Related papers: Observing Quantum Tunneling in Perturbation Series
A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is…
This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from…
We study the effect of back-reaction on the evaporation of quantum black holes. The method used is based on quantum tunneling formalism as proposed in [4]. We give a more realistic picture by considering the fact that a black hole looses…
We compute tunneling in a quantum field theory in 1+1 dimensions for a field potential $U(\Phi)$ of the asymmetric double well type. The system is localized initially in the ``false vacuum''. We consider the case of a {\em compact space}…
A method to determine the quantum state of a scalar field after $O(4)$-symmetric bubble nucleation has been developed recently. The method has an advantage that it concisely gives us a clear picture of the resultant quantum state. In…
This work concerns \emph{ab initio} calculations of the complete potential energy curve and spectroscopic constants for the ground state $X^1\Sigma_g^+$ of the beryllium dimer, Be$_2$. High accuracy and reliability of the results is one of…
The McMillan-Rowell tunneling inversion program, which extracts the electron-phonon spectral function $\alpha^2F(\Omega)$ and the Coulomb pseudopotential $\mu^*$ from experimental tunneling data, is generalized to include the lowest-order…
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical…
We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the…
We systematically improve the recent variational calculation of the imaginary part of the ground state energy of the quartic anharmonic oscillator. The results are extremely accurate as demonstrated by deriving, from the calculated…
We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent…
The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a…
In this paper, we consider the resummation of the divergent Rayleigh-Shrodinger perturbation expansion for the ground state energy of the quartic anharmonic oscillator in one dimension. We apply the Borel-Pade resummation method combined…
If the universe is trapped and cooled in a metastable false vacuum state, that state will eventually decay by bubble nucleation and expansion. For example, many extensions of the standard model incorporate new scalar fields whose potential…
Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel…
Reconstructing a radial (1D) quantum potential, V(r), from a few bound-state energies is a long-standing inverse problem because limited spectral data must constrain an entire potential. We present a Laplace-moment reconstruction pipeline…
In this thesis we explore the physics of renormalons in integrable models under the framework of resurgence. In the first part, we review some background on resurgence, integrability and renormalons, including a discussion of large N…
Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable…
An important non-perturbative effect in quantum physics is the energy gap of superconductors, which is exponentially small in the coupling constant. A natural question is whether this effect can be incorporated in the theory of resurgence.…
We study strong tunneling (i.e. transmission $h/e^2R_T \gg 1$) in the single-electron box with many transverse modes at zero temperature. We develop a new renormalization group method which includes all charge states and requires no initial…