arXiv subjects

Rohit Patil

Publications and source records attributed to Rohit Patil.

9 recordsLinked to original sources

arXiv2026

Random-matrix and transport frequencies in eigenstate spectral functions

The fact that generic isolated many-body quantum systems thermalize is understood using the eigenstate thermalization hypothesis (ETH). In recent years, there has been much interest in the behavior of the ETH spectral functions, which characterize the smooth dependence of the variance of the off-diagonal matrix elements of observables on the associated energy and frequency, and whose low-frequency part contains information about the long-time dynamics. In finite systems described by the ETH, the spectral functions are expected to exhibit plateaus below a characteristic frequency $ω^{}_{\mathrm{ETH}}$. In this regime, the statistics of the matrix elements of observables are expected to be described by random matrix theory. Related frequencies that have been studied in the literature are $ω^{}_{\mathrm{SFF}}$, which controls the onset of random-matrix behavior in the spectral form factor, and the transport frequencies $ω^{}_{\mathrm{tr}}$, which are derived from transport coefficients. However, a direct quantitative comparison of these frequencies is lacking. Using exact diagonalization, we conduct such a comparison for the spectral functions of current operators in clean and disordered quantum spin ladders with diffusive energy and spin transport. We find clear evidence for the expected low-frequency plateaus in the ETH spectral functions. For the accessible system sizes, $ω^{}_{\mathrm{SFF}}$ is consistent with the extent of the plateaus, while the transport frequencies are systematically larger and lie in the nonuniversal regime of the spectral functions. Our findings highlight the need to better understand the origin of these quantitative differences.

cond-mat.stat-mech↗

arXiv2026

Eigenstate thermalization for local versus translationally invariant observables

Local observables and their translationally invariant counterparts are generally thought to provide the same predictions for experiments. While this equivalence holds for expectation values in clean systems (up to finite-size effects), it is often assumed to extend to correlation functions, where it need not hold. We examine this assumption from the perspective of the eigenstate thermalization hypothesis. Specifically, we explore the spectral functions of local and translationally invariant observables in the spin-1 tilted-field Ising chain with periodic and open boundary conditions. We identify the contexts in which these observables and boundary conditions differ and those in which they are interchangeable. We unveil an off-diagonal eigenstate thermalization in translationally invariant systems for matrix elements between energy eigenstates with different quasimomenta.

quant-ph↗

arXiv2026

Eigenstate thermalization

We provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate eigenstate thermalization using random matrix theory and discuss recent complementary results for the volume-law entanglement entropy of Haar-random states. We discuss numerical results that highlight the corresponding behaviors in quantum many-body systems.

quant-ph↗

arXiv2025

Computational Economics in Large Language Models: Exploring Model Behavior and Incentive Design under Resource Constraints

Large language models (LLMs) are limited by substantial computational cost. We introduce a "computational economics" framework that treats an LLM as an internal economy of resource-constrained agents (attention heads and neuron blocks) that must allocate scarce computation to maximize task utility. First, we show empirically that when computation is scarce, standard LLMs reallocate attention toward high-value tokens while preserving accuracy. Building on this observation, we propose an incentive-driven training paradigm that augments the task loss with a differentiable computation cost term, encouraging sparse and efficient activations. On GLUE (MNLI, STS-B, CoLA) and WikiText-103, the method yields a family of models that trace a Pareto frontier and consistently dominate post-hoc pruning; for a similar accuracy we obtain roughly a forty percent reduction in FLOPS and lower latency, together with more interpretable attention patterns. These results indicate that economic principles offer a principled route to designing efficient, adaptive, and more transparent LLMs under strict resource constraints.

cs.CL↗

arXiv2025

Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry

We study the diagonal and off-diagonal matrix elements of observables in the eigenstates of the extended spin-$\frac{1}{2}$ Heisenberg chain, which exhibits the non-Abelian SU(2) symmetry. We explore integrable and nonintegrable regimes, and consider observables that preserve the SU(2) symmetry of the Hamiltonian as well as observables that break it. We study in detail the low-frequency behavior of the off-diagonal matrix elements at and away from integrability. In the nonintegrable regime, we test the non-Abelian eigenstate thermalization hypothesis, paying special attention to the effect of the spin, which is the distinctive conserved quantity introduced by the SU(2) symmetry.

quant-ph↗

arXiv2024

Typical entanglement entropy in systems with particle-number conservation

We calculate the typical bipartite entanglement entropy $\langle S_A\rangle_N$ in systems containing indistinguishable particles of any kind as a function of the total particle number $N$, the volume $V$, and the subsystem fraction $f=V_A/V$, where $V_A$ is the volume of the subsystem. We expand our result as a power series $\langle S_A\rangle_N=a f V+b\sqrt{V}+c+o(1)$, and find that $c$ is universal (i.e., independent of the system type), while $a$ and $b$ can be obtained from a generating function characterizing the local Hilbert space dimension. We illustrate the generality of our findings by studying a wide range of different systems, e.g., bosons, fermions, spins, and mixtures thereof. We provide evidence that our analytical results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems, which is distinct from that of integrable counterparts.

quant-ph↗

arXiv2023

Average pure-state entanglement entropy in spin systems with SU(2) symmetry

We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure states. Focusing on the zero total magnetization sector ($J_z=0$) for different fixed total spin $J$, we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient $s_A$ depends on the spin density $j=J/(\mathfrak{j}L)$, with $s_A(j \rightarrow 0)=\ln (2\mathfrak{j}+1)$ and $s_A(j \rightarrow 1)=0$, where $\mathfrak{j}$ is the microscopic spin. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. In the context of Hamiltonian eigenstates we consider spins $\mathfrak{j}=\frac12$ and $1$, while for our calculations based on random pure states we focus on the spin $\mathfrak{j}=\frac12$ case.

quant-ph↗

arXiv2022

SpiroMask: Measuring Lung Function Using Consumer-Grade Masks

According to the World Health Organisation (WHO), 235 million people suffer from respiratory illnesses and four million people die annually due to air pollution. Regular lung health monitoring can lead to prognoses about deteriorating lung health conditions. This paper presents our system SpiroMask that retrofits a microphone in consumer-grade masks (N95 and cloth masks) for continuous lung health monitoring. We evaluate our approach on 48 participants (including 14 with lung health issues) and find that we can estimate parameters such as lung volume and respiration rate within the approved error range by the American Thoracic Society (ATS). Further, we show that our approach is robust to sensor placement inside the mask.

cs.HC↗

arXiv2020

Blind Motion Deblurring through SinGAN Architecture

Blind motion deblurring involves reconstructing a sharp image from an observation that is blurry. It is a problem that is ill-posed and lies in the categories of image restoration problems. The training data-based methods for image deblurring mostly involve training models that take a lot of time. These models are data-hungry i.e., they require a lot of training data to generate satisfactory results. Recently, there are various image feature learning methods developed which relieve us of the need for training data and perform image restoration and image synthesis, e.g., DIP, InGAN, and SinGAN. SinGAN is a generative model that is unconditional and could be learned from a single natural image. This model primarily captures the internal distribution of the patches which are present in the image and is capable of generating samples of varied diversity while preserving the visual content of the image. Images generated from the model are very much like real natural images. In this paper, we focus on blind motion deblurring through SinGAN architecture.

cs.CV↗