arXiv subjects

Avadhut V. Purohit

Publications and source records attributed to Avadhut V. Purohit.

6 recordsLinked to original sources

arXiv2026

Floquet Recurrences in the Double Kicked Top

We study exact quantum recurrences in the double kicked top (DKT), a driven spin model that extends the quantum kicked top (QKT) by introducing an additional time-reversal symmetry-breaking kick. Reformulating its dynamics in terms of effective parameters $k_r$ and $k_θ$, we analytically show exact periodicity of the Floquet operator for $k_r = jπ/2$ and $k_r = jπ/4$ with distinct periods for integer and half-odd integer $j$. These exact recurrences were found to be independent of $k_θ$. The long-time-averaged entanglement and fidelity rate function show dynamical quantum phase transition (DQPT) for $k_r = jπ/2$ at time-reversal symmetric cases $k_θ= \pm k_r$. In the other time-reversal symmetric case $k_θ= 0$, the DQPT exists only for a half-odd integer $j$. Using level statistics, a smooth transition is observed from integrable to non-integrable nature as $k_r$ is changed away from $jπ/2$. Our work demonstrates that regular and chaotic regimes can be controlled for any system size by tuning $k_r$ and $k_θ$, making the DKT a useful platform for quantum control and information processing applications.

quant-ph↗

arXiv2026

Strong Eigenstate Thermalization from Mean-Ergodic Non-chaotic Dynamics

We report an example of a many-body system, derived from the double kicked top (DKT), with non-chaotic yet mean-ergodic dynamics that displays \textit{strong} eigenstate thermalization hypothesis (ETH) in the quantum regime. The analysis addresses a key open question: whether \textit{strong} ETH is a quantum analog of ergodicity (or mean-ergodicity). Despite non-chaotic dynamics, the fluctuations of the diagonal matrix elements of an observable scale as $D^{-1/2}$, where $D$ denotes the Hilbert space dimension. Furthermore, the off-diagonal matrix elements show parameter-independent distribution, together with a smooth function $f_O(\bar{E}, ω)$ that becomes nearly uniform in the large-$k_θ$ domain. Our findings show that even mean-ergodic and non-chaotic systems can exhibit \textit{strong} ETH.

cond-mat.stat-mech↗

arXiv2026

Quantum Kicked Top: A Paradigmatic Model

The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. In this chapter, we present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, we derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. We then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. The quantum description is developed using Floquet theory, where the periodically driven spin system is represented by a unitary Floquet operator acting on a $(2j+1)$-dimensional Hilbert space. Within this framework, signatures of quantum chaos such as spectral statistics, entanglement generation and recurrences are discussed. The model also admits an interpretation as a system of interacting qubits, enabling explicit few-qubit realizations and direct connections with quantum information measures through reduced density matrices and entanglement entropy. By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science.

quant-ph↗

arXiv2025

Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $π/2$

We study the signatures of quantum integrability (QI) in a spin chain model, having infinite-range Ising interaction and subjected to a periodic pulse of an external magnetic field. We analyze the unitary operator, its eigensystem, the single-qubit reduced density matrix, and the entanglement dynamics for arbitrary initial state for any $N$. The QI in our model can be identified through key signatures such as the periodicity of entanglement dynamics and the time-evolved unitary operator, and highly degenerated spectra or Poisson statistics. In our previous works, these signatures were observed in the model for parameters $τ=π/4$ and $J=1,1/2$, where we provided exact analytical results up to $12$ qubits and numerically for large $N$ [Phys. Rev. B \textbf{110}, 064313,(2024)}; arXiv:2411.16670 (2024)}]. In this paper, we extend the analysis to $τ=mπ/2$, and arbitrary $J$ and $N$. We show that the signatures of QI persist for the rational $J$, whereas for irrational $J$, these signatures are absent for any $N$. Further, we perform spectral statistics and find that for irrational $J$, as well as for rational $J$ with perturbations, the spacing distributions of eigenvalues follow Poisson statistics. The average adjacent gap ratio is obtained as $\langle r \rangle=0.386$, consistent with Poisson statistics. Additionally, we compute the ratio of eigenstate entanglement entropy to its maximum value ($\langle S \rangle /S_{Max}$) and find that it remains significantly below $1$ in the limit $N\rightarrow \infty$, which further confirms the QI. We discuss some potential experimental realizations of our model.

quant-ph↗

arXiv2025

Study of double kicked top: a classical and quantum perspective

We study the double kicked top (DKT), which is an extension of the standard quantum kicked top (QKT) model. The model allows us to study the transition from time-reversal symmetric to broken time-reversal symmetric dynamics. Our transformation in the kick strength parameter space $(k, k') \to (k_r, k_θ)$ reveals interesting features. The transformed kicked strength parameter $k_r$ drives a higher growth of chaos and is equivalent to the standard QKT, whereas the other transformed kicked strength parameter $k_θ$ leads to a weaker growth. We discuss the fixed points, their stability, and verify results obtained by computing the largest Lyapunov exponent (LLE) and the Kolmogorov-Sinai entropy (KSE). We exactly solve 2- to 4-qubit versions of DKT by obtaining its eigenvalues, eigenvectors and the entanglement dynamics. Furthermore, we find the criteria for periodicity of the entanglement dynamics. We investigate measures of quantum correlations from two perspectives: the deep quantum and the semi-classical regime. Signatures of phase-space structure are numerically shown in the long-time averages of the quantum correlations. Our model can be realised experimentally as an extension of the standard QKT.

quant-ph↗

arXiv2023

The status of geometry and matter in re-interpreted WdW equation

I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and matter, with geometry being fundamental. The quantum theory possesses gravitational decoherence when the signature of $R^{(3)}$ changes. The quantum theory resolves singularities dynamically. Application to the FLRW $κ=0$ shows the creation of local geometries during quantum evolution. The 3-metric gets modified near the classical singularity in the case of the Schwarzschild geometry.

gr-qc↗