Related papers: Morse theory for the uniform energy
We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare`…
Using the closed time path formalism in thermal field theory, we give a derivation of the fluctuation-dissipation theorem which is based on the unitarity of the $S$-matrix.
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations).…
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge…
We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of spontaneous curvature effects and for open surfaces with…
We study some aspects of open string theories on D-branes with critical electric fields. We show that the massless open string modes that move in the direction of the electric field decouple. In the 1+1 dimensional case the dual theory is…
Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…
In this paper, we establish the existence of periodic orbits of a twisted geodesic flow on all low energy levels and in all dimensions whenever the magnetic field form is symplectic and spherically rational. This is a consequence of a more…
Using the theory of diffusion in graphs, we propose a model to study mesoscopic transport through a diffusive quantum dot. The graph consists of three quasi-1D regions: a central region describing the dot, and two identical left- and right-…
In this work we study the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the…
Since the initial development of one-dimensional electron gases (1DEG) two decades ago, there has been intense interest in both the fundamental physics and the potential applications, including quantum computation, of these quantum…
A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current intensity factor. A general constitutive…
Understanding how microscopic motility shapes emergent collective behaviors is a challenging task in active matter, especially when self-propulsion is regulated by external cues or via quorum-sensing interactions. To address this problem,…
In the context of $f(\mathcal{R})$ gravity, dark energy is a geometrical fluid with negative equation of state. Since the function $f(\mathcal{R})$ is not known \emph{a priori}, the need of a model independent reconstruction of its shape…
We present extensive new \textit{ab intio} path integral Monte Carlo results for the momentum distribution function $n(\mathbf{k})$ of the uniform electron gas (UEG) in the warm dense matter (WDM) regime over a broad range of densities and…
We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in a…
We develop a geometric framework for irreversible transport phenomena in which macroscopic evolution equations arise from the combined structure of a thermodynamic state metric and an Onsager-based dissipation metric. The construction…
The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of…