Related papers: Geometry along Evolution of Mixed Quantum States
In this paper we introduce a geometric framework for mixed quantum states based on a K\"ahler structure. The geometric framework includes a symplectic form, an almost complex structure, and a Riemannian metric that characterize the space of…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
We numerically investigate quantum rings in graphene and find that their electronic properties may be strongly influenced by the geometry, the edge symmetries and the structure of the corners. Energy spectra are calculated for different…
We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
We consider a problem of geometric phase generation in a system of two interacting bosons confined in a narrow ring potential with a localized defect. Geometric phase emerges from variation of parameters of the defect. Particle interaction…
We study the dynamics of a quantum system in which an intermediate property $m$ is measured in between initial and final measurements of two different non-commuting properties $a$ and $b$. Since this intermediate measurement must involve an…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
We study the quantum dynamics of a particle confined in a twisted tube with a linearly varying cross section. By relating a general linear transformation matrix to the system's Hamiltonian, we use an extended thin-layer method to derive an…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the…
Quantum state tomography faces exponential scaling with system size, while recent neural network approaches achieve polynomial scaling at the cost of losing the geometric structure of quantum state space. We introduce geometric latent space…
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…
We consider the generic problem of suddenly changing the geometry of an integrable, one-dimensional many-body quantum system. We show how the physics of an initial quantum state released into a bigger system can be completely described…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
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 present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…