arXiv subjects

M. S. Santhanam

Publications and source records attributed to M. S. Santhanam.

At least 19 recordsLinked to original sources

arXiv2026

Determining the Number of Symmetry Sectors in Composite Quantum Spectra

The spectral fluctuations in complex quantum systems are modeled in terms of spectra from random matrices. Quantitative agreement with random matrices holds only when the quantum spectrum is a pure sequence, and not a composite spectrum that mixes levels from different symmetry sectors. It was shown earlier that discrete symmetries in composite spectra can be detected using higher-order spacing ratio statistics provided the symmetry sectors are of equal dimensions. The general case is when the symmetry sectors have unequal dimensions, and the symmetries of the Hamiltonian system are unknown or only partially known. In this work, we address how the number of symmetry sectors can be determined from a composite spectrum arising in Hermitian and non-Hermitian settings. A Best Subset Technique is proposed for determining the number of the symmetry sectors by comparing the spectral fluctuations to that of an appropriate random matrix ensemble without requiring de-symmetrization. It is demonstrated using spectra from Gaussian, Wishart and Ginibre ensembles, and also for spectra drawn from many-body quantum systems.

quant-ph↗

arXiv2026

Localization with Hopping Disorder in a Quasiperiodic Synthetic Momentum Lattice

Quasiperiodicity is easily realized with ultracold atoms in optical lattices and has been used to simulate the delocalization-localization transition. Random local potentials can also be implemented by spatial light modulators. Programmable hopping disorder, however, remains difficult to realize in conventional optical lattices. Momentum-space lattice (MSL) offers a platform to address this. We implement the MSL using an $^{87}$Rb Bose-Einstein condensate via multiple Bragg diffraction and benchmark the platform by simulating wavepacket dynamics with hopping disorder on top of the generalized Aubry-André (GAA) model. We test programmable hopping disorder added to localized/delocalized backgrounds tunable by the Aubry-André potential strength, as well as systems with mobility edges. Uncorrelated hopping disorder smooths the AA transition into a crossover between weakly (large localization lengths) and strongly localized regimes; the resulting enhancement in localization suppresses wavepacket spreading. We also implement spatially correlated hopping disorder and compare its dynamics with uncorrelated disorder of the same final width, demonstrating a correlation-induced enhancement in spreading. Measured dynamics agrees with trends from ideal tight-binding simulations. Trends in non-universal features depending on microscopic structure and short-time dynamics as functions of quasiperiodic potential strength, hopping-disorder strength, and GAA deformation also match numerical results, with better agreement at larger hopping-disorder strengths. Numerical simulations of the MSL dynamics provide insights into sources of corrections. Our results demonstrate that MSL provides a versatile platform for realizing general disordered quantum systems with programmable hopping amplitudes beyond quasiperiodic models.

cond-mat.quant-gas↗

arXiv2026

Quantum resonance based encryption protocol with quantum kicked top

We propose a genuine quantum protocol for protecting user's data, either in a shared quantum computer or in a quantum communication system, that is not accessible even to the service provider. The protocol is based on quantum kicked top -- the dynamics of a spin system -- operating in the regime of quantum resonance. This protocol ensures perfect recovery for authorized users while making intercepted states appear mixed to eavesdroppers, with built-in tampering detection. This protocol can be used for secure communication between two parties in geographically different locations, and also for quantum key distribution. The effectiveness of this protocol is demonstrated by assuming a quantum computer with quantum memory and functioning quantum networks. In the absence of the latter, at present, the protocol can be demonstrated in a laboratory using currently available quantum computing platforms.

quant-ph↗

arXiv2026

Probing Chaos and Criticality with Observational Entropy and Finite-Resolution Measurements

Coarse-grained measurements offer a scalable alternative to full state tomography for characterizing complex quantum dynamics. We show that observational entropy (OE), an information-theoretic entropy defined directly from finite-resolution measurement outcomes, provides a unified and experimentally accessible framework for quantifying chaos and probing criticality. From probing the insulator-metal crossover in the Aubry-Andre model to tracking the gradual destruction of Kolmogorov-Arnold-Moser tori in the Kicked Rotor, derivatives of OE provide an accurate and unified diagnostic of probing these transitions. In both cases, the critical points extracted from dynamical evolution and eigenstate analyses converge to the exact theoretical values once the observational resolution exceeds a finite threshold. In the chaotic limit, OE exhibits a linear behavior within the Ehrenfest time regime, and its slope defines an observable Lyapunov exponent. Using a Pretty Good Measurement correction to the Husimi phase-space distribution, this entropy-production rate quantitatively reproduces the classical Lyapunov exponent in both the standard and singular kicked rotors. Our results establish OE as a compact information-theoretic bridge between classical instability, quantum criticality, and realistic finite-resolution measurements.

quant-ph↗

arXiv2026

Approach to network failure due to intrinsic fluctuations

A networked system can fail when most of its components are unable to support flux through the nodes and edges. As studied earlier this scenario can be triggered by an external perturbation such as an intentional attack on nodes or for internal reasons such as due to malfunction of nodes. In either case, the asymptotic failure of the network is preceded by a cascade of nodal failures. In this work, we focus on the nodal failure arising from the intrinsic fluctuations in the flux passing through the nodes. By modeling these as extreme events, it is shown that three distinct nodal failure regimes can be identified before a complete network failure takes place. Further, the approach to network failure through the three regimes is shown to be qualitatively similar on a square lattice, all-to-all, scale free, and Erdos-Renyi networks. We obtain approximate analytical description of the approach to failure for an all-to-all network. This is also demonstrated numerically for real transportation network of flights.

cond-mat.stat-mech↗

arXiv2026

Upper bounds on charging power and tangible advantage in quantum batteries

Quantum battery is expected to outperform its classical counterpart due to quantum effects. Usually, in a quantum battery made of $N$ cells, quantum advantage is demonstrated through super-extensive scaling of the upper bound to the charging power with $N$. In this work, we show that potential quantum advantage as measured by the power bounds need not translate to {\it tangible} advantage in practice. We demonstrate this by considering an all-to-all coupled spin-chain model of a quantum battery with 2-local interactions. It exhibits super-extensive charging when analyzed using the upper bound derived from the uncertainty principle. Unlike the previously studied models, the contribution to this apparent quantum advantage is two-fold -- arising from both the battery and the charger. The model is also experimentally friendly, as it does not require global couplings and yet generates genuine multipartite entanglement. However, we demonstrate that the potential quantum advantage in this scenario is not tangible by employing a tighter upper bound on power. Additionally, we show that even this tighter bound can fail in a range of physical situations and indicate a quantum enhancement that is intangible in practice. Hence, we argue that actual power transferred must be evaluated along with proper characterization of the resources before claiming quantum advantage.

quant-ph↗

arXiv2025

Periodicity of dynamical signatures of chaos in quantum kicked top

A host of dynamical measures of quantum correlations -- out-of-time ordered correlators (OTOC), Loschmidt echo, generalized entanglement and observational entropy -- are useful to infer the underlying classical chaotic dynamics in quantum regime. In this work, these measures are employed to analyse quantum kicked top with kick strength $k$. It is shown that, despite the differences in their definitions, these measures are periodic with $k$, and the periodicity depends on the number of spins represented by the kicked top. The periodic behaviour arises from the structure of the kicked top Floquet operator and spans the regime in which the corresponding classical dynamics is predominantly chaotic. We also point to the reflection symmetry in Loschmidt echo and a special case of time periodicity in OTOC. This result can guide experiments towards the right choice of kick strengths to avoid repetitive dynamics.

quant-ph↗

arXiv2025

Congestion and extreme events in urban street networks

Congestion and extreme events in transportation networks are emergent phenomena with significant socio-economic implications. In this work, we study congestion and extreme event properties on real urban street (planar) networks drawn from four cities and compare it with that on a regular square grid. For dynamics, we employ three variants of random walk with additional realistic transport features. In all the four urban street networks and 2D square grid and with all dynamical models, phase transitions are observed from a free flow to congested phase as a function of birth rate of vehicles. These transitions can be modified by traffic-aware routing protocols, but congestion cannot be entirely mitigated. In organically evolved street networks, we observe a semi-congested regime which has both congested and free-flow components. In the free-flow regime, the extreme event occurrence probability is larger for small degree nodes than for hubs, a feature originally observed in non-planar scale-free networks. In general, with respect to congestion and extreme events, the urban street networks and regular square grid display similar properties.

physics.soc-ph↗

arXiv2025

Probing the localization effects in Krylov basis

Krylov complexity (K-complexity) is a measure of quantum state complexity that minimizes wavefunction spreading across all the possible bases. It serves as a key indicator of operator growth and quantum chaos. In this work, K-complexity and Arnoldi coefficients are applied to probe a variety of localization phenomena in the quantum kicked rotor system. We analyze four distinct localization scenarios -- ranging from compact localization effect arising from quantum anti-resonance to a weaker form of power-law localization -- each one exhibiting distinct K-complexity signatures and Arnoldi coefficient variations. In general, K-complexity not only indicates the degree of localization, but surprisingly also of the nature of localization. In particular, the long-time behaviour of K-complexity and the wavefunction evolution on Krylov chain can distinguish various types of observed localization in QKR. In particular, the time-averaged K-complexity and scaling of the variance of Arnoldi coefficients with effective Planck's constant can distinguish the localization effects induced by the classical regular phase structures and the dynamical localization arising from quantum interferences. Further, the Arnoldi coefficient is shown to capture the transition from integrability to chaos as well. This work shows how localization dynamics manifests in the Krylov basis.

quant-ph↗

arXiv2025

Dichotomy in the effect of chaos on ergotropy

The maximum unitarily extractable work from a quantum system -- ergotropy -- is the basic principle behind quantum batteries, a rapidly emerging field. This work studies ergotropy in two quantum chaotic systems, the quantum kicked top and the kicked Ising spin chain, to illustrate the effects of chaotic dynamics. In an ancilla-assisted scenario, chaos enhances ergotropy when the state is known, a consequence of large entanglement production in the chaotic regime. When the state is unknown, we need to at least partially characterize the state using coarse-grained measurements for useful extraction of work. In this case, chaos impedes ergotropy by suppressing information gained from coarse-grained measurements, while entanglement with an ancilla still facilitates ergotropy. In this scenario, we study the interplay between chaos and entanglement and find a sweet spot in the chaos parameter for optimal work. Our results point to the potential of quantum chaos-assisted batteries for better work extraction.

quant-ph↗

arXiv2025

Extreme Events of Quantum Walks on Graphs

Due to the unitary evolution, quantum walks display different dynamical features from that of classical random walks. In contrast to this expectation, in this work, we show that extreme events can arise in unitary dynamics and its properties are qualitatively similar to that of random walks. We consider quantum walks on a ring lattice and a scale-free graph. Firstly, we obtain quantum version of flux-fluctuation relation and use this to define to extreme events on vertices of a graph as exceedences above the mean flux. The occurrence probability for extreme events on scale-free graphs displays a power-law with the degree of vertices, in qualitative agreement with corresponding classical random walk result. For both classical and quantum walks, the extreme event probability is larger for small degree nodes compared to hubs on the graph. Further, it is shown that extreme event probability scales with threshold used to define extreme events.

quant-ph↗

arXiv2025

Voter Turnouts Govern Key Electoral Statistics

Elections, the cornerstone of democratic societies, are usually regarded as unpredictable due to the complex interactions that shape them at different levels. In this work, we show that voter turnouts contain crucial information that can be leveraged to predict several key electoral statistics with remarkable accuracy. Using the recently proposed random voting model, we analytically derive the scaled distributions of votes secured by winners, runner-ups, and margins of victory, and demonstrating their strong correlation with turnout distributions. By analyzing Indian election data -- spanning multiple decades and electoral scales -- we validate these predictions empirically across all scales, from large parliamentary constituencies to polling booths. Further, we uncover a surprising scale-invariant behavior in the distributions of scaled margins of victory, a characteristic signature of Indian elections. Finally, we demonstrate a robust universality in the distribution of the scaled margin-to-turnout ratios.

physics.soc-ph↗

arXiv2024

Universal Statistics of Competition in Democratic Elections

Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge independent of microscopic details. Despite the availability of empirical election data, such universality, valid at all scales, countries, and elections, has not yet been observed. In this work, we propose a parameter-free voting model and analytically show that the distribution of the victory margin is driven by that of the voter turnout, and a scaled measure depending on margin and turnout leads to a robust universality. This is demonstrated using empirical election data from $34$ countries, spanning multiple decades and electoral scales. The deviations from the model predictions and universality indicate possible electoral malpractices. We argue that this universality is a stylized fact indicating the competitive nature of electoral outcomes.

physics.soc-ph↗

arXiv2024

Higher-order gap ratios of singular values in open quantum systems

Understanding open quantum systems using information encoded in its complex eigenvalues has been a subject of growing interest. In this paper, we study higher-order gap ratios of the singular values of generic open quantum systems. We show that $k$-th order gap ratio of the singular values of an open quantum system can be connected to the nearest-neighbor spacing ratio of positions of classical particles of a harmonically confined log-gas with inverse temperature $β'(k)$ where $β'(k)$ is an analytical function that depends on $k$ and the Dyson's index $β=1,2,$ and $4$ that characterizes the properties of the associated Hermitized matrix. Our findings are crucial not only for understanding long-range correlations between the eigenvalues but also provide an excellent way of distinguishing different symmetry classes in an open quantum system. To highlight the universality of our findings, we demonstrate the higher-order gap ratios using different platforms such as non-Hermitian random matrices, random dissipative Liouvillians, Hamiltonians coupled to a Markovian bath, and Hamiltonians with in-built non-Hermiticity.

cond-mat.stat-mech↗

arXiv2024

Asymmetric dynamical localization and precision measurement of BEC micromotion

We employ a Bose Einstein Condensate (BEC) based atom-optic kicked rotor to generate an asymmetrically localized momentum distribution that depends upon initial velocity of the BEC. Asymmetric features are shown to arise from the early-time dynamics induced by the broken parity symmetry and, asymptotically freeze as the dynamical localization stabilizes. The asymmetry in the momentum distribution critically depends upon the initial launch velocity and is sensitive to very small initial velocities ('micromotion') of the BEC. In this work, we also perform a precise measurement of the 'micromotion'. By utilizing the technique of measuring the early-time asymmetry of momentum distribution, we report measurement of micromotion down to (230 \pm 17 , μ\text{m/s}).

quant-ph↗

arXiv2024

Amplitude Amplification and Estimation using a Floquet system

The quantum kicked rotor (QKR) is a fundamental model of time-dependent quantum chaos and the physics of Anderson localization. It is one of the most well-studied Floquet systems. In this work, it is shown that QKR can be used to implement a quantum algorithm to perform unstructured search; namely Amplitude Amplification, a generalization of Grover's search algorithm. Further, the QKR is employed for amplitude estimation when the amplitude of the marked states is unknown. It is also shown that the characteristic property of dynamical localization of the QKR can be exploited to enhance the performance of the amplitude amplification algorithm by reducing its average runtime. The sensitivity of the success probability of unstructured search to detuning from resonance and the effects of noisy kick strengths are analyzed and the robustness of the QKR based algorithm is demonstrated. The experimental feasibility of every component of the algorithm is discussed.

quant-ph↗

arXiv2024

Individual and team performance in cricket

Advancements in technology have recently allowed us to collect and analyse large-scale fine-grained data about human performance, drastically changing the way we approach sports. Here, we provide the first comprehensive analysis of individual and team performance in One-Day International cricket, one of the most popular sports in the world. We investigate temporal patterns of individual success by quantifying the location of the best performance of a player and find that they can happen at any time in their career, surrounded by a burst of comparable top performances. Our analysis shows that long-term performance can be predicted from early observations and that temporary exclusions of players from teams are often due to declining performances but are also associated with strong comebacks. By computing the duration of streaks of winning performances compared to random expectations, we demonstrate that teams win and lose matches consecutively. We define the contributions of specialists such as openers, all-rounders and wicket-keepers and show that a balanced performance from multiple individuals is required to ensure team success. Finally, we measure how transitioning to captaincy in the team improves the performance of batsmen, but not that of bowlers. Our work emphasizes how individual endeavours and team dynamics interconnect and influence collective outcomes in sports.

physics.soc-ph↗

arXiv2024

Continuous Gated First-Passage Processes

Gated first-passage processes, where completion depends on both hitting a target and satisfying additional constraints, are prevalent across various fields. Despite their significance, analytical solutions to basic problems remain unknown, e.g. the detection time of a diffusing particle by a gated interval, disk, or sphere. In this paper, we elucidate the challenges posed by continuous gated first-passage processes and present a renewal framework to overcome them. This framework offers a unified approach for a wide range of problems, including those with single-point, half-line, and interval targets. The latter have so far evaded exact solutions. Our analysis reveals that solutions to gated problems can be obtained directly from the ungated dynamics. This, in turn, reveals universal properties and asymptotic behaviors, shedding light on cryptic intermediate-time regimes and refining the notion of high-crypticity for continuous-space gated processes. Moreover, we extend our formalism to higher dimensions, showcasing its versatility and applicability. Overall, this work provides valuable insights into the dynamics of continuous gated first-passage processes and offers analytical tools for studying them across diverse domains.

cond-mat.stat-mech↗