Related papers: Quantum-Classical Transitions in Complex Networks
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,…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, non-interacting theories display a rich landscape of…
Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We introduce superposition-based quantum networks composed of (i) the classical perceptron model of multilayered, feedforward neural networks and (ii) the algebraic model of evolving reticular quantum structures as described in quantum…
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…
We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations…
Crystals arise as the result of the breaking of a spatial translation symmetry. Similarly, translation symmetries can also be broken in time so that discrete time crystals appear. Here, we introduce a method to describe, characterize, and…
In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…