Related papers: Quantum geometric tensor and quantum phase transit…
The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric…
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…
The possibilities of curvature of space-time in the metric of quantum states are investigated. The curvature of the metric corresponding to a wave function of Hydrogen atom is determined. Also, Einstein tensor is described for a given…
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…
We show how nonrelativistic many body techniques can be used to study quantum corrections to the classical limit, in particular of the $SU(2)$ Lipkin Model. We show that the quantum corrections are essentially of two types: unitary and…
The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor (QGT). It contains both the Berry curvature, central to the description of topological matter and the quantum metric. So far the full QGT has been measured…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
The relation between quantum phase transitions, entanglement, and geometric phases is investigated with a system of two qubits with XY type interaction. A seam of level crossings of the system is a circle in parameter space of the…
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric…
Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized…
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…
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…
In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for…
Modern cosmological models are constructed in the framework of thermodynamic approaches developed within a Van der Waals-Maxwell theory of the first-order phase transitions. In the present work we study a geometrothermodynamics of…
We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system…
We study the formation of topological defects in nonequilibrium phase transitions of both classical and quantum field theory. We examine three model systems. 1). The phase transition of a quantum scalar field in a FRW universe is analyzed…
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully…
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…
We present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary…
The quantum geometry in the momentum space of semiconductors and insulators, described by the quantum metric of the valence band Bloch state, has been an intriguing issue owing to its connection to various material properties. Because the…