Related papers: Quantum Geometry and Nonlinear Responses in Magnet…
Nonlinear transport has emerged as a powerful approach to probe the quantum geometry of electronic wavefunctions, such as Berry curvature and quantum metric, in topological materials. While nonlinear responses governed by bulk quantum…
Quantum geometry plays a pivotal role in the second-order response of $\cal PT$-symmetric antiferromagnets. Here we study the nonlinear response of 2D altermagnets protected by $C_n\cal T$ symmetry and show that their leading nonlinear…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
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…
This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of…
We present a quantum response approach to momentum-space gravity in dissipative multiband systems, which dresses both the quantum geometry--through an interband Weyl transformation--and the equations of motion. In addition to clarifying the…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
Electronic properties of quantum materials solids are often well understood via the low energy dispersion of Bloch bands, motivating single band approximations in many metals and semiconductors. However, a closer look reveals length and…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
We study nonlinear response in weakly coupled nonequilibrium $\phi^4$ theory in the context of both classical transport theory and real time quantum field theory, based on a generalized Kubo formula which we derive. A novel connection…
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…
Application of the noncommutative geometry to several physical models is considered.
The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological…
The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…
Noncentrosymmetric superconductors offer fascinating phenomena of quantum transport and optics such as nonreciprocal and nonlinear responses. Time-reversal symmetry breaking often plays an essential role in the emergence and enhancement of…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
Quantum geometry of the electron wave function plays a significant role in the linear and non-linear responses of crystalline materials. Here, we study quantum geometry induced second harmonic generation. We identify non-linear responses…