Time-dependent quantum geometric tensor and some applications

• URL: http://arxiv.org/abs/2502.01788v1
• Date: Mon, 03 Feb 2025 20:08:02 GMT
• Title: Time-dependent quantum geometric tensor and some applications
• Authors: Bogar Díaz, Diego Gonzalez, Marcos J. Hernández, J. David Vergara,
• Abstract summary: We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time- parameter space for a quantum state. This tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states.
• Score: 0.0
• License:
• Abstract: 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 standard quantum geometric tensor, this tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states and encoding new information about these systems. In particular, the time-time component of this tensor is related to the energy dispersion of the system. We applied this framework to a harmonic/inverted oscillator, a time-dependent harmonic oscillator, and a chain of generalized harmonic/inverted oscillators. We show some results on the scalar curvature associated with the time-dependent quantum geometric tensor and the generalized Berry curvature behavior on the transition from harmonic oscillators to inverted ones. Furthermore, we analyze the entanglement for the chain through purity analysis, obtaining that the purity for any excited state is zero in the mentioned transitions.

Related papers

• Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. We showcase the method's effectiveness simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D. Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Time-dependent Hamiltonians and Geometry of Operators Generated by Them [0.0]
  We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system. We show that an equivalence exists between the total costs of obtaining an operator through time evolution.
  arXiv  Detail & Related papers  (2024-05-23T10:32:29Z)
• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure [49.1574468325115]
  We study the entanglement of a single particle under continuous measurements. We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
  arXiv  Detail & Related papers  (2023-04-06T09:45:11Z)
• Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator [0.0]
  We study the time-dependent behaviour of quantum correlations of a system governed by out-of-equilibrium dynamics. Next, we study a specific case, where the system exhibits chaotic behaviour by computing the quantum Lyapunov from the time-dependent behaviour of OTOC.
  arXiv  Detail & Related papers  (2022-10-03T18:00:02Z)
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields [0.0]
  In time-independent quantum systems, entanglement entropy possesses an inherent scaling symmetry that the energy of the system does not have. We show that such systems have dynamical scaling symmetry that leaves the evolution of various measures of quantum correlations invariant.
  arXiv  Detail & Related papers  (2022-05-26T13:20:46Z)
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase [0.9176056742068814]
  We show the emergence of Berry phase in a forced harmonic oscillator system placed in the quantum space-time of Moyal type. Adiabatic evolution over time-period $mathcalT$ is studied in Heisenberg picture to compute the expression of geometric phase-shift.
  arXiv  Detail & Related papers  (2021-10-10T08:05:18Z)
• Quantized dynamics in closed quantum systems [0.0]
  We propose an approach to process data from interferometric measurements on a closed quantum system at random times. A classical limit exists which is separated from the quantum fluctuations. Some generic properties are linked to a quantized Berry phase.
  arXiv  Detail & Related papers  (2020-12-07T14:15:46Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Synchronisation phase as an indicator of persistent quantum correlations between subsystems [68.8204255655161]
  Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. We show that our analysis applies to a variety of spontaneously synchronising open quantum systems.
  arXiv  Detail & Related papers  (2020-06-29T17:21:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.