Related papers: Network Models: Action formulation
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
A new formulation of four dimensional quantum field theories, such as scalar field theory, is proposed as a large N limit of a special NxN matrix model. Our reduction scheme works beyond planar approximation and applies for QFT with finite…
Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit,…
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…
Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of…
Using geometric approach we formulate quantum theory in terms of Jordan algebras. We analyze the notion of (quasi)particle (=elementary excitation of translation-invariant stationary state) and the scattering of (quasi)particles in this…
Distributed quantum networks will allow users to perform tasks and to interact in ways which are not possible with present-day technology. Their implementation is a key challenge for quantum science and requires the development of…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
The behaviour of electrical networks can be described with many different representations, each with their distinct benefits. In this paper, we consider Z, Y, G, H, ABCD, S and T parameters. Formulas exist to go from one representation to…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
The embedding method for the calculation of the conductance through interacting systems connected to single channel leads is generalized to obtain the full complex transmission amplitude that completely characterizes the effective…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…