相关论文: One-dimensionality of the minimizers for a diffuse…

In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM…

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This…

Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…

We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of…

We perform a systematic analysis of the soft supersymmetry-breaking terms arising from four-dimensional strings. The analysis does not assume any specific supersymmetry-breaking mechanism but provides a means of parametrizing our ignorance…

An explicit representation of the Gamma limit of a single-well Modica--Mortola functional is given for one-dimensional space under the graph convergence which is finer than conventional $L^1$-convergence or convergence in measure. As an…

Assumption of certain hierarchy of soft ferromagnet energy terms, realized in small enough flat nano-elements, allows to obtain explicit expressions for their magnetization distributions. By minimising the energy terms sequentially, from…

Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded domain. One phase is assumed to be magnetic, the other phase…

We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is…

We study a class of variational transmission problems driven by nonlinear energies with discontinuous coefficients across a prescribed interface. The model setting consists of integral functionals of the form \[…

We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by…

This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…

Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a…

In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter $\epsilon$, representing the interface thickness between the tumorous and non tumorous cells,…

We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…

We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between…

For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…

We study a class of nonlocal conformal field theories in two dimensions which are obtained as deformations of the Virasoro minimal models. The construction proceeds by coupling a relevant primary operator $\phi_{r,s}$ of the $m$-th minimal…

Quasi-realistic string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopoulos D-term that breaks supersymmetry at the one--loop level in string perturbation theory. Supersymmetry…

To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its…