54 research outputs found
Thermodynamics of N-dimensional quantum walks
The entanglement between the position and coin state of a -dimensional
quantum walker is shown to lead to a thermodynamic theory. The entropy, in this
thermodynamics, is associated to the reduced density operator for the evolution
of chirality, taking a partial trace over positions. From the asymptotic
reduced density matrix it is possible to define thermodynamic quantities, such
as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc.
We study in detail the case of a -dimensional quantum walk, in the case of
two different initial conditions: a non-separable coin-position initial state,
and a separable one. The resulting entanglement temperature is presented as
function of the parameters of the system and those of the initial conditions.Comment: 10 pages, 4 fig
Modelling an Imperfect Market
We propose a simple market model where agents trade different types of
products with each other by using money, relying only on local information.
Value fluctuations of single products, combined with the condition of maximum
profit in transactions, readily lead to persistent fluctuations in the wealth
of individual agents.Comment: 12 pages RevTeX and 5 Postscript figure
Directed cycles and related structures in random graphs: II--Dynamic properties
We study directed random graphs (random graphs whose edges are directed) as
they evolve in discrete time by the addition of nodes and edges. For two
distinct evolution strategies, one that forces the graph to a condition of near
acyclicity at all times and another that allows the appearance of nontrivial
directed cycles, we provide analytic and simulation results related to the
distributions of degrees. Within the latter strategy, in particular, we
investigate the appearance and behavior of the strong components that were our
subject in the first part of this study.Comment: submitted to Physica
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