Related papers: An anharmonic alliance: exact WKB meets EPT

In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was…

The role of quantum effects in excitonic energy transport (EET) has been scrutinised intensely and with increasingly sophisticated experimental techniques. This increased complexity requires invoking correspondingly elaborate models to fit…

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…

Using the NU method [A.F.Nikiforov, V.B.Uvarov, Special Functions of Mathematical Physics, Birkhauser,Basel,1988], we investigated the real eigenvalues of the complex and/or $PT$- symmetric, non-Hermitian and the exponential type systems,…

Degeneracies of non-Hermitian Hamiltonian i.e., exceptional points (EPs) of parity-time (PT)-symmetric systems have received considerable research attention due to their various possible applications in optical devices. At EPs, at least two…

Quantum Singular Value Transformation (QSVT) provides a unified framework for applying polynomial functions to the singular values of a block-encoded matrix. QSVT prepares a state proportional to $\bA^{-1}\bb$ with circuit depth…

An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…

The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a…

The optimized effective potential (OEP) is the exact Kohn-Sham potential for explicitly orbital-dependent energy functionals, e.g., the exact exchange energy. We give a proof for the OEP equation which does not depend on the chain rule for…

In this paper, the asymptotic behavior of abstract strongly coupled hyperbolic equations with one infinite memory term is investigated, one specific case of which is the model for describing the dynamical behaviour of magnetic effected…

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As…

Photon-counting detector based computed tomography (PCCT) has greatly advanced in recent years. However, spectral inconsistency, referring to inter-pixel variations in detected counts per energy bin, can easily leads to ring or band…

We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…

We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose…

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen…

So far the spectra $E_n(N)$ of the paradigm model of complex PT(Parity-Time)-symmetric potential $V_{BB}(x,N)=-(ix)^N$ is known to be analytically continued for $N > 4$. Consequently, the well known eigenvalues of the Hermitian cases…

Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode…

We present a new first-principles linear-response theory of changes due to perturbations in the quasiparticle self-energy operator within the $GW$ method. This approach, named $GW$ perturbation theory ($GW$PT), is applied to calculate the…

Bohr's complementarity principle has long been a fundamental concept in quantum mechanics, positing that, within a given experimental setup, a quantum system (or quanton) can exhibit either its wave-like character, denoted as $W$, or its…

In this paper, we present a comprehensive analysis of the one-loop self-energy correction at finite temperature for the bound electron. In this approach, we study the influence of thermal radiation on atomic systems. Along the way, we found…