arXiv subjects

Udaysinh T. Bhosale

Publications and source records attributed to Udaysinh T. Bhosale.

At least 19 recordsLinked to original sources

arXiv2026

Transport Information Beyond Strong Eigenstate Thermalization

Strong eigenstate thermalization (ETH) in operationally mean-ergodic, non-chaotic systems provides an opportunity to investigate whether Floquet eigenstates retain information about classical transport beyond their leading thermodynamic behavior. We address this question using the double kicked top (DKT), which exhibits nonmixing transport and dynamics consistent with weak mixing transport under variation of its control parameters. We show that the coefficient $m$ of the leading finite-size correction to the normalized eigenstate entanglement entropy (EE) $s$ tracks the restructuring between these transport regimes even when the thermodynamic-limit entropy $c$ becomes nearly insensitive to them. This coefficient $m$ is positive for nonmixing transport and negative when dynamics consistent with weak mixing transport dominate. The coefficient's sign reversal in the coexistence regime remains stable as the semiclassical resolution increases. Our results demonstrate that finite-size eigenstate structure can encode signatures of classical transport that are invisible in the thermodynamic-limit entropy, providing an eigenstate-based diagnostic of dynamical organization beyond the leading thermodynamic behavior associated with strong ETH.

quant-ph↗

arXiv2026

Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range $p$-Spin Kicked Top Model

We study the signatures of quantum integrability (QI) in a $p$-spin kicked top model with infinite-range Ising interactions, subjected to periodic pulses of an external magnetic field, with the precession angle fixed at $α=mπ$. We analytically compute the unitary operator, its eigensystem, time evolution, single-qubit reduced density matrix, and entanglement dynamics for arbitrary initial states. We show that the spectrum of the unitary operator exhibits pronounced clustering of eigenphases in some regions, leading to strongly non-uniform spectral features with $p$. The entanglement measures and unitary operator dynamics exhibit periodic behavior, while the eigenvalue spectrum shows strong degeneracies when the kicking strength $k'$ is a rational multiple of $π$ for even $p$. For odd $p$, both the periodic behavior and spectral degeneracies persist for all values of $k'$. This periodic behavior extends to the strong-kicking regime ($k'=J j^{p-1}π$), where for rational values of $J$ the dynamics remain periodic. For any $k'$ and $p$ the spectral statistics shows Poissonian behavior and the average adjacent gap ratio $\langle r \rangle = 2\ln 2 - 1$, consistent with integrable behaviour. The spectral form factor further supports this nature. Additionally, we compute the ratio of average eigenstate entanglement entropy to its maximum value ($\langle S \rangle /S_{Max}$) and find that it remains significantly far below from $1$ in the limit $N\rightarrow \infty$. These results collectively establish robust signatures of QI across all $k', p,$ and system sizes. We also discuss possible experimental realizations of the model.

quant-ph↗

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

Higher-order spacings in the superposed spectra of random matrices with comparison to spacing ratios and application to complex systems

Higher-order spacing statistics in the $m$ superposed spectra of circular random matrices of the same class are studied numerically. We conjecture that for given $m$ (or order $k$) and $β$, the sequence of modified Dyson index $β'(k)$ (or $β'(m)$) obtained using the sum of absolute differences between the cumulative distribution functions method (denoted as $D(β')$) is unique. Also, for a given $k$, the distribution tends to the corresponding $k$-th order Poisson statistics in the limit $m\rightarrow \infty$. The quantum chaotic kicked top model for various Hilbert space dimensions is studied, and it is found to satisfy our conjecture. This involves the numerical verification of $m=2$ case of COE results. Our result can be used as a tool for the characterization of a system and to determine the symmetry structure of the system without desymmetrization of the spectra. Additionally, the comparative study of the higher-order spacing and ratio distributions in both $m=1$ and $m=2$ cases of COE as well as GOE is performed within and across these ensembles numerically using the $D(β')$ method. This study is carried out both by varying the dimension and keeping the number of realizations constant, and vice-versa. The same asymptotic higher-order statistics are observed across COE and GOE in terms of a given spectral fluctuation measure. But, within a given ensemble of COE or GOE, the results of higher-order spacing and ratio distributions agree with each other only up to some lower $k$, and beyond that, they start deviating from each other. Further, the spectral fluctuations of the intermediate map of various dimensions are studied. Various important observations and discussions from the analysis of our extensive numerical computations are presented.

physics.data-an↗

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 Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System

Sharma and Bhosale [\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.014412}{Phys. Rev. B \textbf{109}, 014412 (2024)}; \href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.064313}{Phys. Rev. B \textbf{110}, 064313,(2024)}] recently introduced an $N$-spin Floquet model with infinite-range Ising interactions. There, we have shown that the model exhibits the signatures of quantum integrability for specific parameter values $J=1,1/2$ and $τ=π/4$. We have found analytically the eigensystem and the time evolution of the unitary operator for finite values of $N$ up to $12$ qubits. We have calculated the reduced density matrix, its eigensystem, time-evolved linear entropy, and the time-evolved concurrence for the initial states $\ket{0,0}$ and $\ket{π/2,-π/2}$. For the general case $N>12$, we have provided sufficient numerical evidences for the signatures of quantum integrability, such as the degenerate spectrum, the exact periodic nature of entanglement dynamics, and the time-evolved unitary operator. In this paper, we have extended these calculations to arbitrary initial state $\ket{θ_0,ϕ_0}$, such that $θ_0 \in [0,π]$ and $ϕ_0 \in [-π,π]$. Along with that, we have analytically calculated the expression for the average linear entropy for arbitrary initial states. We numerically find that the average value of time-evolved concurrence for arbitrary initial states decreases with $N$, implying the multipartite nature of entanglement. We numerically show that the values $\langle S\rangle/S_{Max} \rightarrow 1$ for Ising strength ($J\neq1,1/2$), while for $J=1$ and $1/2$, it deviates from $1$ for arbitrary initial states even though the thermodynamic limit does not exist in our model. This deviation is shown to be a signature of integrability in earlier studies where the thermodynamic limit exist.

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↗

arXiv2024

Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System

In a recent work Sharma and Bhosale [Phys. Rev. B, 109, 014412 (2024)], $N$-spin Floquet model having infinite range Ising interaction was introduced. In this paper, we generalized the strength of interaction to $J$, such that $J=1$ case reduces to the aforementioned work. We show that for $J=1/2$ the model still exhibits integrability for an even number of qubits only. We analytically solve the cases of $6$, $8$, $10$, and $12$ qubits, finding its eigensystem, dynamics of entanglement for various initial states, and the unitary evolution operator. These quantities exhibit the signature of quantum integrability (QI). For the general case of even-$N > 12$ qubits, we conjuncture the presence of QI using the numerical evidences such as spectrum degeneracy, and the exact periodic nature of both the entanglement dynamics and the time-evolved unitary operator. We numerically show the absence of QI for odd $N$ by observing a violation of the signatures of QI. We analytically and numerically find that the maximum value of time-evolved concurrence ($C_{\mbox{max}}$) decreases with $N$, indicating the multipartite nature of entanglement. Possible experiments to verify our results are discussed.

quant-ph↗

arXiv2023

Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system

We study $N$ qubits having infinite-range Ising interaction and subjected to periodic pulse of external magnetic field. We solve the cases of $N=5$ to $11$ qubits analytically, finding its eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities shows signatures of quantum integrability. For the general case of $N>11$ qubits, we provide a conjecture on quantum integrability based on the numerical evidences like degenerate spectrum, and the exact periodic nature of the time-evolved unitary evolution operator and the entanglement dynamics. Using linear entropy we show that for class of initial unentangled state the entanglement displays periodically maximum and zero values.

quant-ph↗

arXiv2023

Universal scaling of higher-order spacing ratios in Gaussian random matrices

Higher-order spacing ratios are investigated analytically using a Wigner-like surmise for Gaussian ensembles of random matrices. For $k$-th order spacing ratio $(r^{(k)}$, $k>1)$ the matrix of dimension $2k+1$ is considered. A universal scaling relation for this ratio, known from earlier numerical studies, is proved in the asymptotic limits of $r^{(k)}\rightarrow0$ and $r^{(k)}\rightarrow \infty$.

math-ph↗

arXiv2021

Superposition and higher-order spacing ratios in random matrix theory with application to complex systems

The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the discrete symmetries present in the system. Superposition of spectra of $m$ such circular orthogonal, unitary and symplectic ensembles are studied numerically using higher-order spacing ratios. For given $m$ and the Dyson index $β$, the modified index $β'$ is tabulated whose nearest neighbor spacing distribution is identical to that of $k$-th order spacing ratio. For the case of $m=2$ ($m=3$) in COE (CUE) a scaling relation between $β'$ and $k$ is given. For COE, it is conjectured that for $k=m+1$ ($m\geq2$) and $k=m-3$-th ($m\geq5$) order spacing ratio distribution the $β'$ is $m+2$ and $m-4$ respectively. Whereas in the case of CSE, for $k=m+1$ ($m\geq2$) and $k=m-1$-th ($m\geq3$) the $β'$ is $2m+3$ and $2(m-2)$ respectively. We also conjecture that for given $m$ ($k$) and $β$, the sequence of $β'$ as a function of $k$ ($m$) is unique. Strong numerical evidence in support of these results is presented. These results are tested on complex systems like the measured nuclear resonances, quantum chaotic kicked top and spin chains.

cond-mat.stat-mech↗

arXiv2018

Scaling in the eigenvalue fluctuations of the empirical correlation matrices

The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In the last two decades, random matrix theory-based tools such as the nearest neighbour eigenvalue spacing and eigenvector distributions have been employed to extract the significant modes of variability present in such empirical correlations. In this work, we present an alternative analysis in terms of the recently introduced spacing ratios, which does not require the cumbersome unfolding process. It is shown that the higher order spacing ratio distributions for the Wishart ensemble of random matrices, characterized by the Dyson index $β$, is related to the first order spacing ratio distribution with a modified value of co-dimension $β'$. This scaling is demonstrated for Wishart ensemble and also for the spectra of empirical correlation matrices drawn from the observed stock market and atmospheric pressure data. Using a combination of analytical and numerics, such scalings in spacing distributions are also discussed.

physics.data-an↗

arXiv2018

Periodicity of quantum correlations in the quantum kicked top

Quantum kicked top is a fundamental model for time-dependent, chaotic Hamiltonian system and has been realized in experiments as well. As the quantum kicked top can be represented as a system of qubits, it is also popular as a testbed for the study of measures of quantum correlations such as entanglement, quantum discord and other multipartite entanglement measures. Further, earlier studies on kicked top have led to a broad understanding of how these measures are affected by the classical dynamical features. In this work, relying on the invariance of quantum correlation measures under local unitary transformations, it is shown exactly these measures display periodic behaviour either as a function of time or as a function of the chaos parameter in this system. As the kicked top has been experimentally realised using cold atoms as well as superconducting qubits, it is pointed out that these periodicities must be factored in while choosing of experimental parameters so that repetitions can be avoided.

quant-ph↗

arXiv2018

NMR studies of quantum chaos in a two-qubit kicked top

Quantum chaotic kicked top model is implemented experimentally in a two qubit system comprising of a pair of spin-1/2 nuclei using Nuclear Magnetic Resonance techniques. The essential nonlinear interaction was realized using indirect spin-spin coupling, while the linear kicks were realized using RF pulses. After a variable number of kicks, quantum state tomography was employed to reconstruct the single-qubit density matrices using which we could extract various measures such as von Neumann entropies, Husimi distributions, and Lyapunov exponents. These measures enabled the study of correspondence with classical phase space as well as to probe distinct features of quantum chaos, such as symmetries and temporal periodicity in the two-qubit kicked top.

quant-ph↗

arXiv2018

Higher order spacing ratios in random matrix theory and complex quantum systems

The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems, and also in atomic and nuclear physics. In contrast to the level spacing distribution, which requires the cumbersome and at times ambiguous unfolding procedure, the ratios of spacings do not require unfolding and are easier to compute. In this work, for the class of Wigner-Dyson random matrices with nearest neighbor spacing ratios $r$ distributed as $P_β(r)$ for the three ensembles indexed by $β=1,2, 4$, their $k-$th order spacing ratio distributions are shown to be identical to $P_{β'}(r)$, where $β'$, an integer, is a function of $β$ and $k$. This result is shown for Gaussian and circular ensembles of random matrix theory and for several physical systems such as spin chains, chaotic billiards, Floquet systems and measured nuclear resonances.

quant-ph↗

arXiv2017

Entanglement transitions induced by large deviations

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as $A$ and $B$, is computed analytically using a Coulomb gas method. It is shown that this probability, for large $N$, goes as $\exp[-βN^2Φ(ζ)]$, where the parameter $β$ is the Dyson index of the ensemble, $ζ$ is the large deviation parameter while the rate function $Φ(ζ)$ is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems $1$ and $2$, obtained by further partitioning the subsystem $A$, using the properties of the density matrix's partial transpose $ρ_{12}^Γ$. The density of states of $ρ_{12}^Γ$ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter $ζ$. Log negativity is used to quantify the entanglement between subsystems $1$ and $2$. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

quant-ph↗

arXiv2017

Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. The measures of quantum correlations do not have a classical analog and yet are influenced by the classical dynamics. In this work, by modelling the quantum kicked top as a multi-qubit system, the effect of classical bifurcations on the measures of quantum correlations such as quantum discord, geometric discord, Meyer and Wallach $Q$ measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of the trivial fixed points of the kicked top, scaling function decays as a power-law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the $Q$ measure. We also suggest that it can have experimental consequences.

quant-ph↗