We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of 〈σx(t)〉 and 〈σz(t)〉 for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of bo...

We identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact, convergent periodic orbit expansions for individual energy levels, thus obtaining an analytical solution f...

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have a rational form. This approach gives us not only a truly periodic solution but also the frequency of motion as a function of the amplitude of oscillation. Three truly nonlinear oscillators ...

We address the existence and properties of one-dimensional solitons maintained by localized parametric gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We found that the family of fundamental solitons is partly stable in focusing nonlinear medium, and completely stable in defocusing medium, while all higher-order ...

The problem of uniform exact model matching is studied via state and output feedback, for a class of linear time-varying analytic systems. The following two major issues are resolved: The nessecary and sufficient conditions for the problem to have a solution and the general analytical expressions for the controller matrices. A major feature of the proposed approach, is that it reduces the unifo...

Analytical gas-permeation models for predicting the separation process across  membranes (exit compositions and area requirement) constitutes an important and necessary step in understanding the overall performance of  membrane modules. But, the exact (numerical) solution methods suffer from the complexity of the solution. Therefore, solutions of nonlinear ordinary differential equations th...

In this paper, we propose an efficient modification of a New Homotopy Perturbation Method (NHPM) to obtain approximate and exact analytical solutions of Partial Differential-Algebraic Equations (PDAEs). The NHPM is first applied to the PDAE to obtain the exact solution in convergent series form. To improve the solution obtained from NHPM’s truncated series, a post-treatment combining Laplace tr...

We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the nth-order differential equation to a system of n linear differential equations with unit...

Analytical series solution is proposed for the transient boundary-value problem ofmultilayer heat conduction in r–h spherical coordinates. Spatially non-uniform, but time-independent, volumetric heat sources may exist in the concentric layers. Proposed solution is valid for any combination of homogenous boundary conditions of the first or second kind in the h -direction. However, inhomogeneous ...

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of single-parameter scaling in this model. According to this criterion, states with energies within the conduction band of the underlying nonrandom system satisfy sin...