Curves in quantum state space, geometric phases, and the brachistophase

Chryssomalakos C.; Flores-Delgado A. G.; Guzmán-González E.; L. Hanotel; Serrano-Ensástiga E.

doi:10.1088/1751-8121/acdcd2

Publications

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Curves in quantum state space, geometric phases, and the brachistophase

Journal of Physics A: Mathematical and Theoretical. 2023. Vol. 56. No. 28. Article 285301.

Chryssomalakos C., Flores-Delgado A. G., Guzmán-González E., Hanotel L., Serrano-Ensástiga E.

Given a curve in quantum spin state space, we inquire what is the relation between its geometry and the geometric phase accumulated along it. Motivated by Mukunda and Simon’s result that geodesics (in the standard Fubini-Study metric) do not accumulate geometric phase, we find a general expression for the derivatives (of various orders) of the geometric phase in terms of the covariant derivatives of the curve. As an application of our results, we put forward the brachistophase problem: given a quantum state, find the (appropriately normalized) Hamiltonian that maximizes the accumulated geometric phase after time t—we find an analytical solution for all spin values, valid for small t . For example, the optimal evolution of a spin coherent state consists of a single Majorana star separating from the rest and tracing out a circle on the Majorana sphere.

Research target: Physics Mathematics

Language: English

DOI

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Keywords: geometric phases geometry and quantum mechanics geometry of quantum systems

Turbulent Exchange Tensor in the Atmospheric Boundary Layer: An Inverse-Problem Approach Using Radiosonde Wind Observations with High Vertical Resolution

Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51

An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...

Added: October 16, 2026

Diversity of chaos with additional zero Lyapunov exponents in heterogeneous ensemble of quasi-periodic and chaotic systems

Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309

We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...

Added: October 16, 2026

A Reproducible Microscopy Acquisition Pipeline and Microscopy-Aware Attention for Classification, Detection, and Segmentation of Microorganisms

Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330

Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...

Added: October 14, 2026

On Calculation of Robustness and Stability of Formal Concepts Based on Delta Measure

Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992

The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...

Added: October 14, 2026

Shrimps as a fundamental object of nonlinear dynamics. Overview, properties and quasi-periodic generalization

Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592

Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...

Added: October 14, 2026

Sandpile Cellular Automata with Manna Rule on the Chung-Lu Graph: Application to X Social Network

Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255

Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...

Added: October 13, 2026

Sandpile Cellular Automata with Manna Rule on the Chung-Lu Graph: Application to X Social Network

Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273

A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...

Added: October 13, 2026

Неравновесное состояние в квазиодномерных сверхпроводящих каналах

Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16

Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...

Added: October 13, 2026

When universal machine learning models fail in capacitance prediction for carbon-based supercapacitors: Leakage-aware validation and electrolyte screening

Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159

Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors; however, most published models assume that a single predictive framework can describe both conventional porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related descriptors. Three ML algorithms ...

Added: October 13, 2026

Toponomic Quantum Computation

Chryssomalakos C., Hanotel L., Guzman Gonzalez E. et al., Modern Physics Letters A 2022 Vol. 37 No. 27 Article 2250184

Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of subspaces, for which a sequence of rotations results in a non-abelian holonomy of a topological nature, so that it is invariant under any SU(3)-perturbation. Making use ...

Added: December 15, 2022

Symmetric multiqudit states: Stars, entanglement, and rotosensors

Chryssomalakos C., Hanotel L., Guzman Gonzalez E. et al., Physical Review A: Atomic, Molecular, and Optical physics 2021 Vol. 104 No. 1

A constellation of N = d − 1 Majorana stars represents an arbitrary pure quantum state of dimension d or a permutation-symmetric state of a system consisting of n qubits. We generalize the latter construction to represent in a similar way an arbitrary symmetric pure state of k subsystems with d levels each. For d = 3, ...

Added: October 1, 2022

When geometric phases turn topological

Aguilar P., Chryssomalakos C., Guzman Gonzalez E. et al., Journal of Physics A: Mathematical and Theoretical 2020 Vol. 53 No. 6

Geometric phases, accumulated when a quantum system traces a cycle in quantum state space, do not depend on the parametrization of the cyclic path, but do depend on the path itself. In the presence of noise that deforms the path, the phase gets affected, compromising the robustness of possible applications, e.g. in quantum computing. We ...

Added: October 1, 2022