Related papers: A Note on Instantons in a 1D Same-Level Asymmetric…
The level splitting formula of an asymmetric double well potential is calculated taking into account the multi-instanton contributions (dilute gas approximation). Results can be related with known semiclassical ones obtained with a…
We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. We derive a generalization of instanton theory for these asymmetric…
Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude, up to the two-loops order. Some mistakes made in the previous works are corrected. The same method is applied to the next-order…
The Euclidean path integral method is applied to a quantum tunneling model which accounts for finite size ($L$) effects. The general solution of the Euler Lagrange equation for the double well potential is found in terms of Jacobi elliptic…
We show that for the triple well potential with non-equivalent vacua, instantons generate for the low lying energy states a singlet and a doublet of states rather than a triplet of equal energy spacing. Our energy splitting formulae are…
Coupled instantons are introduced by generalizing the double well potential to multiple mutually coupled wells. Physically this corresponds to the simultaneous tunneling of multiple degrees of freedom. A system with four equal minima is…
The path-integral approach to the double well has long been limited by the dilute instanton gas approximation. We show that if the finite Euclidean-time structure is taken seriously by using exact saddles, the dilute gas can be sidestepped,…
We present a new way to compute and interpret quantum tunneling in a 1-D double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been…
Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in…
This paper deals with quantum fluctuations near the classical instanton configuration. Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude (the instanton density) in the three-loop order for…
Instanton calculations are demonstrated from a viewpoint of twisted topological field theory. Various properties become manifest such that perturbative corrections are terminated at one-loop, and norm cancellations occur between bosonic and…
For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each well, the energy eigenvalues of the low lying excited states…
The energy levels of the double-well potential receive, beyond perturbation theory, contributions which are non-analytic in the coupling strength; these are related to instanton effects. For example, the separation between the energies of…
Instanton-like transitions (``shadow processes'') are considered in (1+1) dimensional models with one scalar field whose potential is a quadratic well with a cliff. The corresponding classical boundary value problem is solved, and the…
We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a…
We study an asymmetric double InGaAs quantum well using optical two-dimensional coherent spectroscopy. The collection of zero-quantum, one-quantum, and two-quantum two-dimensional spectra provides a unique and comprehensive picture of the…
The structure of the energy levels in a deep triple well is analyzed using simple quantum mechanical considerations. The resultant spectra of the first three energy levels are found to be composed of a ground state localized at the central…
Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phasespace…
A prime example of quantum tunnelling is the semiclassical 'energy splitting' of the levels of a symmetrical double well potential, or equivalently the flipping rate of an instanton. Curiously the accepted expression for the ground state…
Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact…