arXiv subjects

Rupak Majumder

Publications and source records attributed to Rupak Majumder.

7 recordsLinked to original sources

arXiv2026

Synchronization with Annealed Disorder and Higher-Harmonic Interactions in Arbitrary Dimensions: When Two Dimensions Are Special

The impact of disorder on collective phenomena depends crucially on whether it is quenched or annealed. In synchronization problems, quenched disorder in higher dimensional Kuramoto models is known to produce unconventional dimensional effects, including a striking odd even dichotomy: synchronization transitions are continuous in even dimensions and discontinuous in odd dimensions. By contrast, the impact of annealed disorder has received comparatively little attention. Here we study a D dimensional Kuramoto model with both fundamental and higher-harmonic interactions under annealed disorder, and develop an arbitrary dimensional center-manifold framework to analyze the nonlinear dynamics near the onset of collective behavior. We show that annealed disorder fundamentally alters the role of dimensionality. With fundamental coupling alone, it completely removes the odd even dichotomy, yielding continuous synchronization transitions with universal mean-field scaling in all dimensions. Higher-harmonic interactions preserve this universality while rendering the synchronization transition tunable between continuous and discontinuous. At the same time, they give rise to a novel, correlation-driven transition between a symmetry-protected incoherent phase and a symmetry broken state lacking global synchronization, which is therefore invisible to the conventional Kuramoto order parameter. This transition is continuous in two dimensions but discontinuous in higher dimensions, revealing an emergent and previously-unrecognized special role of two dimensions.

cond-mat.stat-mech↗

arXiv2026

Stability of Collective Neutrino Oscillations -- A Distributional Approach

We study the stability of collective neutrino oscillations using a distributional approach motivated by the statistical mechanics of Kuramoto synchronization. Treating the ensemble of neutrino flavor polarization vectors in the thermodynamic limit $N\to\infty$, we derive an exact nonlinear Fokker--Planck (continuity) equation for the one-body distribution $F(\vec{\mathbf{S}},ω,t)$ on the flavor sphere. This equation admits a two-parameter family of azimuthally symmetric stationary solutions, whose stability we analyze by linearizing around them. The resulting eigenvalue condition determines the growth or decay rate of small perturbations from \emph{any} initial distribution -- not merely from a state close to full flavor coherence -- thereby going significantly beyond the conventional linear stability analysis of collective modes. In special limits the condition reproduces known synchronization thresholds in the two-beam model, providing a non-trivial check of the framework. We present analytical results for the eigenvalue equation and explore stability phase diagrams for physically relevant frequency distributions.

hep-ph↗

arXiv2026

Analytical approach to subsystem resetting in generalized Kuramoto models

Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are simultaneously reset, recent work has shown that resetting only a subset of degrees of freedom (subsystem resetting) can qualitatively alter collective behavior in interacting many-body systems. In this work, we develop a general theoretical framework for analysing subsystem resetting in Kuramoto-type coupled-oscillator systems. Building on a continued-fraction approach, we derive self-consistent equations for the stationary-state order parameter of the non-reset subsystem, applicable to both noisy and noiseless dynamics and to models with arbitrary interaction harmonics. Using this framework, we systematically investigate how the stationary state and phase transitions depend on the resetting rate, the size of the reset subsystem, and the reset configuration. We show that subsystem resetting can shift or even suppress synchronization transitions, and can give rise to nontrivial features such as re-entrant behavior and restructuring of phase boundaries. In specific cases, including the noiseless Kuramoto model with a Lorentzian frequency distribution, our results recover known analytical predictions and extend them to more general settings. These results establish subsystem resetting as a versatile control protocol for engineering collective dynamics in nonequilibrium interacting systems.

cond-mat.stat-mech↗

arXiv2026

Constructing Non-Hermitian Theories with Tunable Exceptional Points and Controlled State Purification

Exceptional points (EP's) are a hallmark of non-Hermitian quantum systems. We show that momentum-space deformation provides a general design principle for creating and controlling EP's in quadratic many-body Hamiltonians. We identify universal criteria for the momentum sectors to host EP's and the corresponding critical deformation strengths, while revealing that a single momentum-sector EP induces quite remarkably an exponential proliferation of many-body eigenvector coalescences. We further establish EP's as a universal mechanism for purifying arbitrary mixed quantum states, uncovering distinct purification regimes and a fundamental odd-even system-size dichotomy in the thermodynamic limit. Our framework also provides a systematic reverse-engineering protocol for generating short- and long-range, reciprocal and nonreciprocal non-Hermitian quantum matter, together with an explicit Lindblad embedding. These results thus establish momentum-space deformation as a unified route to exceptional-point engineering and controlled design of many-body non-Hermitian quantum systems.

quant-ph↗

arXiv2025

Finite-size fluctuations for stochastic coupled oscillators: A general theory

Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central challenge. We develop a general framework to quantify these finite-size effects in synchronization transitions of generic stochastic, globally-coupled nonlinear oscillators. By applying a center-manifold reduction to the nonlinear stochastic PDE for the single-oscillator distribution in finite systems, we derive a mesoscopic description that yields the complete time evolution of the order parameter in the form of a Langevin equation. In particular, this equation provides the first closed-form steady-state distribution of the order parameter, fully capturing finite-size effects. Free from integrability constraints and the celebrated Ott-Antonsen ansatz, our theory shows excellent agreement with simulations across diverse coupling functions and frequency distributions, demonstrating broad applicability. Strikingly, it surpasses recent approaches near criticality and in the incoherent phase, where finite-size fluctuations are most pronounced.

cond-mat.stat-mech↗

arXiv2025

Manipulating phases in many-body interacting systems with subsystem resetting

Stabilizing thermodynamically unstable phases in many-body systems, such as suppressing pathological neuronal synchronization in Parkinson's disease or maintaining magnetic order across broad temperature ranges, remains a persistent challenge. In traditional approaches, such phases are stabilized through intervening in the dynamics of all system constituents or introducing additional interactions. Here, we offer a hitherto-unexplored alternative, namely, subsystem resetting, whereby intervention in the dynamics of only a part of the system, and that too only occasionally in time, is implemented through resetting its state to a reset configuration. Just playing with a few parameters, e.g., the nature of the reset configuration and the size of the reset subsystem, one achieves a remarkable and robust control over the phase diagram of the bare dynamics. We demonstrate that these universal effects span a wide variety of scenarios, including equilibrium and non-equilibrium, mean-field and non-mean-field dynamics, with and without quenched disorder. Despite the challenges posed by memory effects, we obtain explicit analytical predictions, validated by simulations.

cond-mat.stat-mech↗

arXiv2024

Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it

We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with simultaneous resets at random times, while the remaining constituents evolve solely under the bare dynamics. We pursue our investigation within the ambit of the well-known Kuramoto model of coupled phase-only oscillators of distributed natural frequencies. Here, the reset protocol corresponds to a chosen set of oscillators being reset to a synchronized state at random times. We find that the mean $ω_0$ of the natural frequencies plays a defining role in determining the long-time state of the system. For $ω_0=0$, the system reaches a synchronized stationary state at long times, characterized by a time-independent non-zero value of the synchronization order parameter. Moreover, we find that resetting even an infinitesimal fraction of the total number of oscillators has the drastic effect of synchronizing the entire system, even when the bare evolution does not support synchrony. By contrast, for $ω_0 \ne 0$, the dynamics allows at long times either a synchronized stationary state or an oscillatory synchronized state, with the latter characterized by an oscillatory behavior as a function of time of the order parameter, with a non-zero time-independent time average. Our results thus imply that the non-reset subsystem always gets synchronized at long times through the act of resetting of the reset subsystem. Our results, analytical using the Ott-Antonsen ansatz as well as those based on numerical simulations, are obtained for two representative oscillator frequency distributions, namely, a Lorentzian and a Gaussian. We discuss how subsystem resetting may be employed as an efficient mechanism to control attainment of global synchrony.

cond-mat.stat-mech↗