a single bond-update half-sweep. The errors can be eliminated (or at least
radically reduced) by updating the bonds in a random order or in an aperiodic
manner. It also helps to use a generator of large modulus (e.g. 60 or more
bits).Comment: Revtex4, 4 page

### A Spinorial Formulation of the Maximum Clique Problem of a Graph

We present a new formulation of the maximum clique problem of a graph in
complex space. We start observing that the adjacency matrix A of a graph can
always be written in the form A = B B where B is a complex, symmetric matrix
formed by vectors of zero length (null vectors) and the maximum clique problem
can be transformed in a geometrical problem for these vectors. This problem, in
turn, is translated in spinorial language and we show that each graph uniquely
identifies a set of pure spinors, that is vectors of the endomorphism space of
Clifford algebras, and the maximum clique problem is formalized in this setting
so that, this much studied problem, may take advantage from recent progresses
of pure spinor geometry

### Anomalous diffusion at percolation threshold in high dimensions on 10^18 sites

Using an inverse of the standard linear congruential random number generator,
large randomly occupied lattices can be visited by a random walker without
having to determine the occupation status of every lattice site in advance. In
seven dimensions, at the percolation threshold with L^7 sites and L < 420, we
confirm the expected time-dependence of the end-to-end distance (including the
corrections to the asymptotic behavior).Comment: 8 pages including figures, presentation improved, for
Int.J.Mod.Phys.

### Molecular dynamics simulations of ballistic annihilation

Using event-driven molecular dynamics we study one- and two-dimensional
ballistic annihilation. We estimate exponents $\xi$ and $\gamma$ that describe
the long-time decay of the number of particles ($n(t)\sim t^{-\xi}$) and of
their typical velocity ($v(t)\sim t^{-\gamma}$). To a good accuracy our results
confirm the scaling relation $\xi + \gamma =1$. In the two-dimensional case our
results are in a good agreement with those obtained from the Boltzmann kinetic
theory.Comment: 4 pages; some changes; Physical Review E (in press

### Complementary algorithms for graphs and percolation

A pair of complementary algorithms are presented. One of the pair is a fast
method for connecting graphs with an edge. The other is a fast method for
removing edges from a graph. Both algorithms employ the same tree based graph
representation and so, in concert, can arbitrarily modify any graph. Since the
clusters of a percolation model may be described as simple connected graphs, an
efficient Monte Carlo scheme can be constructed that uses the algorithms to
sweep the occupation probability back and forth between two turning points.
This approach concentrates computational sampling time within a region of
interest. A high precision value of pc = 0.59274603(9) was thus obtained, by
Mersenne twister, for the two dimensional square site percolation threshold.Comment: 5 pages, 3 figures, poster version presented at statphys23 (2007

### Information-Based Physics: An Observer-Centric Foundation

It is generally believed that physical laws, reflecting an inherent order in
the universe, are ordained by nature. However, in modern physics the observer
plays a central role raising questions about how an observer-centric physics
can result in laws apparently worthy of a universal nature-centric physics.
Over the last decade, we have found that the consistent apt quantification of
algebraic and order-theoretic structures results in calculi that possess
constraint equations taking the form of what are often considered to be
physical laws. I review recent derivations of the formal relations among
relevant variables central to special relativity, probability theory and
quantum mechanics in this context by considering a problem where two observers
form consistent descriptions of and make optimal inferences about a free
particle that simply influences them. I show that this approach to describing
such a particle based only on available information leads to the mathematics of
relativistic quantum mechanics as well as a description of a free particle that
reproduces many of the basic properties of a fermion. The result is an approach
to foundational physics where laws derive from both consistent descriptions and
optimal information-based inferences made by embedded observers.Comment: To be published in Contemporary Physics. The manuscript consists of
43 pages and 9 Figure

### A Formal Definition of SOL

This paper gives a formal definition of SOL, a general-purpose algorithmic language useful for describing and simulating complex systems. SOL is described using meta-linguistic formulas as used in the definition of ALGOL 60. The principal differences between SOL and problem-oriented languages such as ALGOL or FORTRAN is that SOL includes capabilities for expressing parallel computation, convenient notations for embedding random quantities within arithmetic expressions and automatic means for gathering statistics about the elements involved. SOL differs from other simulation languages such as SIMSCRIPT primarily in simplicity of use and in readability since it is capable of describing models without including computer-oriented characteristics

### The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study

The one dimensional Bose-Hubbard model at a unit filling factor is studied by
means of a very high order symbolic perturbative expansion. Analytical
expressions are derived for the ground state quantities such as energy per
site, variance of on-site occupation, and different correlation functions.
These findings are compared to numerics and good agreement is found in the Mott
insulator phase. Our results provide analytical approximations to important
observables in the Mott phase, and are also of direct relevance to future
experiments with ultra cold atomic gases placed in optical lattices. We also
discuss the symmetry of the Bose-Hubbard model associated with the sign change
of the tunneling coupling.Comment: 7 pages, 4 figures, 1 table. Significantly expanded version with
respect to former submission (to appear in Phys. Rev. A

### SOL - A Symbolic Language for General-Purpose Systems Simulation

This paper illustrates the use of SOL, a general-purpose algorithmic language useful for describing and simulating complex systems. Such a system is described as a number of individual processes which simultaneously enact a program very much like a computer program. (Some features of the SOL language are directly applicable to programming languages for parallel computers, as well as for simulation.) Once a system has been described in the language, the program can be translated by the SOL compiler into an interpretive code, and the execution of this code produces statistical information about the model. A detailed example of a SOL model for a multiple on-line console system is exhibited, indicating the notational simplicity and intuitive nature of the language

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