Related papers: Applying the linear delta expansion to `i phi^3'
We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation,…
We draw attention to the fact that a Hermitian matrix is always diagonalizable and has real discrete spectrum whereas the Hermitian Schr{\"o}dinger Hamiltonian: $H=p^2/2\mu+V(x)$, may not be so. For instance when $V(x)=x, x^3, -x^2$, $H$…
Let $(G,c)$ be an infinite network, and let $\mathcal{E}$ be the canonical energy form. Let $\Delta_2$ be the Laplace operator with dense domain in $\ell^2(G)$ and let $\Delta_{\mathcal{E}}$ be the Laplace operator with dense domain in the…
In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian Hamiltonian model which is given as $\hat{\mathcal{H}}=\omega (\hat{b}^{\dag}\hat{b}+1/2)+ \alpha (\hat{b}^{2}-(\hat{b}^{\dag})^{2})$ where $\omega$ and $\alpha$…
We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion - order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the…
The PT-symmetric Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon$ real) exhibits a phase transition at $\epsilon=0$. When $\epsilon\geq0$, the eigenvalues are all real, positive, discrete, and grow as $\epsilon$ increases. However, when…
We construct a Hamiltonian H whose discrete spectrum contains, in a certain limit, the Riemann zeros. H is derived from the action of a massless Dirac fermion living in a domain of Rindler spacetime, in 1+1 dimensions, that has a boundary…
We start with a realisation of a Lie algebra with the basis operators $L=\langle Q_m\rangle$, $Q_m=\zeta_{mj}(x_i)\partial_{x_j}$, where $x_i$ are some variables that may be regarded as dependent or independent in construction of some…
In this paper, we study the local-in-time validity of the Hilbert expansion for the relativistic Landau equation. We justify that solutions of the relativistic Landau equation converge to small classical solutions of the limiting…
I have made an ample study of one dimensional quantum oscillators, ranging from logarithmic to exponential potentials. I have found that the eigenvalues of the hamiltonian of the oscillator with the limiting (approachissimo) harmonic…
A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic…
We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…
We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian,$H(\beta)=-d^2/dx^2+x^2+i\sqrt{\beta}x^3$,for $\beta$ in the cut plane $\C_c:=\C\backslash (-\infty, 0)$. Moreover, we prove that the spectrum…
We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at…
The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
For a fixed $\theta^2=1/m$, $m \in \mathbb{N}_+$, let $x \in [0, \theta)$ and $[a_1(x) \theta, a_2(x) \theta, \ldots]$ be the $\theta$-expansion of $x$. Our first goal is to extend for $\theta$-expansions the results of Jarnik \cite{J-1928}…
The Fock-space Hamiltonian truncation method is developed further, paying particular attention to the treatment of the scalar field zero mode. This is applied to the two-dimensional Phi^4 theory in the phase where the Z_2-symmetry is…
With the discovery of Dark Energy, $\Lambda_{DE}$, there is now a universal length scale, $\ell_{DE}=c/(\Lambda_{DE} G)^{1/2}$, associated with the universe that allows for an extension of the geodesic equations of motion. In this paper, we…
We explicitly construct the series expansion for a certain class of solutions to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric solutions. We express the Taylor coefficients through some universal combinatorial…