Related papers: Quantum geometry encoded to pair potentials
Field mediated entanglement experiments probe the quantum superposition of macroscopically distinct field configurations. We show that this phenomenon can be described by using a transparent quantum field theoretical formulation of…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that…
The momentum space of conventional superconductors is recently recognized to possess a quantum metric defined from the overlap of filled quasihole states at neighboring momenta. For multiband superconductors with arbitrary intraband and…
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
Nontrivial quantum geometry of electronic bands has been argued to facilitate superconductivity even for the case of flat dispersions where the conventional contribution to the superfluid weight is suppressed by the large effective mass.…
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.…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
The quantum general linear supergroup GLq(m|n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theory, and applied to develop the representation theory of…
Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…
As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which…
Collective excitations of many-body electron systems can carry internal structure, tied to the quantum geometry of the Hilbert space in which they are embedded. This has been shown explicitly for particle-hole-like excitations, which carry…
The density functional theory calculations and tight-binding models for the copper-doped lead apatite support flat bands, which could be susceptible to the emergence of high-temperature superconductivity. We develop theory for the geometric…
We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is…
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
Quantum point contacts (QPC) are fundamental building blocks of nanoelectronic circuits. For their emission dynamics as well as for interaction effects such as the 0.7-anomaly the details of the electrostatic potential are important, but…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…