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Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states…
We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in…
Dynamic Hubbard models have been proposed as extensions of the conventional Hubbard model to describe the orbital relaxation that occurs upon double occupancy of an atomic orbital. These models give rise to pairing of holes and…
A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent…
There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…
A computational framework is presented for the sampling of the energy surface of magnetic systems via the systematic identification of first-order saddle points that determine connectivity of metastable states and define the mechanisms of…
Localization in non-Hermitian quasicrystals can differ fundamentally from its Hermitian counterpart when non-reciprocity is spatially disordered. Here we study a one-dimensional non-Hermitian Aubry-Andr\'{e}-Harper chain with a Bernoulli…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
Mesoscale structures are an integral part of the abstraction and analysis of complex systems. They reveal a node's function in the network, and facilitate our understanding of the network dynamics. For example, they can represent…
Originating from image recognition, methods of machine learning allow for effective feature extraction and dimensionality reduction in multidimensional datasets, thereby providing an extraordinary tool to deal with classical and quantum…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model…
The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
We derive the asymptotic forms of the Green's function at the open edges of general non-Hermitian band systems in all dimensions in the long-time limit, using a modified saddle-point approximation and the analytic continuation of the…
This work presents some outcomes of a theoretical investigation of incompressible high-order networks defined by a generalized graph representation. We study some of their network topological properties and how these may be related to…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder. Here, we investigate the spreading dynamics in the archetypal non-Hermitian Aubry-Andr\'e model with…
The relationship between the quasi-exactly solvable problems and W-algebras is revealed. This relationship enabled one to formulate a new general method for building multi-dimensional and multi-channel exactly and quasi-exactly solvable…