Related papers: The Quantum Geometric Tensor in a Parameter Depend…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…
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…
The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…
Topological Physics relies on the specific structure of the eigenstates of Hamiltonians. Their geometry is encoded in the quantum geometric tensor containing both the celebrated Berry curvature, crucial for topological matter, and the…
In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
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…
It is known that the Frenet-Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet-Serret apparatus specifies important geometric invariants, including the…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
The ultimate extension of Penrose's Spin Geometry Theorem is given. It is shown how the \emph{local} geometry of any \emph{curved} Lorentzian 4-manifold (with $C^2$ metric) can be derived in the classical limit using only the observables in…
The quantum geometric tensor and quantum Fisher information have recently been shown to provide a unified geometric description of the linear response of many-body systems. However, a similar geometric description of higher-order…
A nonperturbative quantization procedure based on a nonassociative decomposition of quantum field operators on nonassociative constituents is considered. It is shown that such approach gives rise to quantum corrections by calculations of…
In this work we provide a possible geometrical interpretation of the spin of elementary particles. In particular, it is investigated how the wave equations of matter are altered by the addition of an antisymmetric contribution to the metric…
We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in…
The quantum geometry of Bloch wavefunctions underpins a wealth of emergent phenomena in quantum materials. Its imaginary part, the Berry curvature, has long been recognized as a key source for hallmark effects such as quantum Hall and…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
An idea for an application of the quantum annealing mechanism to construct a projection measurement in a collective space is proposed. We use the annealing mechanism to drive the pointer degree of freedom associated with the measurement…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this,…