arXiv subjects

Jakub Novotný

Publications and source records attributed to Jakub Novotný.

5 recordsLinked to original sources

arXiv2026

The use of Peres lattices in periodically driven systems

We demonstrate the strength of the method of Peres lattices in periodically driven quantum systems. The method, which has previously been used mostly in stationary systems, enables us to efficiently detect resonances in the driven system, to monitor the onset of chaos, and to recognize critical properties of the Floquet modes. It also allows quick comparisons of the spectra of Floquet modes for various driving Hamiltonians and transparent tests of the iterative approximation techniques based on effective stationary Hamiltonians.

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arXiv2026

Quantum geometry of connected state manifolds: When diabolic points act as bridges between eigenstate manifolds

Parametric Hamiltonians often exhibit point-like spectral degeneracies (diabolic points, or conical intersections), which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a coordinate transformation and develop a formalism in which diabolic points act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold. We characterise the topology of this structure and refine the rules for nodal lines governing the Berry phase. The connected state manifold restores the numerical stability near diabolic points, enlarges the class of geodesics allowing for new geodesic shortcuts, and provides a new mechanism for Berry phase computation, even along paths traversing diabolic points.

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arXiv2026

Tracing complex zeros of the quantum survival amplitude: How the energy distribution controls dynamical phase transitions

Motivated by the advance of dynamical quantum phase transitions (DQPTs), we analyze the zeros of the complex-time survival (Loschmidt) amplitude in finite quantum systems and develop a general framework for their approximation based on the stability of zeros of holomorphic functions. We show that the large-scale properties of the distribution of zeros are governed by the envelope of the energy distribution of the initial state and can be constructed from chains of periodic zeros associated with its dominant contributions. In this picture, zeros reach the real-time axis when two or more eigenstates become equally populated at the maximum of the envelope, providing a finite-size precursor of DQPTs. We apply the method to quenched ground states in the Ising model with tunable interaction range and demonstrate close agreement between the approximate and exact distributions of zeros. We prove that the approximate construction becomes exact for BCS ground-state quenches in two-band models. To describe short-time dynamics, we introduce a minimal Gaussian model with a nearly equidistant spectrum. Slow dephasing continuously deforms the initial zero pattern into the asymptotic two-level structure, explaining anomalous DQPTs as a delayed approach of zeros to the real-time axis. Our results identify the energy envelope as the key ingredient shaping dynamical critical behavior and provide a universal interpretation of the whole zero distribution of the complex-time survival amplitude.

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arXiv2025

Excited-state quantum phase transitions in constrained systems

We extend the standard semiclassical theory of Excited-State Quantum Phase Transitions (ESQPTs), based on a classification of stationary points in the classical Hamiltonian, to constrained systems. We adopt the method of Lagrange multipliers to find all stationary points and their properties directly from the Hamiltonian constrained by an arbitrary number of integrals of motion, and demonstrate the procedure on an algebraic u(3) boson model with two independent constraints. We also elaborate the Holstein-Primakoff (HP) mapping, used to eliminate one degree of freedom in bosonic systems constrained by a conserved number of excitations, and address the fact that this mapping leads, in the classical limit, to a compact phase space with singular behaviour that conceals some stationary points at the phase space boundary. It is shown that the HP method reveals all ESQPTs only after constructing a complete atlas of different HP mappings.

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arXiv2023

Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator

A detailed numerical study reveals that the asymptotic values of the standard deviation-to-mean ratio of the out-of-time-ordered correlator can be successfully used as a measure of the quantum chaoticity of the system. We employ a finite-size fully connected quantum system with two degrees of freedom, namely the algebraic u(3) model, and demonstrate a clear correspondence between the relative oscillations of the correlators and the ratio of the chaotic part of the volume of phase space in the classical limit of the system. We also show how the relative oscillations scale with the system size and conjecture that the scaling exponent can also serve as a robust chaos indicator.

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