Related papers: Orbital approach to microstate free entropy
We extend the recently-developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric response of periodic insulators. Working in the independent-particle framework, we find…
In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These notions are related to the liberation process introduced by D.…
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
A Ginzburg-Landau free energy for a superconducting chiral p-wave order parameter is derived from a two-dimensional tight binding lattice model with weak spin-orbit coupling included as a general symmetry-breaking field. Superconductivity…
The purpose of this paper is to rigorously investigate the orbital magnetism of core electrons in 3-dimensional crystalline ordered solids and in the zero-temperature regime. To achieve that, we consider a non-interacting Fermi gas…
We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that…
In this article we continue to study the concept of entropy introduced in [4], [15]-[17]. We calculate entropy for a wider class of finite-dimensional operators in comparison with [15]. We also approximate the entropy of a unitary operator…
The relationship between the exact kinetic energy density in a quantum system in the frame of Density Functional Theory and the semiclassical functional expression for the same quantity is investigated. The analysis is performed with Monte…
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to…
Recent theoretical studies on the nonlinear response of spin and orbital degrees of freedom have discovered spin and orbital analogs of the photocurrent, with potential for characterizing topological materials and for applications. In this…
We describe a variational theory of multi-band two-dimensional electron gases that captures the interplay between electrostatic confining potentials, orbital-dependent interlayer electronic hopping and electron-electron interactions, and…
In the unit ball B(0,1), let $u$ and $\Omega$ (a domain in $\R$) solve the following overdetermined problem: $$\Delta u =\chi_\Omega\quad \hbox{in} B(0,1), \qquad 0 \in \partial \Omega, \qquad u=|\nabla u |=0 \quad \hbox{in} B(0,1)\setminus…
We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI$_{h}$ models that admit an isotropic…
Using the orbit method we attempt to reveal geometric and algebraic meaning of separation of variables for the integrable systems on coadjoint orbits in an $\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits embedded…
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…
We first explain how to endow the space of subequivalence relations of any non-singular countable equivalence relation with a Polish topology, extending the framework of Kechris' recent monograph on subequivalence relations of probability…
Quadrature bases that incorporate spatio-temporal degrees of freedom are derived as eigenstates of momentum dependent quadrature operators. The resulting bases are shown to be orthogonal for both the particle-number and spatio-temporal…
In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…