Related papers: Essay: Where Can Quantum Geometry Lead Us?
The quantum metric is a fundamental ingredient of band quantum geometry and has recently at tracted intense interest, with most of its transport signatures appearing in the intrinsic second order nonlinear conductivity. In the clean limit,…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
For pure states, the quantum Berry curvature was well studied. However, the quantum curvature for mixed states has received less attention. From the concept of symmetric logarithmic derivative, we introduce a mixed-state quantum curvature…
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
Classical thermodynamics admits a geometric formulation in which work is associated with areas enclosed by cycles in state space. Whether an analogous structure persists in driven, dissipative quantum systems remains an open question. Here…
Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann…
The impact of quantum fluctuations on the phase diffusion in resistively shunted superconducting quantum points subject to an external ac-voltage is studied. Based on an extension of the classical Smoluchowski equation to the quantum…
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…
A critical result in superconductivity is that flat bands, though dispersionless, can still host nonzero superfluid weight due to quantum geometry. We show that the derivation of the mean field superfluid weight in previous literature is…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
We study characteristics of quantum evolution which can be called curvature and torsion. The curvature shows a deviation of the state vector in quantum evolution from the geodesic line. The torsion shows a deviation of state vector from the…
Several physical phenomena in superconductors, such as helical superconductivity and the diode effect, rely on breaking time-reversal symmetry. This symmetry-breaking is usually accounted for via the Lifshitz invariant, a contribution to…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…