arXiv subjects

N. D. Chavda

Publications and source records attributed to N. D. Chavda.

At least 19 recordsLinked to original sources

arXiv2026

Hidden Ergodic Relaxation in the Quench Dynamics of a Bichromatic Mott Lattice

We investigate the nonequilibrium dynamics of strongly interacting bosons in a finite bichromatic Mott lattice following a sudden quench of the secondary lattice amplitude. The coefficient entropies and second R\'enyi entropy exhibit pronounced growth toward their Gaussian Orthogonal Ensemble (GOE) predictions from random-matrix theory, consistent with GOE-like statistical spreading in the employed multiconfigurational representation. In striking contrast, experimentally accessible observables, including the momentum distribution, fragmentation, and Glauber correlation functions, remain nearly unchanged throughout the evolution. For the sampled strong quenches, the coefficient entropies, second R\'enyi entropy, and the $N$-body coefficient spreading collapse onto a common relaxation trajectory that becomes largely independent of the perturbation strength. Our results reveal an emergent hidden ergodic relaxation beneath the persistent local Mott-like order. An effective embedded random-matrix model captures the qualitative crossover from restricted to extensive Hilbert-space spreading, providing an interpretive framework for the observed relaxation dynamics.

cond-mat.quant-gas↗

arXiv2026

Embedded Random Matrix Ensembles to Statistical Shell Model: Operation of $q$-normal forms

Embedded random matrix ensembles operating in nuclear shell model spaces, with nucleons occupying a finite set of single particle orbits and interacting via a two-body interaction, form the basis for statistical shell model. With sufficiently strong interaction, the level densities in shell model spaces take close to a Gaussian form and transition strength distributions close to a bivariate Gaussian form. In practice, partitioning via spherical configurations ($\tilde{m}$) and angular momentum $J$ (also isospin where appropriate) are essential. The resulting statistical spectroscopy or statistical shell model was applied successfully in the past in some studies of nuclear level densities, orbit occupancies, $\beta$-decay matrix elements and so on. Going beyond these, recently it is recognized that embedded ensembles, in a better approximation, generate in-fact $q$-normal form ($q=1$ gives Gaussian and $q=0$ Wigner's semi-circle) for density of eigenvalues, bivariate $q$-normal form for transition strengths and conditional $q$-normal form for strength functions. These then allow us to develop statistical shell model with $q$-normal forms. These new developments in embedded ensembles and statistical shell model are briefly reviewed in this paper. Also described, using some examples, is the role of the $q$ parameter in generating statistical properties of general quantum many-particle systems.

nucl-th↗

arXiv2026

Negative Interaction Quench Dynamics of Density-Ordered Dipolar Bosons in a One-Dimensional Optical Lattice

We explore the nonequilibrium dynamics of a density-ordered dipolar Bose gas in a finite one-dimensional optical lattice following a negative interaction quench, using the numerically exact multiconfigurational time-dependent Hartree method for bosons. The interaction sign reversal, effectively driving a crossover from long-range to short-range interactions, generates rich intra- and interwell tunneling dynamics spanning superfluid, Mott-insulating, and fragmented regimes. A striking finding is the robustness of the underlying crystal-state correlations against the quench, despite the strong dynamical response. We identify emergent excitation modes, including local breathing and dipole-like oscillations, via real- and momentum-space observables, and quantify tunneling through site-resolved position variance. One- and two-body Glauber correlation functions further uncover a direct connection between tunneling and correlation dynamics. Moreover, we show that combining interaction quenches with lattice-depth ramping enables controllable dynamical engineering, establishing dipolar lattice systems as a promising platform for nonequilibrium quantum simulation.

cond-mat.quant-gas↗

arXiv2026

Entropy Signatures of Collective Modes and Vortex Dynamics in Rotating Two--Dimensional Bose--Einstein Condensates

We investigate the nonequilibrium dynamics of a two-dimensional rotating Bose gas confined in a symmetric anharmonic trap, employing the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study states ranging from vortex-free configurations to multicharged (giant) vortices, prepared by tuning the rotation frequency, and analyze their response to sudden interaction and trap quenches. In vortex-free states, interaction quenches induce regular breathing--like dynamics, whereas in the presence of giant vortices they lead to symmetry-breaking surface excitations. In contrast, trap deformations that excite quadrupole-like modes produce stable oscillations in vortex-free condensates but trigger rapid, irregular, and effectively chaotic splitting dynamics in multicharged vortices. To characterize these processes beyond conventional density and phase observables, we employ information-theoretic measures, including marginal and joint entropies, mutual information, and Kullback-Leibler (KL) divergence, supplemented by an angular-resolved KL measure that captures symmetry breaking and azimuthal localization. We find that chaotic splitting is accompanied by a pronounced growth of information-theoretic indicators, signaling the buildup of many-body correlations and increasing complexity in the system dynamics. Our results demonstrate the extreme sensitivity of giant vortices to excitation protocols and establish information-theoretic measures as a powerful framework to quantify correlations and complexity in rotating quantum gases.

cond-mat.quant-gas↗

arXiv2025

Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles

We present numerical investigations demonstrating the result that the distribution of the lowest eigenvalue of finite many-boson systems (say we have $m$ number of bosons) with $k$-body interactions, modeled by Bosonic Embedded Gaussian Orthogonal [BEGOE($k$)] and Unitary [BEGUE($k$)] random matrix Ensembles of $k$-body interactions, exhibits a smooth transition from Gaussian like (for $k = 1$) to a modified Gumbel like (for intermediate values of $k$) to the well-known Tracy-Widom distribution (for $k = m$) form. We also provide ansatz for centroids and variances of the lowest eigenvalue distributions. In addition, we show that the distribution of normalized spacing between the lowest and the next lowest eigenvalues exhibits a transition from Wigner's surmise (for $k = 1$) to Poisson (for intermediate $k$ values with $k \le m/2$) to Wigner's surmise (starting from $k = m/2$ to $k = m$) form. We analyze these transitions as a function of $q$ parameter defining $q$-normal distribution for eigenvalue densities.

quant-ph↗

arXiv2023

Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions

We study the mechanism of thermalization in finite many-fermion systems with random $k$-body interactions in presence of a mean-field. The system Hamiltonian $H$, for $m$ fermions in $N$ single particle states with $k$-body interactions, is modeled by mean field one-body $h(1)$ and a random $k$-body interaction $V(k)$ with strength $λ$. Following the recent application of $q$-Hermite polynomials to these ensembles, a complete analytical description of parameter $q$, which describes the change in the shape of state density from Gaussian for $q=1$ to semi-circle for $q=0$ and intermediate for $0<q<1$, and variance of the strength function are obtained in terms of model parameters. The latter gives the thermalization marker $λ_t$ defining the thermodynamic region. For $λ\ge λ_t$, the smooth part of the strength functions is very well represented by conditional $q$-normal distribution ($f_{CN}$), which describes the transition in strength functions from Gaussian to semi-circle as the $k$-body interaction changes from $k = 2$ to $m$ in $H$. In the thermodynamic region, ensemble averaged results for the first four moments of the strength functions and inverse participation ratio (IPR) are found to be in good agreement with the corresponding smooth forms. For higher body rank of interaction $k$, system thermalizes faster.

nlin.CD↗

arXiv2022

Average-fluctuation separation in energy levels in many-particle quantum systems with $k$-body interactions using $q$-Hermite polynomials

Separation between average and fluctuation parts in the state density in many-particle quantum systems with $k$-body interactions, modeled by the $k$-body embedded Gaussian orthogonal random matrices (EGOE($k$)), is demonstrated using the method of normal mode decomposition of the spectra and also verified through power spectrum analysis, for both fermions and bosons. The smoothed state density is represented by the $q$-normal distribution ($f_{qN}$) (with corrections) which is the weight function for $q$-Hermite polynomials. As the rank of interaction $k$ increases, the fluctuations set in with smaller order of corrections in the smooth state density. They are found to be of GOE type, for all $k$ values, for both fermion and boson systems.

quant-ph↗

arXiv2022

Dynamics of order-disorder and complexity for interacting bosons in optical lattice

The present work reports on the dynamical measures of order, disorder and complexity for the interacting bosons in optical lattice. We report results both for the relaxed state as well as quench dynamics. Our key observations are: (1) Lattice depth can be taken as order-disorder parameter. (2) The superfluid to Mott insulator transition can be treated as `order-disorder' transition. Our main motivation is to find how the system organize by itself during quench and how it optimizes the complexity. We find dynamical measures of order and disorder are more sensitive tool than entropy measures. We specifically calculate the time scale of entry and exit of different phases during time evolution. Initially the system exhibits collapse revival trend, however gradually looses its ability to turn back to superfluid phase and finally Settle to Mott insulator phase.

cond-mat.quant-gas↗

arXiv2021

Eigenstate structure in many-body bosonic systems: Analysis using random matrices and $q$-Hermite polynomials

We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus $k$-body random interactions. The quantities employed are the number of principal components (NPC), the localization length ($l_H$) and the entropy production $S(t)$. The numerical results are compared with the analytical formulas obtained using random matrices which are based on bivariate $q$-Hermite polynomials for local density of states $F_k(E|q)$ and the bivariate $q$-Hermite polynomial form for bivariate eigenvalue density $ρ_{biv:q}(E,E_k)$ that are valid in the strong interaction domain. We also compare transport efficiency in many-body bosonic systems using BEGOE in absence and presence of centrosymmetry. It is seen that the centrosymmetry enhances quantum efficiency.

quant-ph↗

arXiv2021

Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles

The probability distribution of the closest neighbor and farther neighbor spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded GOE of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a $3 \times 3$ random matrix model and other related quantities by Srivastava et. al [{\it J. Phys. A: Math. Theor.} {\bf 52} 025101 (2019)]. This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.

cond-mat.stat-mech↗

arXiv2021

Structure of wavefunction for interacting bosons in mean-field with random $k$-body interactions

Wavefunction structure is analyzed for dense interacting many-boson systems using Hamiltonian $H$, which is a sum of one-body $h(1)$ and an embedded GOE of $k$-body interaction $V(k)$ with strength $λ$. In the first analysis, a complete analytical description of the variance of the strength function as a function of $λ$ and $k$ is derived and the marker $λ_t$ defining thermalization region is obtained. In the strong coupling limit ($λ> λ_t$), the conditional $q$-normal density describes Gaussian to semi-circle transition in strength functions as body rank $k$ of the interaction increases. In the second analysis, this interpolating form of the strength function is utilized to describe the fidelity decay after $k$-body interaction quench and also to obtain the smooth form for the number of principal components, a measure of chaos in finite interacting many-particle systems. The smooth form very well describes embedded ensemble results for all $k$ values.

cond-mat.stat-mech↗

arXiv2019

Distribution of Higher Order Spacing Ratios in Interacting Many Particle Systems

We study the distribution of non-overlapping spacing ratios of higher-orders for complex interacting many-body quantum systems, with and without spin degree of freedom (in addition to the particle number). The Hamiltonian of such systems is well represented by embedded one- plus two-body random matrix ensembles (with and without spin degree of freedom) for fermionic as well as bosonic systems. We obtain a very good correspondence between the numerical results and a recently proposed generalized Wigner surmise like scaling relation. These results confirm that the proposed scaling relation is universal in understanding spacing ratios in complex many-body quantum systems. Using spin ensembles, we demonstrate that the higher order spacing ratio distributions can also reveal quantitative information about the underlying symmetry structure.

cond-mat.stat-mech↗

arXiv2017

Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?

We perform a thorough analysis of the spectral statistics of experimental molecular resonances, of bosonic erbium $^{166}$Er and $^{168}$Er isotopes, produced as a function of magnetic field($B$) by Frisch et al. [Nature 507, (2014) 475], utilizing some recently derived surmises which interpolate between Poisson and GOE and without unfolding. Supplementing this with an analysis using unfolded spectrum, it is shown that the resonances are close to semi-Poisson distribution. There is an earlier claim of missing resonances by Molina et al. [Phys. Rev. E 92, (2015) 042906]. These two interpretations can be tested by more precise measurements in future experiments.

cond-mat.stat-mech↗

arXiv2017

Localization-Delocalization Transitions in Bosonic Random Matrix Ensembles

Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one- plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis, considered are bosonic EGOE(1+2) for two-species boson systems with a fictitious ($F$) spin degree of freedom [called BEGOE(1+2)-$F$]. Numerical calculations are carried out as a function of the two-body interaction strength ($λ$). It is shown that, in the region (defined by $λ>λ_c$) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit-Wigner to Gaussian transition for $λ>λ_{F_k}>λ_c$. Further, analyzing information entropy and participation ratio, it is established that there is a region defined by $λ\simλ_t$ where the system exhibits thermalization. The $F$-spin dependence of the transition markers $λ_{F_k}$ and $λ_t$ follow from the propagator for the spectral variances. These results, well tested near the center of the spectrum and extend to the region within $\pm2σ$ to $\pm3σ$ from the center ($σ^2$ is the spectral variance), establish universality of the transitions generated by embedded ensembles. In the second analysis, entanglement entropy is studied for spin-less BEGOE(1+2) ensemble and shown that the results generated are close to the recently reported results for a Bose-Hubbard model.

nlin.CD↗

arXiv2016

Fidelity decay and entropy production in many-particle systems after random interaction quench

We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic(bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin $S$. The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving $S$ for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ($t_{sat}$) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.

cond-mat.stat-mech↗

arXiv2014

Poisson to GOE transition in the distribution of the ratio of consecutive level spacings

Probability distribution for the ratio ($r$) of consecutive level spacings of the eigenvalues of a Poisson (generating regular spectra) spectrum and that of a GOE random matrix ensemble are given recently. Going beyond these, for the ensemble generated by the Hamiltonian $H_λ= (H_0+λV)/\sqrt{1+λ^2}$ interpolating Poisson ($λ=0$) and GOE ($λ\rightarrow \infty$) we have analyzed the transition curves for $\langle r\rangle$ and $\langle \tilde{r}\rangle$ as $λ$ changes from $0$ to $\infty$; $\tilde{r} = min(r,1/r)$. Here, $V$ is a GOE ensemble of real symmetric $d \times d$ matrices and $H_0$ is a diagonal matrix with a Gaussian distribution (with mean equal to zero) for the diagonal matrix elements; spectral variance generated by $H_0$ is assumed to be same as the one generated by $V$. Varying $d$ from 300 to 1000, it is shown that the transition parameter is $Λ\sim λ^2\,d$, i.e. the $\langle r\rangle$ vs $λ$ (similarly for $\langle \tilde{r}\rangle$ vs $λ$) curves for different $d$'s merge to a single curve when this is considered as a function of $Λ$. Numerically, it is also found that this transition curve generates a mapping to a $3 \times 3$ Poisson to GOE random matrix ensemble. Example for Poisson to GOE transition from a one dimensional interacting spin-1/2 chain is presented.

cond-mat.stat-mech↗

arXiv2014

Level spacing statistics and spectral correlations in the diffuse van der Waals clusters

We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution $P(s)$, the level number variance $Σ^2(L)$, and the Dyson-Mehta $Δ_3-$statistics for various cluster sizes. For large clusters we find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to be valid, it does not exhibit true signatures of quantum chaos. However contrasting conjecture of Berry and Tabor is observed with smaller cluster size. For small number of bosons, we observe the existence of large number of quasi-degenerate states in low-lying excitation which exhibits the Shnirelman peak in $P(s)$ distribution. We also find a narrow region of intermediate spectrum which can be described by semi-Poisson statistics whereas the higher levels are regular and exhibit Poisson statistics. These observations are further supported by the analysis of the distribution of the ratio of consecutive level spacings $P(r)$ which is independent of unfolding procedure and thereby provides a tool for more transparent comparison with experimental findings than $P(s)$. Thus our detail numerical study clearly shows that the van der Waals clusters become more correlated with the increase in cluster size.

quant-ph↗

arXiv2013

Probability Distribution of the Ratio of Consecutive Level Spacings in Interacting Particle Systems

We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between the numerical results and the recently derived analytic form for the distribution and other related quantities is found to be close. This establishes conclusively that local level fluctuations generated by embedded ensembles follow the results of classical Gaussian ensembles.

nlin.CD↗