arXiv subjects

Ritam Basu

Publications and source records attributed to Ritam Basu.

7 recordsLinked to original sources

arXiv2026

The Information Content of Krylov Observables: A Machine Learning Approach

We employ machine learning to quantify the information carried by three Krylov-space observables: the spread complexity $\mathcal{C}(t)$, the discrete Wigner negativity $N(t)$, and the normalized negativity $\chi(t)=N(t)/|S(t)|$, with $S(t)$ the survival amplitude, recently proposed as a second-moment infall probe (arXiv:2607.04065). Small residual networks (16-32 neurons) and boosted trees are trained on half of $\sim 57{,}000$ labeled evolutions spanning the GUE, GOE and Poisson ensembles, the integrable $SL(2,\mathbb{R})$/CFT sector, and the chaos interpolation $H(\varepsilon)=H_{SL(2,\mathbb{R})}+\varepsilon R_0 W_{GUE}$. Either moment determines the thermofield temperature at $R^2\simeq 0.999$. Neither reconstructs the fine spectral form factor ($R^2\simeq 0.18$ in every ensemble); smoothing the target does not repair this, and windows wide enough to help erase the dip-ramp physics itself: the SFF strictly refines both moments. The coarse $e^S$ plateau is nevertheless recovered at $R^2=0.861$, mostly from the first 20% of $\mathcal{C}(t)$. A single curve identifies the symmetry class at up to 98% accuracy. In the integrable sector the observables are informationally equivalent, as exact negative-binomial slaving demands, while the negativity best resolves the $(h,\alpha)$ degeneracy ($N\to h$: 0.999). Along the interpolation the asymmetry gap of $\chi$ over $\mathcal{C}$ switches on with chaos, growing from +0.33 to +0.77 as the level statistics cross to GUE, while the raw-$N$ gap decays to zero. The second-moment informational surplus is therefore a signature of chaos, carried specifically by the normalized negativity, and we derive an analytical mechanism and a quantitative bound for it.

hep-th↗

arXiv2026

The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$

In spread complexity, the average position of an operator along its Krylov chain, recovers the right radial momentum of an infalling particle in AdS, yet it is a measure of the first moment, irrespective of the spread of the wavepacket away from its classical trajectory. The rate of a normalized Krylov-Wigner negativity can be proposed as a diagnostic of the second moment of the boundary state that captures this spreading. Starting with the seed-normalized Krylov-Wigner distribution -- that is, the Wigner transform of the descendant cloud, with the decaying return amplitude divided out -- we obtain an analytic Bessel form in the macroscopic limit and compute its total negativity explicitly. Retaining the Bessel variable all the way through, we find that the negativity goes as $\sinh^{4\Delta}(\pi t/\beta)$, while the raw, normalized-state negativity saturates, as dictated by the $O(\sqrt{D})$ bound. Using the exact negative binomial statistics of the Krylov chain, the normalized negativity in late times a fixed power of the second moment of the Krylov wavepacket, $\mathcal{N}(t)\propto\bigl[\mathrm{Var}(n)\bigr]^{\Delta}$, for every dimension $\Delta$. The relation linearizes precisely at $\Delta=1$: only at this dimension does the negativity rate track the growth rate of the Krylov variance, and there, through the momentum dictionary of Caputa et al. [arXiv:2410.23334], the rate becomes the product of the proper radial position and momentum, $\dot{\mathcal{N}}\propto\mathcal{C} P_\rho$, i.e., the rate of the tidal stretch of nearby geodesics falling into the horizon. We comment on the direction for future research, in particular the interpretation of the transverse string size operator in terms of the Krylov number operator through the common $\text{SU}(1,1)$ discrete series.

hep-th↗

arXiv2025

On the stabilizer complexity of Hawking radiation

We study the complexity of Hawking radiation for an evaporating black hole from the perspective of the stabilizer theory of quantum computation. Specifically, we calculate Wigner negativity -- a magic monotone which can be interpreted as a measure of the stabilizer complexity, or equivalently, the complexity of classical simulation -- in various toy models for evaporating black holes. We first calculate the Wigner negativity of Hawking radiation in the PSSY model directly using the gravitational path integral, and show that the negativity is $O(1)$ before the Page transition, but becomes exponentially large past the Page transition. We also derive a universal, information theoretic formula for the negativity which interpolates between the two extremes. We then study the Wigner negativity of radiation in a dynamical model of black hole evaporation. In this case, the negativity shows a sharp spike at early times resulting from the coupling between the black hole and the radiation system, but at late times when the system settles down, we find that the negativity satisfies the same universal formula as in the PSSY model. Finally, we also propose a geometric formula for Wigner negativity in general holographic states using intuition from fixed area states and random tensor networks, and argue that a python's lunch in the entanglement wedge implies a stabilizer complexity which is exponentially large in $\frac{1}{8G_N}$ times the difference between the areas corresponding to the outermost and minimal extremal surfaces.

hep-th↗

arXiv2025

Wigner negativity, random matrices and gravity

Given a choice of an ordered, orthonormal basis for a $D$-dimensional Hilbert space, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents any quantum state as a real, normalized function on a discrete phase space. The Wigner function, in general, takes on negative values, and the amount of negativity in the Wigner function gives an operationally meaningful measure of the complexity of simulating the quantum state on a classical computer. Further, Wigner negativity also gives a lower bound on an entropic measure of spread complexity. In this paper, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. In arXiv:2402.13694, a perturbative argument was given to show that the Krylov basis minimizes the early time growth of Wigner negativity in the large-$D$ limit. Using tools from random matrix theory, here we show that for a generic choice of basis, the Wigner negativity for a classical initial state becomes exponentially large in an $O(1)$ amount of time evolution. On the other hand, we show that in the Krylov basis the negativity grows at most as a power law, and becomes exponentially large only at exponential times. We take this as evidence that the Krylov basis is ideally suited for a dual, semi-classical effective description of chaotic quantum dynamics for large-$D$ at sub-exponential times. For the Gaussian unitary ensemble, this effective description is the $q\to 0$ limit of $q$-deformed JT gravity.

hep-th↗

arXiv2024

Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy

In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy, a measure of the extractable work from a system under unitary evolution monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.

quant-ph↗

arXiv2024

Complexity Growth and the Krylov-Wigner function

For any state in a $D$-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function can, in general, take on negative values, and the amount of negativity in the Wigner function has an operational meaning as a resource for quantum computation. In this note, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. We introduce the Krylov-Wigner function, i.e., the Wigner function defined with respect to the Krylov basis (with appropriate phases), and show that this choice of basis minimizes the early time growth of Wigner negativity in the large $D$ limit. We take this as evidence that the Krylov basis (with appropriate phases) is ideally suited for a dual, semi-classical description of chaotic quantum dynamics at large $D$. We also numerically study the time evolution of the Krylov-Wigner function and its negativity in random matrix theory for an initial pure state. We observe that the negativity rises gradually for a time of $O(D)$ and then saturates close to its upper bound of $\sqrt{D}$.

hep-th↗

arXiv2021

Reappraising Domain Generalization in Neural Networks

Given that Neural Networks generalize unreasonably well in the IID setting (with benign overfitting and betterment in performance with more parameters), OOD presents a consistent failure case to better the understanding of how they learn. This paper focuses on Domain Generalization (DG), which is perceived as the front face of OOD generalization. We find that the presence of multiple domains incentivizes domain agnostic learning and is the primary reason for generalization in Tradition DG. We show that the state-of-the-art results can be obtained by borrowing ideas from IID generalization and the DG tailored methods fail to add any performance gains. Furthermore, we perform explorations beyond the Traditional DG (TDG) formulation and propose a novel ClassWise DG (CWDG) benchmark, where for each class, we randomly select one of the domains and keep it aside for testing. Despite being exposed to all domains during training, CWDG is more challenging than TDG evaluation. We propose a novel iterative domain feature masking approach, achieving state-of-the-art results on the CWDG benchmark. Overall, while explaining these observations, our work furthers insights into the learning mechanisms of neural networks.

cs.LG↗