The Bounce Method in the Theory of Quantum Decay

V. G. Emel'Yanov, Dimitri P. Kostomarov, V. I. Kukulin

S. V. Mousavi, Salvador Miret-Artés

Daniela Mugnai, Anedio Ranfagni

According to the instanton method, the decay from a metastable state is described by a sequence of bounces, each of them represents an attempt to traverse the energy barrier. Analogously to Büttiker-Landauer tunnelling time interpretation, it is suggested that a real time is spent by the system also during the attempts of tunnelling (instanton bounces).

Luciano Fonda, G. C. Ghirardi

Kfir Blum, Ipak Fadakar, Omri Rosner +1 more

A quantum tunneling event in field theory is usually depicted as the materialization of a spherical bubble of true vacuum. The bubble appears at rest, and its profile is the time-symmetric slice of Coleman's bounce, the Euclidean solution that controls the decay rate. However, the bubble is spherical only in the leading semiclassical approximation: at the next order the configuration is a Gaussian ensemble of fluctuations around the bounce. We derive the wave functional of the field on the nucleation slice from the half-bounce path integral, and use it to compute the root-mean-square quadrupole moment of a bubble at nucleation. The relative deformation of the bubble wall radius $R$ is $δR/R\sim(\hbar/S_b)^{1/2}$, with $S_b$ the bounce action. Thus $δR/R\sim0.1$ for a typical cosmological phase transition with $S_b/\hbar\sim100$.

Oliver Janssen, Joel Karlsson, Flavio Riccardi +1 more

We present a formalism for semiclassical time evolution in quantum mechanics, building on a century of work. We identify complex saddle points in real time, real saddle points in complex time, and complex saddle points in complex time that reproduce the known answers in classic problems. For the decay of a metastable state, we find finite time and finite energy analogs of the "bounce" which do not have strict zero or negative modes. The one-loop phase of the wave function and the multiplicity of bounce solutions at late times are discussed. The motivation of this work is to learn how to compute decay rates in quantum field theory in situations with non-trivial time dependence, by first taking a humble step backwards to the fascinating world of quantum mechanics.