Related papers: The geometric tensor for classical states
We study the concepts of adiabatic driving and geometric phases of classical integrable systems under the Koopman-von Neumann formalism. In close relation to what happens to a quantum state, a classical Koopman-von Neumann eigenstate will…
In these lecture notes, partly based on a course taught at the Karpacz Winter School in March 2014, we explore the close connections between non-adiabatic response of a system with respect to macroscopic parameters and the geometry of…
The adiabatic gauge potential (AGP) is the generator of unitary transformations which preserve the eigenbasis of a quantum Hamiltonian under parametric variation. While its usefulness in quantum mechanics has been thoroughly demonstrated in…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
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…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
Geometric phases of simple harmonic oscillator system are studied. Complete sets of "eigenfunctions" are constructed, which depend on the way of choosing classical solutions. For an eigenfunction, two different motions of the probability…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
We study the eigenfunctions of the classical Liouville operator and investigate the conditions they must obey to be separable as a product state. We point out that the conditions for separability are equivalent to requirements of…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…
We study the role of the quantum geometric tensor (QGT) in the evolution of quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wavepacket…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate…
The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay…
We introduce a curvature atlas for left-invariant metrics on SU(2), based on the inertial curvature field derived from the Euler-Poincare equations. We prove that the classical integrable cases of the heavy top--spherical, Lagrange,…
Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to…