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We provide a link between the virial theorem in functional analysis and the method of multipliers in theory of partial differential equations. After giving a physical insight into the techniques, we show how to use them to deduce the…
Identifying the nature of interactions in a quantum system is essential in understanding any physical phenomena. Acquiring information on the Hamiltonian can be a tough challenge in many-body systems because it generally requires access to…
We reveal a novel topological property of the exceptional points in a two-level parity-time symmetric system and then propose a scheme to detect the topological exceptional points in the system, which is embedded in a larger Hilbert space…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We study the entanglement Hamiltonian of two disjoint blocks in the harmonic chain on the line and in its ground state. In the regime of large mass, the non vanishing terms are only the on-site and the nearest-neighbour ones. Analytic…
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
We examine a class of Hamiltonians characterized by interatomic, interorbital even-odd parity hybridization as a model for a family of topological insulators without the need for spin-orbit coupling. Non-trivial properties of these…
This paper discusses some features of the spectral line profile theory used in the treatment of measured atomic transitions. It is shown that going beyond the established linear approximation for the spectral line contour in the case of its…
We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value…
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their…
Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on…
The emerging field of ultracold molecules with their rich internal structure is currently attracting a lot of interest. Various methods have been developed to produce ultracold molecules in pre-set quantum states. For future experiments it…
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…
A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results…
In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites $i$ and $j$ may…
A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy…
The eigenspectrum of a non-normal matrix, which does not commute with its Hermitian conjugate, is a central issue of non-Hermitian physics that has been extensively studied in the past few years. There is, however, another characteristic of…
Avoided crossings are fundamental phenomena in quantum mechanics and photonics that originate from the interaction between coupled energy levels and have been extensively studied in linear dispersive dynamics. Their manifestation in open,…
Duality relations are explicitly established relating the Hamiltonians and basis classification schemes associated with the number-conserving unitary and number-nonconserving quasispin algebras for the two-level system with pairing…