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We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space,…
We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix…
Pseudoentangled states are defined by their ability to hide their entanglement structure: they are indistinguishable from random states to any observer with polynomial resources, yet can have much less entanglement than random states.…
A variety of physical phenomena, such as amplification, absorption, and radiation, can be effectively described using non-Hermitian operators. However, the introduction of non-uniform non-Hermiticity can lead to the formation of exceptional…
Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…
In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from…
Quasinormal modes and frequencies are the eigenvectors and eigenvalues of a non-Hermitian differential operator. They hold crucial significance in the physics of black holes. The analysis of quasinormal modes of black holes in…
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have…
The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian…
The collective spin and charge excitations of doped cuprates and their relationship to superconductivity are not yet fully understood, particularly in the case of the charge excitations. Here, we study the doping-dependent dynamical spin…
In this paper we formulate our results on the essential spectrum of many-particle pseudorelativistic Hamiltonians without magnetic and external potential fields in the spaces of functions, having arbitrary type $\alpha$ of the permutational…
The hidden Bose-Einstein singularities of correlated electron systems, whose possible existence has been pointed out in a previous paper based on quantum field theory of ordered phases [T. Kita, J. Phys. Soc. Jpn. {\bf 93}, 124704 (2024)],…
We present a coherent picture of the quantum mechanics of black holes. The picture does not require the introduction of any drastically new physical effect beyond what is already known; it arises mostly from synthesizing and…
We calculate the one-electron Green's function of the 2D attractive Hubbard model by coupling the electrons to pair fluctuations. The latter are approximated by homogeneous amplitude fluctuations and phase correlations corresponding to the…
We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential…
The formation and evaporation of small AdS black holes in a theory with a holographic dual is governed by the usual rules of quantum mechanics. The eigenstate thermalization hypothesis explains the validity of semiclassical gravity for…
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…
The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^8-10^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The…