Related papers: Geometric flows and the Swampland
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
We use a hydrodynamic model to describe the relaxation of optically injected currents in quantum wells on a picosecond time scale, numerically solving the continuity and velocity evolution equations with the Hermite-Gaussian functions…
In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with…
In this paper, basing on a generalized Newtonian dynamics (GND) approach which has been proposed elsewhere we present a conjecture for turbulent flow. We firstly utilize the GND to reasonably unify the two phenomenological methods recently…
In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate…
This paper presents a geometric microcanonical ensemble perspective on two-dimensional Truncated Euler flows, which contain a finite number of (Fourier) modes and conserve energy and enstrophy. We explicitly perform phase space volume…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
The geometric evolution equations provide new ways to address a variety of non-linear problems in Riemannian geometry, and, at the same time, they enjoy numerous physical applications, most notably within the renormalization group analysis…
We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild spacetime, and we introduce a version of the finite volume method which is formulated…
The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed,…
The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal…
In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our…
The flows of phase trajectories of cosmological models based on the vacuum classical Higgs field and their behavior on the Einstein-Higgs surface near singular points of a dynamical system are investigated by numerical simulation. The…