How to Count Kinks: From the Continuum to the Lattice and Back

We present a simulation strategy for the real-time dynamics of quantum fields, inspired by reinforcement learning. It builds on the complex Langevin approach, which it amends with system specific prior information, a necessary prerequisite to overcome this exceptionally severe sign problem. The optimization process underlying our machine learning approach is made possible by deploying inherently stable solvers of the complex Langevin stochastic process and a novel optimality ...

We propose a quantum approach to nonequilibrium dynamics which combines the successful aspects of classical-statistical simulations on a lattice with the ability to take into account quantum corrections. It is based on the 2PI effective action for inhomogeneous fields and a volume average. This procedure does not involve any double counting which could appear in sampling prescriptions for inhomogeneous quantum evolutions. As an example, we study nonequilibrium dynamics of def...

We study the $\lambda\phi^4_{1+1}$ kink solion and the zero-mode contribution to the Kink soliton mass in regions beyond the semiclassical regime. The calculations are done in the non-trivial scaling region and where appropriate the results are compared with the continuum, semiclassical values. We show, as a function of parameter space, where the zero-mode contributions become significant.

We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation functions are calculated by the method of differential equations. This method can be used for Euclidean and Minkowskian signature alike. The lattice correlation functions have a power series expansion in $1/\sqrt{\lambda}$, where $\lambda$ is the coupling. We show that this series is convergent for all ...

Interaction is so ubiquitous that imaging a world free from it is a difficult fantasy exercise. At the same time, in understanding any complex physical system, our ability of accounting for the mutual interaction of its constituents is often insufficient when not the restraining factor. Many strategies have been devised to control particle-particle interaction and explore the diverse regimes, from weak to strong interaction. Beautiful examples of these achievements are the ex...

A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the...

The computation of real-time properties, such as transport coefficients or bound state spectra of strongly interacting quantum fields in thermal equilibrium is a pressing matter. Since the sign problem prevents a direct evaluation of these quantities, lattice data needs to be analytically continued from the Euclidean domain of the simulation to Minkowski time, in general an ill-posed inverse problem. Here we report on a novel approach to improve the determination of real-time...

We investigate lattice simulations of scalar and nonabelian gauge fields in Minkowski space-time. For SU(2) gauge-theory expectation values of link variables in 3+1 dimensions are constructed by a stochastic process in an additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and the use of a tilted real-time contour leads to converging results in general. All fixed point solutions are shown to fulfil the infinite hierarchy of Dyson-Schwinger identities, ...

The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic (in the appropriate lattice sense), and which is operationally indistinguishable from the standard quantum theory. The generalization to a broad class of lattice theories is briefly described.

We study the $1+1$ flat spacetime dynamics of a classical field configuration corresponding to an ensemble of sine-Gordon kinks and antikinks, semi-classically coupled to a quantum field. This coupling breaks the integrability of the sine-Gordon model resulting in the background's decay into quantum radiation as kink-antikink pairs annihilate. We find evidence that, on average, the energy of the ensemble scales as $t^{-\alpha}$ with $\alpha<1$ and independent of the coupling ...