Related papers: Instantonic Methods for Quantum Tunneling in Finit…
A solution to the classical field equations in the massless (1+1)-dimensional O(3) sigma model is found, which describes a multi-particle instanton-like transition at high energy. In the limit of small number of initial particles, the…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
Unlike flat space quantum field theories that focus on scattering amplitudes, the main observables in quantum cosmology are correlation functions. The systematic way of calculating correlators is called in-in formalism, which requires only…
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
Collective spin systems -- spin ensembles coupled to a common reservoir and effectively described by a single macrospin -- play an important role in both atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple…
A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam${\acute e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the…
We use path integral methods and topological quantum field theory techniques to investigate a generic classical Hamiltonian system. In particular, we show that Floer's instanton equation is related to a functional Euler character in the…
A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact…
We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of…
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…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
The finite size theory of metastability in a quartic potential is developed by the semiclassical path integral method. In the quantum regime, the relation between temperature and classical particle energy is found in terms of the first…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value…
We study the geometry of Euclidean instantons in loop quantum cosmology (LQC) such as those relevant for the no-boundary proposal. Confining ourselves to the simplest case of a cosmological constant in minisuperspace cosmologies, we analyze…
Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to computing thermal reaction rates for complex molecular systems including quantum tunneling effects. There have been a number of attempts to…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
We quantize scalar fluctuations in 1+1 dimensions above a classical background kink. The properties of the effective action for the corresponding classical field are studied with an exact functional method, alternative to exact Wilsonian…
We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for…