23,290 research outputs found
Lattice gauge theories simulations in the quantum information era
The many-body problem is ubiquitous in the theoretical description of
physical phenomena, ranging from the behavior of elementary particles to the
physics of electrons in solids. Most of our understanding of many-body systems
comes from analyzing the symmetry properties of Hamiltonian and states: the
most striking example are gauge theories such as quantum electrodynamics, where
a local symmetry strongly constrains the microscopic dynamics. The physics of
such gauge theories is relevant for the understanding of a diverse set of
systems, including frustrated quantum magnets and the collective dynamics of
elementary particles within the standard model. In the last few years, several
approaches have been put forward to tackle the complex dynamics of gauge
theories using quantum information concepts. In particular, quantum simulation
platforms have been put forward for the realization of synthetic gauge
theories, and novel classical simulation algorithms based on quantum
information concepts have been formulated. In this review we present an
introduction to these approaches, illustrating the basics concepts and
highlighting the connections between apparently very different fields, and
report the recent developments in this new thriving field of research.Comment: Pedagogical review article. Originally submitted to Contemporary
Physics, the final version will appear soon on the on-line version of the
journal. 34 page
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows
at high Reynolds numbers is one of the last open problems of classical physics.
In this review we discuss recent developments related to the application of
instanton methods to turbulence. Instantons are saddle point configurations of
the underlying path integrals. They are equivalent to minimizers of the related
Freidlin-Wentzell action and known to be able to characterize rare events in
such systems. While there is an impressive body of work concerning their
analytical description, this review focuses on the question on how to compute
these minimizers numerically. In a short introduction we present the relevant
mathematical and physical background before we discuss the stochastic Burgers
equation in detail. We present algorithms to compute instantons numerically by
an efficient solution of the corresponding Euler-Lagrange equations. A second
focus is the discussion of a recently developed numerical filtering technique
that allows to extract instantons from direct numerical simulations. In the
following we present modifications of the algorithms to make them efficient
when applied to two- or three-dimensional fluid dynamical problems. We
illustrate these ideas using the two-dimensional Burgers equation and the
three-dimensional Navier-Stokes equations
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