Related papers: Weak value picture on quantum observables: gauge-i…
The higher Berry curvature was introduced by Kapustin and Spodyneiko as an extension of the Berry curvature in quantum mechanical systems with finite degrees of freedom to quantum many-body systems in finite spatial dimensions. In this…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak…
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM…
We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for…
The Berry connection encodes the momentum-space geometry of occupied Bloch states in gapped insulators and plays a central role in topological materials. While gauge-invariant quantities can be evaluated from overlap matrices between…
Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with…
The voltage-controlled Berry phases in two vertically coupled InGaAs/GaAs quantum dots are investigated theoretically. It is found that Berry phases can be changed dramatically from 0 to 2$\pi$ (or 2$\pi$ to 0) only simply by turning the…
We propose a semi-classical interpretation of the geometric scalar and vector potentials that arise due to Berry's phase when an atom moves slowly in a light field. Starting from the full quantum Hamiltonian, we turn to a classical…
Quantum geometric tensor (QGT), including a symmetric real part defined as quantum metric and an antisymmetric part defined as Berry curvature, is essential for understanding many phenomena. We studied the photogalvanic effect of a…
Viewing gravitational energy momentum $p_G^\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\mu$ requires two different symmetries to account for their independent conservations - spacetime and inner…
Gauge freedom in quantum electrodynamics (QED) outside of textbook regimes is reviewed. It is emphasized that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. This…
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the…
Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators.…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
Experimental access to many-body quantum systems is often limited by measurement backaction, and key dynamical properties are typically obtained by perturbing a system and measuring its response. Here we replace this active paradigm with a…
The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region \textit{inaccessible} to the particle. Classically,…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum…