Related papers: Cryptohermitian Hamiltonians on graphs
We consider bipartite tight-binding graphs composed by $N$ nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability…
A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For…
We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which…
A recent paper [J. Math. Phys. {\bf 59}, 082105 (2018)] constructs a Hamiltonian for the (dissipative) damped harmonic oscillator. We point out that non-Hermiticity of this Hamiltonian has been ignored to find real discrete eigenvalues…
We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
We say that a Hamilton cycle $C=(x_1,\ldots,x_n)$ in a graph $G$ is $k$-symmetric, if the mapping $x_i\mapsto x_{i+n/k}$ for all $i=1,\ldots,n$, where indices are considered modulo $n$, is an automorphism of $G$. In other words, if we lay…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral graph theory. We display results and simulations which…
Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice…
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply…
A $\mathcal{PT}$-symmetric, non-Hermitian Hamiltonian in the $\mathcal{PT}$-unbroken regime can lead to unitary dynamics under the appropriate choice of the Hilbert space. The Hilbert space is determined by a Hamiltonian-compatible inner…
We consider time periodic Hamiltonian on periodic graphs and estimate the number of its quasi-energy eigenvalues on the finite interval.
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
The determination of the quantum chromatic number of graphs has attracted considerable attention recently. However, there are few families of graphs whose quantum chromatic numbers are determined. A notable exception is the family of…