相关论文: Orbital approach to microstate free entropy
We study the minimum problem for the functional $\int_{\Omega}\bigl( \vert \nabla \mathbf{u} \vert^{2} + Q^{2}\chi_{\{\vert \mathbf{u}\vert>0\}} \bigr)dx$ with the constraint $u_i\geq 0$ for $i=1,\cdots,m$ where…
In the paper, we obtain a formula for topological free entropy dimension in the orthogonal sum (or direct sum) of unital C^* algebras. As a corollary, we compute the topological free entropy dimension of any family of self-adjoint…
Orbital-free density functional theory (OF-DFT) provides an alternative approach for calculating the molecular electronic energy, relying solely on the electron density. In OF-DFT, both the ground-state density is optimized variationally to…
Utilizing the electron orbital degree of freedom in heterostructures is attracting increasing attention due to the possibility of achieving much larger conversion rates between charge and orbital angular momentum flow compared to the…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
I first calculate the charged spherical Renyi entropy by a numerical method that does not require knowledge of any eigenvalue degeneracies, and applies to all odd dimensions. An image method is used to relate the full sphere values to those…
We study the entanglement entropies of an interval adjacent to the boundary of the half line for the free fermionic spinless Schr\"odinger field theory at finite density and zero temperature, with either Neumann or Dirichlet boundary…
Both the Barrow and Tsallis $\delta$ entropies are one-parameter generalizations of the black-hole entropy, with the same microcanonical functional form. The ensuing deformation is quantified by a dimensionless parameter $\Delta$, which in…
If one encodes the gravitational degrees of freedom in an orthonormal frame field there is a very natural first order action one can write down (which in four dimensions is known as the Goldberg action). In this essay we will show that this…
In this paper, the isolated horizons with rotation are considered. It is shown that the symplectic form is the same as that in the nonrotating case. As a result, the boundary degrees of freedom can be also described by an SO$(1,1)$ BF…
We analyze the coupling between the internal degrees of freedom of neutron stars in a close binary, and the stars' orbital motion. Our analysis is based on the method of matched asymptotic expansions and is valid to all orders in the…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
The extension $k \mapsto \mu^{\boxplus k}$ of the concept of a free convolution power to the case of non-integer $k \geq 1$ was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory.…
The aim of this paper is to construct many examples of rational surface automorphisms with positive entropy by means of the concept of orbit data. We show that if an orbit data satisfies some mild conditions, then there exists an…
Causal diamond-shaped subsets of space-time are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to…
We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…
The entanglement entropy of a free quantum field in a coherent state is independent of its stress energy content. We use this result to highlight the fact that while the Einstein equations for first order variations about a locally…
Point sets of number-theoretic origin, such as the visible lattice points or the $k$-th power free integers, have interesting geometric and spectral properties and give rise to topological dynamical systems that belong to a large class of…
Orbital entropies, pair entropies, and mutual information have become popular tools for analysis of strongly correlated wave functions. They can quantitatively measure how strongly an orbital participates in the electron correlation and…