相关论文: Density Matrix Geometry and Sum Rules

We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic…

The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…

We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…

A quantum theory of gravity implies a fine-grained structure of spacetime, which can be conveniently modeled as some form of pixelation at the Planck scale, with potentially observable consequences. In this work, we build upon previous…

Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…

In dimension 2 and above, the Burgers dynamics, the so-called "adhesion model" in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is…

We establish that boundary degrees of freedom associated with a generic co-dimension one null surface in $D$ dimensional pure Einstein gravity naturally admit a thermodynamical description. We expect the $\textit{null surface…

Recently, it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a wellknown fact that according to Einstein's gravity theory, gravity and…

This review paper comprehensively examines the influence of spatial torsion on quantum fluctuations from the perspectives of Metric-Affine Gravity (MAG) and the Stochastic Variational Method (SVM). We first outline the fundamental framework…

A new conjecture is proposed that there are two sorts of matter called s-matter and v-matter which are symmetric and whose gravitational masses are opposite to each other, although both masses are positive. Therefore, there are two sorts of…

We perform large-scale Quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a 2D optical lattice trap, and confirm an excellent agreement with the benchmarking in-situ density measurements by the Chicago group [1]. We…

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit…

It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…

Frequency sum rules are derived in extended quantum systems of non relativistic fermions from a minimal set of assumptions on dynamics in infinite volume, for ground and thermal states invariant under space translations or a lattice…

We have investigated the vacuum maximally symmetric solutions of recently proposed density-metric unimodular gravity theory,the results are widely different from inflationary senario.The exponential dependence on time in deSitter space is…

We revisit a theory of heat transport in the light of a gauge theory of gravity and find the proper heat current with a corresponding gauge field, which yields the natural definitions of the heat magnetization and the Kubo-formula…

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can…

Dispersion forces (van der Waals force and Casimir force) originating from quantum fluctuations are crucial in the cohesion of microscale and nanoscale particles. In reality, these particles have a variety of irregular shapes that differ…

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar…

Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattice to simulate models for unsolved strongly correlated systems, so as to…