9,544 research outputs found
Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases
We study the structure of Fermionic networks, i.e., a model of networks based
on the behavior of fermionic gases, and we analyze dynamical processes over
them. In this model, particle dynamics have been mapped to the domain of
networks, hence a parameter representing the temperature controls the evolution
of the system. In doing so, it is possible to generate adaptive networks, i.e.,
networks whose structure varies over time. As shown in previous works, networks
generated by quantum statistics can undergo critical phenomena as phase
transitions and, moreover, they can be considered as thermodynamic systems. In
this study, we analyze Fermionic networks and opinion dynamics processes over
them, framing this network model as a computational model useful to represent
complex and adaptive systems. Results highlight that a strong relation holds
between the gas temperature and the structure of the achieved networks.
Notably, both the degree distribution and the assortativity vary as the
temperature varies, hence we can state that fermionic networks behave as
adaptive networks. On the other hand, it is worth to highlight that we did not
find relation between outcomes of opinion dynamics processes and the gas
temperature. Therefore, although the latter plays a fundamental role in gas
dynamics, on the network domain its importance is related only to structural
properties of fermionic networks.Comment: 19 pages, 5 figure
Ring Exchange and Phase Separation in the Two-dimensional Boson Hubbard model
We present Quantum Monte Carlo simulations of the soft-core bosonic Hubbard
model with a ring exchange term K. For values of K which exceed roughly half
the on-site repulsion U, the density is a non-monotonic function of the
chemical potential, indicating that the system has a tendency to phase
separate. This behavior is confirmed by an examination of the density-density
structure factor and real space images of the boson configurations. Adding a
near-neighbor repulsion can compete with phase separation, but still does not
give rise to a stable normal Bose liquid.Comment: 12 pages, 23 figure
Gaussian Networks Generated by Random Walks
We propose a random walks based model to generate complex networks. Many
authors studied and developed different methods and tools to analyze complex
networks by random walk processes. Just to cite a few, random walks have been
adopted to perform community detection, exploration tasks and to study temporal
networks. Moreover, they have been used also to generate scale-free networks.
In this work, we define a random walker that plays the role of
"edges-generator". In particular, the random walker generates new connections
and uses these ones to visit each node of a network. As result, the proposed
model allows to achieve networks provided with a Gaussian degree distribution,
and moreover, some features as the clustering coefficient and the assortativity
show a critical behavior. Finally, we performed numerical simulations to study
the behavior and the properties of the cited model.Comment: 12 pages, 6 figure
Unsupervised landmark analysis for jump detection in molecular dynamics simulations
Molecular dynamics is a versatile and powerful method to study diffusion in
solid-state ionic conductors, requiring minimal prior knowledge of equilibrium
or transition states of the system's free energy surface. However, the analysis
of trajectories for relevant but rare events, such as a jump of the diffusing
mobile ion, is still rather cumbersome, requiring prior knowledge of the
diffusive process in order to get meaningful results. In this work, we present
a novel approach to detect the relevant events in a diffusive system without
assuming prior information regarding the underlying process. We start from a
projection of the atomic coordinates into a landmark basis to identify the
dominant features in a mobile ion's environment. Subsequent clustering in
landmark space enables a discretization of any trajectory into a sequence of
distinct states. As a final step, the use of the smooth overlap of atomic
positions descriptor allows distinguishing between different environments in a
straightforward way. We apply this algorithm to ten Li-ionic systems and
conduct in-depth analyses of cubic LiLaZrO, tetragonal
LiGePS, and the -eucryptite LiAlSiO. We
compare our results to existing methods, underscoring strong points,
weaknesses, and insights into the diffusive behavior of the ionic conduction in
the materials investigated
Clustering and the Three-Point Function
We develop analytical methods for computing the structure constant for three
heavy operators, starting from the recently proposed hexagon approach. Such a
structure constant is a semiclassical object, with the scale set by the inverse
length of the operators playing the role of the Planck constant. We reformulate
the hexagon expansion in terms of multiple contour integrals and recast it as a
sum over clusters generated by the residues of the measure of integration. We
test the method on two examples. First, we compute the asymptotic three-point
function of heavy fields at any coupling and show the result in the
semiclassical limit matches both the string theory computation at strong
coupling and the tree-level results obtained before. Second, in the case of one
non-BPS and two BPS operators at strong coupling we sum up all wrapping
corrections associated with the opposite bridge to the non-trivial operator, or
the "bottom" mirror channel. We also give an alternative interpretation of the
results in terms of a gas of fermions and show that they can be expressed
compactly as an operator-valued super-determinant.Comment: 52 pages + a few appendices; v2 typos correcte
Clustering of exceptional points and dynamical phase transitions
The eigenvalues of a non-Hermitian Hamilton operator are complex and provide
not only the energies but also the lifetimes of the states of the system. They
show a non-analytical behavior at singular (exceptional) points (EPs). The
eigenfunctions are biorthogonal, in contrast to the orthogonal eigenfunctions
of a Hermitian operator. A quantitative measure for the ratio between
biorthogonality and orthogonality is the phase rigidity of the wavefunctions.
At and near an EP, the phase rigidity takes its minimum value. The lifetimes of
two nearby eigenstates of a quantum system bifurcate under the influence of an
EP. When the parameters are tuned to the point of maximum width bifurcation,
the phase rigidity suddenly increases up to its maximum value. This means that
the eigenfunctions become almost orthogonal at this point. This unexpected
result is very robust as shown by numerical results for different classes of
systems. Physically, it causes an irreversible stabilization of the system by
creating local structures that can be described well by a Hermitian Hamilton
operator. Interesting non-trivial features of open quantum systems appear in
the parameter range in which a clustering of EPs causes a dynamical phase
transition.Comment: A few improvements; 2 references added; 28 pages; 7 figure
Simulating and detecting artificial magnetic fields in trapped atoms
A Bose-Einstein condensate exhibiting a nontrivial phase induces an
artificial magnetic field in immersed impurity atoms trapped in a stationary,
ring-shaped optical lattice. We present an effective Hamiltonian for the
impurities for two condensate setups: the condensate in a rotating ring and in
an excited rotational state in a stationary ring. We use Bogoliubov theory to
derive analytical formulas for the induced artificial magnetic field and the
hopping amplitude in the limit of low condensate temperature where the impurity
dynamics is coherent. As methods for observing the artificial magnetic field we
discuss time of flight imaging and mass current measurements. Moreover, we
compare the analytical results of the effective model to numerical results of a
corresponding two-species Bose-Hubbard model. We also study numerically the
clustering properties of the impurities and the quantum chaotic behavior of the
two-species Bose-Hubbard model.Comment: 14 pages, 9 figures. Published versio
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