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Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a…
We analytically derive the general pseudo-potential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems, using the frame work developed by Huang and Yang for 3D scattering. We also…
We scrutinize the real-frequency structure of the self-energy in the superconducting state of the attractive Hubbard model within the dynamical mean-field theory. Within the strong-coupling superconducting phase which has been understood in…
Low-lying baryon resonances have been explored using Hamiltonian Effective Field Theory (HEFT), in a formalism where resonances with a three-quark component are described by both two-particle meson-baryon states and a bare basis state.…
The conventional technique for solving the equations of quantum chemistry (of solid state) is extended unconventionally to the structures possessing certain symmetries. This proposal concerns changing the way for selection of occupied…
We define a set of pseudo-observables characterizing the properties of Higgs decays in generic extensions of the Standard Model with no new particles below the Higgs mass. The pseudo-observables can be determined from experimental data,…
This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate…
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…
We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum - horizonless - black hole…
Pseudogap formation is an ubiquitous phenomena in strongly-correlated superconductors, for example cuprates, heavy-fermion superconductors, and iron pnictides. As the system is cooled, an energy gap opens in the excitation spectrum before…
First-principles calculations rely heavily on pseudopotentials, yet their impact on accuracy is hardly addressed. In this work, we show that most pseudopotentials to date introduce errors, which manifest themselves as errors of atomic…
In conventional superconductors, a gap exists in the energy absorption spectrum only below the transition temperature (Tc), corresponding to the energy price to pay for breaking a Cooper pair of electrons. In high-Tc cuprate superconductors…
For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct…
We examine and explain the Luttinger-liquid character of models solvable by the Bethe ansatz by introducing a suitable bosonic operator algebra. In the case of the Hubbard chain, this involves two bosonic algebras which apply to {\it all}…
We introduce the concept of pseudo-reality for complex numbers. We show that this concept, applied to quantum fields, provides a unifying framework for two distinct approaches to pseudo-Hermitian quantum field theories. The first approach…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
Recently some authors have broadened the scope of canonical quantum mechanics by replacing the conventional Hermiticity condition on the Hamiltonian by a weaker requirement through the introduction of the notion of pseudo-Hermiticity. In…
The representation of the Hubbard operators in terms of the spin$-\frac{1}{2}$ operators and the fermion operator with spin$-\frac{1}{2}$ is proposed. In the low-energy limit this representation is reduced to the representation following…
A family of orthonormal bases, the ultrametric wavelet bases, is introduced in quadratically integrable complex valued functions spaces for a wide family of ultrametric spaces. A general family of pseudodifferential operators, acting on…
We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain…