849 research outputs found
Quantum phase transitions and quantum fidelity in free fermion graphs
In this paper we analyze the ground state phase diagram of a class of
fermionic Hamiltonians by looking at the fidelity of ground states
corresponding to slightly different Hamiltonian parameters. The Hamiltonians
under investigation can be considered as the variable range generalization of
the fermionic Hamiltonian obtained by the Jordan-Wigner transformation of the
XY spin-chain in a transverse magnetic field. Under periodic boundary
conditions, the matrices of the problem become circulant and the models are
exactly solvable. Their free-ends counterparts are instead analyzed
numerically. In particular, we focus on the long range model corresponding to a
fully connected directed graph, providing asymptotic results in the
thermodynamic limit, as well as the finite-size scaling analysis of the second
order quantum phase transitions of the system. A strict relation between
fidelity and single particle spectrum is demonstrated, and a peculiar gapful
transition due to the long range nature of the coupling is found. A comparison
between fidelity and another transition marker borrowed from quantum
information i.e., single site entanglement, is also considered.Comment: 14 pages, 5 figure
Bipartite quantum states and random complex networks
We introduce a mapping between graphs and pure quantum bipartite states and
show that the associated entanglement entropy conveys non-trivial information
about the structure of the graph. Our primary goal is to investigate the family
of random graphs known as complex networks. In the case of classical random
graphs we derive an analytic expression for the averaged entanglement entropy
while for general complex networks we rely on numerics. For large
number of nodes we find a scaling where both
the prefactor and the sub-leading O(1) term are a characteristic of
the different classes of complex networks. In particular, encodes
topological features of the graphs and is named network topological entropy.
Our results suggest that quantum entanglement may provide a powerful tool in
the analysis of large complex networks with non-trivial topological properties.Comment: 4 pages, 3 figure
Religious diversity and inter-faith competition: the politics of camouflage in Italian cities
Is minimising the convergence rate the best choice for efficient Optimized Schwarz preconditioning in heterogeneous coupling? The Stokes-Darcy case
Optimized Schwarz Methods (OSM) are domain decomposition techniques based on Robin-type interface condition that have became increasingly popular in the last two decades. Ensuring convergence also on non-overlapping decompositions, OSM are naturally advocated for the heterogeneous coupling of multi-physics problems. Classical approaches optimize the coefficients in the Robin condition by minimizing the effective convergence rate of the resulting iterative algorithm. However, when OSM are used as preconditioners for Krylov solvers of the resulting interface problem, such parameter optimization does not necessarily guarantee the fastest convergence. This drawback is already known for homogeneous decomposition, but in the case of heterogeneous decomposition, the poor performance of the classical optimization approach becomes utterly evident. In this paper, we highlight this drawback for the Stokes/Darcy problem and we propose a more effective alternative optimization procedure.European Union Seventh Framework Programme (FP7/2007-2013; grant 294229) to M. Discacciat
Optimized Schwarz Methods in the Stokes-Darcy Coupling
This article studies optimized Schwarz methods for the Stokes–Darcy problem. Robin transmission conditions are introduced, and the coupled problem is reduced to a suitable interface system that can be solved using Krylov methods. Practical strategies to compute optimal Robin coefficients are proposed, which take into account both the physical parameters of the problem and the mesh size. Numerical results show the effectiveness of our approach.European Union Seventh Framework Programme (FP7/2007-2013; grant 294229) to M. Discacciat
Optimized schwarz methods for the bidomain system in electrocardiology
The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in accelerating the convergence of such algorithms. The latter are based on interface matching conditions more efficient than the classical Dirichlet or Neumann ones. In this paper we analyze an Optimized Schwarz approach for the numerical solution of the Bidomain problem. We assess the convergence of the iterative method by means of Fourier analysis, and we investigate the parameter optimization in the interface conditions. Numerical results in 2D and 3D are given to show the effectiveness of the method
Bures metric over thermal state manifolds and quantum criticality
We analyze the Bures metric over the manifold of thermal density matrices for
systems featuring a zero temperature quantum phase transition. We show that the
quantum critical region can be characterized in terms of the temperature
scaling behavior of the metric tensor itself. Furthermore, the analysis of the
metric tensor when both temperature and an external field are varied, allows to
complement the understanding of the phase diagram including cross-over regions
which are not characterized by any singular behavior. These results provide a
further extension of the scope of the metric approach to quantum criticality.Comment: 9 pages, 4 figures, LaTeX problems fixed, references adde
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