Related papers: Accurate calculation of resonances in multiple-wel…
In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. We show that the plasmon mode is equivalent to the eigenvalue problem…
General analytical expressions for Double Quantum Nuclear Magnetic Resonance (NMR) kinetic curves of many-spin I=1/2 systems are derived with an accuracy of the second cumulant approximation. The expressions obtained exactly describe the…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
Employing the concept of time-delay, a relation is found which counts the number of quantal resonances supported by a potential. Several simple and advanced illustrations include a treatment of square-well, Dirac delta barrier, an…
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
We compute the three-loop non-singlet corrections to the photon-quark form factors taking into account the full dependence on the virtuality of the photon and the quark mass. We combine the method of differential equations in an effective…
We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…
Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution…
A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by $V= m^2 x^2+g x^4$ at arbitrary $g \geq 0$ for…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
In this work, we discuss a new method for calculation of extremal eigenvectors and eigenvalues in systems or regions of parameter space where direct calculation is problematic. This technique relies on the analytic continuation of the power…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
In the correspondence between spectral problems and topological strings, it is natural to consider complex values for the string theory moduli. In the spectral theory side, this corresponds to non-Hermitian quantum curves with complex…
A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}= -\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by $V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using the Sinc collocation method…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…