arXiv subjects

Soumya Kanti Pal

Publications and source records attributed to Soumya Kanti Pal.

7 recordsLinked to original sources

arXiv2026

Non-reciprocally interacting Ornstein-Uhlenbeck processes: Exceptional points, Anomalous relaxation, Pseudo-equilibrium and Boundary refrigeration

Non-reciprocal interactions are ubiquitous in active, biological, and disordered systems, generically driving them out of equilibrium. Here, we introduce a hierarchy of non-reciprocally interacting Ornstein-Uhlenbeck (NROU) models governed by a tunable non-reciprocity parameter $g$. At a special point $g=g^*$, the drift matrix becomes non-diagonalizable, realizing exceptional points (EP's) of different orders, where eigenvalues and eigenvectors simultaneously coalesce. The hierarchy encompasses non-reciprocally coupled dimers, their disordered counterparts, and a many-body chain exactly mapping onto the paradigmatic Hatano-Nelson model in the arena of non-Hermitian quantum systems. For the disordered model, we show that the distribution of the EP location $g^*$ across disorder realizations develops a universal edge singularity precisely at the clean-system EP, and is manifestly non-self-averaging. Across all models, we find that at the EP, the usual exponential relaxation of the autocorrelation and covariance functions is dressed by a polynomial-in-time prefactor whose degree is set by the order of the EP and whose detailed structure encodes the spatial architecture of the chain. At complete asymmetry, the many-body chain exhibits ``pseudo-equilibrium'': its steady-state distribution factorizes into equilibrium-like single-particle measures despite a nonzero steady-state current. Moreover, the $N$-particle interacting system decomposes into $N/2$ independent complex OU processes. Finally, using the Harada-Sasa relation, we obtain a closed-form expression for the total steady-state heat dissipation and uncover a boundary refrigeration effect, in which the boundary particles switch from acting as a hot to a cold reservoir as the non-reciprocity is tuned.

cond-mat.stat-mech↗

arXiv2026

Fragmented ETH and Ensemble Inequivalence

We investigate thermalization in finite quantum systems with strong long-range interactions. Nearly conserved quantities inherited from the fully connected limit organize the Hilbert space into weakly coupled sectors and split the many-body spectrum into energy bands. Despite the resulting breakdown of global ergodicity, quantum chaos develops within individual energy bands, enabling the definition of microcanonical ensembles within the bands. This supports a band-resolved formulation of thermalization, which we term fragmented eigenstate thermalization hypothesis (fETH). Unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description has consequences for equilibrium statistical mechanics. While microcanonical ensembles remain confined to a single band, canonical ensembles mix different bands. This mismatch explains ensemble inequivalence without invoking equilibrium phase transitions. Our results apply broadly to Hamiltonians near a fully permutation-symmetric limit.

cond-mat.stat-mech↗

arXiv2026

Observable- and state-selective prethermalization and bounds on prethermal lifetimes

Prethermalization describes long-lived intermediate regimes that precede equilibrium and can dominate experimentally accessible dynamics. Here, we show that a separation of spectral energy scales, despite giving rise to a hierarchy of dynamical timescales, does not by itself guarantee the appearance of a prethermal plateau. Under the same Hamiltonian, some observables may exhibit prethermal behavior, while others relax directly toward equilibrium. We uncover the mechanism governing this selectivity, showing that the emergence of a prethermal plateau depends not only on the Hamiltonian, but also on the observable and the initial state. Our results apply broadly to systems close to a fully permutation-symmetric limit and are illustrated with a long-range interacting spin model. We further prove that the Loschmidt echo provides a lower bound on the prethermal lifetime of any bounded observable whenever the prethermal and exact dynamics are unitary.

quant-ph↗

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↗

arXiv2026

Fragmented eigenstate thermalization versus robust integrability in long-range models

Understanding the stability of integrability in many-body quantum systems is key to controlling dynamics and predicting thermalization. While the breakdown of integrability in short-range interacting systems is well understood, the role of long-range couplings -- ubiquitous and experimentally realizable -- remains unclear. We show that in fully connected models, integrability is either robust or extremely fragile, depending on whether perturbations are non-extensive, extensive one-body, or extensive two-body. In contrast to finite short-range systems, where any of these perturbations can induce chaos at finite strength, in fully connected finite models, chaos is triggered by extensive two-body perturbations and even at infinitesimal strength. Chaos develops within energy bands defined by symmetries, leading to a fragmented realization of the eigenstate thermalization hypothesis and clarifying how microcanonical shells can be constructed in such systems. We also introduce a general symmetry-based framework that explains the stability of integrability.

cond-mat.stat-mech↗

arXiv2026

Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems

Inspired by the avalanche scenario for many-body localization (MBL) instability, we reverse the conventional set-up and ask whether a large weakly-disordered chain can thermalize a smaller, strongly-disordered chain when the composite system evolves unitarily. Using transport as a dynamical probe, we identify three distinct thermalization regimes as a function of the disorder strength of the smaller chain: (i) complete thermalization with self-averaging at weak disorder, (ii) realization-dependent thermalization with strong sample-to-sample fluctuations at intermediate disorder, and (iii) absence of thermalization at strong disorder. We find that for a fixed length of the smaller chain, the non-self-averaging regime broadens with the size of the weakly-disordered chain, revealing a nuanced interplay between disorder and system size. These results highlight how inhomogeneous disorder can induce emergent thermalization thresholds in closed quantum systems, providing direct access to disorder regimes where thermalization or its absence can be reliably observed.

cond-mat.stat-mech↗

arXiv2025

Canonical equilibrium of mean-field $O(n)$~models in the presence of random fields

We study canonical-equilibrium properties of Random Field $O(n)$ Models involving classical continuous vector spins of $n$ components with mean-field interactions and subject to disordered fields acting on individual spins. To this end, we employ two complementary approaches: the mean-field approximation, valid for any disorder distribution, and the replica trick, applicable when the disordered fields are sampled from a Gaussian distribution. On the basis of an exact analysis, we demonstrate that when replica symmetry holds, both the approaches yield identical expression for the free energy per spin of the system. As consequences, we study the case of $n=2$ ($XY$ spins) and that of $n=3$ (Heisenberg spins) for two representative choices of the disorder distribution, namely, a Gaussian and a symmetric bimodal distribution. For both $n=2$ and $n=3$, we demonstrate that while the magnetization exhibits a continuous phase transition as a function of temperature for the Gaussian case, the transition could be either continuous or first-order with an emergent tricriticality when the disorder distribution is bimodal. We also discuss in the context of our models the issue of self-averaging of extensive variables near the critical point of a continuous phase transition.

cond-mat.stat-mech↗