Emptiness formation in polytropic quantum liquids

We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.

Higgs vacuum decay in a braneworld

We examine the effect of large extra dimensions on vacuum decay in the Randall–Sundrum (RS) braneworld paradigm. We assume the scalar field is confined to the brane, and compute the probability for forming an “anti-de Sitter” (AdS) bubble inside a critical flat RS brane. We present the first full numerical solutions for the brane instanton considering two test potentials for the scalar field. We explore the geometrical impact of thin and thick bubble walls, and compute the instanton action in a range of cases. We conclude by commenting on a more physically realistic potential relevant for the Standard Model Higgs. For bubbles with large backreaction, the extra dimension has a dramatic effect on the tunnelling rate, however, for the weakly backreacting bubbles more relevant for realistic Standard Model potentials, the extra dimension has little impact.

NUCLEAR FISSION WITHIN THE MEAN-FIELD APPROACH

We discuss the mean-field instanton method for calculating decay rates of the sponteneous fission. Based on our recent work, we stress the role of the velocity-momentum relations which make the instanton action minimal, and the choice of a time-even density matrix and a time-odd hermitian operator as special variables making the adiabatic limit transparent. We also present an analytic study of a simple model of barrier tunneling, which illustrates the importance of the velocity-momentum constraints.

VACUUM SELECTION BY INFLATION AS THE ORIGIN OF THE DARK ENERGY

I propose a new mechanism to account for the observed tiny but finite dark energy in terms of a non-Abelian Higgs theory, which has infinitely many perturbative vacua characterized by a winding number, in the framework of inflationary cosmology. Inflation homogenizes field configuration and practically realizes a perturbative vacuum with vanishing winding number, which is expressed by a superposition of eigenstates of the Hamiltonian with different vacuum energy density. As a result, we naturally find a nonvanishing vacuum energy density with fairly large probability, under the assumption that the cosmological constant vanishes in some vacuum state. Since the predicted magnitude of dark energy is exponentially suppressed by the instanton action, we can fit observation without introducing any tiny parameters.

TOPOLOGICAL EFFECTS OF INSTANTON DUE TO DEFECTS

A new doublet variable is proposed to decompose non-Abelian gauge field for describing the topological effects of instantons due to the defects in appropriate phase of SU(2) Yang–Mills theory. It is shown that the instanton number can be directly related to the isospin defects of the doublet order parameter and contributed from topological charges of these defects. The θ-term in instanton action is found to be the delta-function form of the doublet and the Lagrangian of instantons in terms of new variables is also presented.

FERMIONS, ANOMALY AND UNITARITY IN HIGH ENERGY ELECTROWEAK INTERACTIONS

We report on the "state of the art" of the problem of B + L violation in high energy electroweak scatterings. Results of various analyses point to (but do not prove rigorously yet) "half-suppression," i.e. the (B + L)-violating cross section remains suppressed at least by the negative exponent of the single instanton action, at all energies. The most interesting techniques developed in this field are reviewed. Particular attention is paid to unitarity constraints on the anomalous cross section, and to some conceptual problems involving the use of the optical theorem in the presence of instantons.

INSTANTON-INDUCED CROSS-SECTION AT HIGH ENERGIES: LEADING ORDER AND BEYOND

We study the total cross-section of high energy collisions in the one-instanton sector of purely bosonic theories with instantons. We find that in the limit g2 → 0, E/E sph = fixed , the leading behavior of the total cross-section is σ lot ~ exp [1/g2(−2S0 + F(E/E sph ))], where S0 is the instanton action. In the electroweak theory at E/E sph ≪ 1, the function F(E/E sph ) is determined by the gauge boson part of the instanton configuration and its explicit form is found.