Related papers: Analysis of nonperturbative fluctuations in a trip…
Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular…
Fredholm integral operators that commute with the Hamiltonians of certain quantum mechanical problems with quartic potentials are introduced. The operators are expressed in terms of an Airy function, and their eigenvalues fall off…
For suitable parameters, the classical Duffing oscillator has a known bistability in its stationary states, with low- and high-amplitude branches. As expected from the analogy with a particle in a double-well potential, transitions between…
We propose a new approach for computing tunneling rates in quantum or thermal field theory with multiple scalar fields. It is based on exact analytical solutions of piecewise linear potentials with many segments that describes any given…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We study the semiclassical fluctuation problem around bounce solutions for a self-interacting scalar field in curved space. As in flat space, the fluctuation problem separates into partial waves labeled by an integer l, and we determine the…
I show that the method of finding if the ground state energy is nonzero or not by saturating the functional integral directly with instanton-anti-instanton type fluctuations is not reliable either for the double or for the triple well…
In this note we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm determinant can be exploited in…
Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton…
We investigate the quantum dynamics of a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential shape with a superconducting circuit comprised of a loop interrupted…
We derive the expression of the abelian axial anomaly in the so-called multi-Weyl and triple-point crossing semimetals. No simplifying restrictions are assumed on the symmetry of the spectrum. Three different computation methods are…
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…
A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [$\textit{ J.…
We study the statistical properties of currents in two particular systems of capacitively coupled parallel transport channels. In the first system, each transport channel contains a single quantum dot in contact with two electron…
Recently there has been increasing interest in alternate methods to compute quantum tunneling in field theory. Of particular interest is a stochastic approach which involves (i) sampling from the free theory Gaussian approximation to the…
In this thesis, several aspects of Yang-Mills theory are studied. It begins with the constrained quantization in the Coulomb gauge, using the Dirac bracket formalism. A nonperturbative analysis of the infrared asymptotics of propagators in…
In this work we analyse how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which actually behaves as fractals, allow for…
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…