Related papers: Oscillatory behavior of large eigenvalues in quant…

The problem of finding the large order asymptotics for the eigenfunction perturbation theory in quantum mechanics is studied. The relation between the wave function argument x and the number of perturbation theory order k that allows us to…

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time dependent oscillation of the…

A two-level quantum system coherently driven by a resonant electromagnetic field oscillates sinusoidally between the two levels at frequency $\Omega$ which is proportional to the field amplitude [1]. This phenomenon, known as the Rabi…

We discuss the Jaynes-Cummings model in different representations of the algebra of canonical commutation relations. The first conclusion is that all the irreducible representations lead to equivalent physical predictions. However, the…

The non-commutative harmonic oscillator (NCHO) is a matrix valued differential operator originally introduced as a generalization of the quantum harmonic oscillator having a weaker $\mathfrak{sl}_2(\mathbb{R})$-symmetry. The spectrum of the…

Consider the eigenvalue problem of a linear second order elliptic operator: \begin{equation} \nonumber -D\Delta \varphi -2\alpha\nabla m(x)\cdot \nabla\varphi+V(x)\varphi=\lambda\varphi\ \ \hbox{ in }\Omega, \end{equation} complemented by…

We consider the Laplacian eigenvalues for smooth planar domains with strongly attractive Robin conditions imposed on a part of the boundary and Neumann condition on the remaining boundary. The asymptotics of individual eigenvalues is…

For a beta-Jacobi ensemble determined by parameters a_1, a_2 and n, under the restriction that the three parameters go to infinity with n and a_1 being of small orders of a_2, we obtain both the bulk and the edge scaling limits. In…

We study finite-rank normal deformations of rotationally invariant non-Hermitian random matrices. Extending the classical Baik-Ben Arous-P\'ech\'e (BBP) framework, we characterize the emergence and fluctuations of outlier eigenvalues in…

We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…

In this paper we study the main properties of the first eigenvalue and its eigenfunctions of a class of highly nonlinear elliptic operators in a bounded Lipschitz domain, assuming a Robin boundary condition. Moreover, we prove a Faber-Krahn…

We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the…

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we…

Parity describing the symmetry of quantum mechanics wavefunction under space inversion transformation not only plays an essential role in solving quantum systems but also can be used to manipulate and measure the motional quantum states of…

We consider the flavor transformation of neutrinos through oscillatory matter profiles. We show that the neutrino oscillation Hamiltonian in this case describes a Rabi system with an infinite number of Rabi modes. We further show that, in a…

We consider Jacobi matrices with eventually increasing sequences of diagonal and off-diagonal Jacobi parameters. We describe the asymptotic behavior of the subordinate solution at the top of the essential spectrum, and the asymptotic…

We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the…

Using extended coherent states, an analytically exact study has been carried out for the quantum Rabi model with two equivalent qubits. Compact transcendental functions of one variable have been derived leading to exact solutions. The…

We investigate the dissipative phase transitions of the anisotropic quantum Rabi model with cavity decay and demonstrate that large spin fluctuations persist in the stationary state, having important consequences on the phase diagram and…

In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…