相关论文: Density Matrix Geometry and Sum Rules
We present a geometric formulation of optical, thermoelectric, and thermal linear response in clean, zero temperature band insulators based on a single object: a generalized time-dependent quantum geometric tensor (g-tQGT) built from…
Quantum geometry of Bloch wavefunctions has gained considerable interest with the discovery of moir\'e materials that exhibit bands flattened by quantum interference. The quantum metric, the symmetric part of the quantum geometric tensor,…
Sum rules for linear response functions give powerful and experimentally-relevant relations between frequency moments of response functions and ground state properties. In particular, renewed interest has been drawn to optical conductivity…
We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. We identify the stochastic variable of the effective statistical theory that we derive as a…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e. the Hall viscosity, the Wen-Zee…
The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed,…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
In this paper, we develop the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix…
Matter at extreme temperatures and pressures -- commonly known as warm dense matter (WDM) in the literature -- is ubiquitous throughout our Universe and occurs in a number of astrophysical objects such as giant planet interiors and brown…
The theory of the intrinsic nonlinear Hall effect, a key probe of quantum geometry, is plagued by conflicting expressions for the conductivity that is independent of the dissipation strength (rate, $\Gamma^0$). We clarify the origin of this…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
We propose a fluctuation-dissipation theorem in open quantum systems from an information-theoretic perspective. We define the fidelity susceptibility that measures the sensitivity of the systems under perturbation and relate it to the…
The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
The kernel of the evolution equation is used to build a mathematical theory of thermal phenomena of gaseous and condensed matter. The group velocity of sound and the molar density are proposed to be its two thermal variables that replace…
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
We display an interesting sum rule for the dynamical thermal conductivity for many standard models of condensed matter in terms of the expectation of a thermal operator. We present the thermal operator for several model systems of current…