Related papers: Flow Equation for Supersymmetric Quantum Mechanics
Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast…
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
We study the long-time behavior of a particle in $\mathbb{R}^d$, $d \geq 2$, subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the divergence of a stationary random stream matrix $\mathbf{k}…
One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization problem that includes many nonlinear, non convex constraints as…
We perform a systematic analysis of flow-like solutions in theories of Einstein gravity coupled to multiple scalar fields, which arise as holographic RG flows as well as in the context of cosmological solutions driven by scalars. We use the…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
By employing the gradient flow exact renormalization group (GFERG), we study the renormalization group (RG) flow of a manifestly gauge or BRST invariant non-perturbative ansatz of the 1PI Wilson action in quantum electrodynamics. The gauge…
Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
We determine the most general form of the covariant drag force exerted on a quark moving through a fluid dynamical flow. Up to first order in derivative expansion, our general formula requires the specification of seven coefficient…
We study dynamics of (anomalous) Galilean superfluid up to first order in derivative expansion, both in parity-even and parity-odd sectors. We construct a relativistic system -- null superfluid, which is a null fluid (introduced in…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
We study holographic RG flows in a 3d supergravity model from the side of the dynamical system theory. The gravity equations of motion are reduced to an autonomous dynamical system. Then we find equilibrium points of the system and analyze…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
We study the gradient flow equation for the O(N) nonlinear sigma model in two dimensions at large N. We parameterize solution of the field at flow time t in powers of bare fields by introducing the coefficient function X_n for the n-th…
We study topological properties of a quantum mechanical system with $U(1)$-symmetry within the functional renormalisation group (fRG) approach. These properties include the vacuum energy structure and the topological susceptibility. Our…
In this thesis, we present and discuss the quantum statistical foundations of relativistic hydrodynamics with special emphasis on the entropy current. We show that it is possible to provide a rigorous definition for this quantity in the…
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials…