Related papers: Quantum geometry of common semiconductors
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
We discuss several problems concerning domain walls in the spin $S$ Ising model at zero temperature in a magnetic field, $H/(2S)$, applied in the $x$ direction. Some results are also given for the planar ($y$-$z$) model in a transverse…
Quantum geometry appears as a key factor in understanding the optical properties of quantum materials, with the anticipation on diverging or quantized responses near the Dirac and Weyl points. Here we investigate linear and nonlinear…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such…
A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the…
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…
Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain…
Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of geometry of quantum type I…
We investigate the quantum geometric tensor, which is comprised of the Berry curvature and quantum metric, in a generalized Dirac two-band system with non-integer dispersion $E(\mathbf{k})\sim k^{\alpha}$. Our analysis reveals that this…
The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…
The higher dimensional Quantum General Relativity of a Riemannian manifold being an embedded space in a space-time being a Lorentzian manifold is investigated. The model of quantum geometrodynamics, based on the Wheeler-DeWitt equation…
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in…
We calculate quantum transport for metal-graphene nanoribbon heterojunctions within the atomistic self-consistent Schr\"odinger/Poisson scheme. Attention is paid on both the chemical aspects of the interface bonding as well the…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
Exploring the topological characteristics of electronic bands is essential in condensed matter physics. Moir\'e materials featuring flat bands provide a versatile platform for engineering band topology and correlation effects. In moir\'e…
The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…