Related papers: Dual-Level Approach to Instanton Theory
Accurate simulations of molecules require high-level electronic-structure theory in combination with rigorous methods for approximating the quantum dynamics. Machine-learning approaches can significantly reduce the computational expense of…
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.…
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…
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical…
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…
Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very…
Background: Quantum tunneling in many-body systems is the subject of many experimental and theoretical studies in fields ranging from cold atoms to nuclear physics. However, theoretical description of quantum tunneling with strongly…
We prove formulas for the multi-instanton corrections to the overlap and energies of a 1D same-level asymmetric double well using the Euclidean path integral. Both the odd and even instanton sectors are summed to all orders. The double well…
Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological…
In the study of quantum-mechanical tunneling processes, numerous approaches have been developed to determine the decay rate of states initially confined within a metastable potential region. Virtually all analytical treatments, however,…
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…
Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory…
Marcus-Levich-Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects into the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into…
A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a…
In this paper, we study a nonlinear two-dimensional two-particle quantum tunnel effect with dissipation in diatomic H-H system. We use an instanton technique based on the path integral approach, and present analytical solutions, in the…
The instanton configuration in the SU(2)-gauge system with a Higgs doublet is constructed by using the new valley method. This method defines the configuration by an extension of the field equation and allows the exact conversion of the…
Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate…
Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high…
The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…