arXiv subjects

Pallab Basu

Publications and source records attributed to Pallab Basu.

At least 19 recordsLinked to original sources

arXiv2026

Analytic Spread Complexity from Level Statistics: From Chaos to Integrability

Spread complexity has emerged as a useful probe of quantum chaos, yet the microscopic spectral origin of its characteristic finite-time peak remains incompletely understood. We develop an analytic framework that relates spread complexity directly to local spectral statistics. Starting from an energy-space representation of the Krylov kernel, we show that the kernel is approximately banded, leading to a rapidly convergent diagonal expansion dominated by nearby levels in the ordered spectrum. Motivated by this structure, we propose an approximate kernel-universality hypothesis: after unfolding, the Krylov kernel is well approximated by that of a uniform lattice. Combining this universal kernel with local spectral statistics yields a simple analytic expression for spread complexity in terms of the Fourier transforms of the $k$-th nearest-neighbour spacing distributions. In particular, at leading order, the finite-time peak is controlled by the Fourier transform of the nearest-neighbour spacing distribution. The resulting framework describes both chaotic random-matrix ensembles and the integrable Poisson limit, identifies the spectral origin of the complexity peak and its late-time behaviour, and provides a direct connection between Krylov dynamics and spectral statistics.

hep-th↗

arXiv2025

Complexity of Quadratic Quantum Chaos

We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the corresponding hard-core boson models exhibit genuinely chaotic dynamics, closely paralleling the Sachdev-Ye-Kitaev (SYK) model in its spin representation. This chaotic behavior is diagnosed through spectral statistics and measures of operator growth, including Krylov complexity and the late-time decay of higher-order out-of-time-ordered correlators (OTOCs); the latter reveals the emergence of freeness in the sense of free probability. Moreover, the fractal dimension and Stabilizer Renyi entropy of a representative mid-spectrum eigenstate show finite-size deviations yet converge toward Haar-randomness as the system size increases. This convergence, constrained by local interactions, highlights the "weakly chaotic" character of these eigenstates. Owing to its simplicity and bosonic nature, these minimal models may constitute promising and resource-efficient candidates for probing quantum chaos and information scrambling on near-term quantum devices.

hep-th↗

arXiv2025

An Analytic Zeta Function Ramp at the Black Hole Thouless Time

Black hole normal modes have intriguing connections to logarithmic spectra, and the spectral form factor (SFF) of $E_n = \log n$ is the mod square of the Riemann zeta function (RZF). In this paper, we first provide an analytic understanding of the dip-ramp-plateau structure of RZF and show that the ramp at $\beta \equiv \Re(s)=0$ has a slope precisely equal to 1. The $s=1$ pole of RZF can be viewed as due to a Hagedorn transition in this setting, and Riemann's analytic continuation to $\Re(s)< 1$ provides the quantum contribution to the truncated $\log n$ partition function. This perspective yields a precise definition of RZF as the ''full ramp after removal of the dip'', and allows an unambiguous determination of the Thouless time. For black hole microstates, the Thouless time is expected to be $\mathcal{O}(1)$--remarkably, the RZF also exhibits this behavior. To our knowledge, this is the first black hole-inspired toy model that has a demonstrably $\mathcal{O}(1)$ Thouless time. In contrast, it is $\mathcal{O}(\log N)$ in the SYK model and expected to be $\mathcal{O}(N^{\#})$ in supergravity fuzzballs. We trace the origins of the ramp to a certain reflection property of the functional equation satisfied by RZF, and suggest that it is a general feature of $L$-functions--we find evidence for ramps in large classes of $L$-functions. As an aside, we also provide an analytic determination of the slopes of (non-linear) ramps that arise in power law spectra using Poisson resummation techniques.

hep-th↗

arXiv2023

On the Observer Dependence of the Quantum Effective Potential

In this short paper, we investigate the consequences of observer dependence of the quantum effective potential for an interacting field theory. Specializing to $d+2$ dimensional Euclidean Rindler space, we develop the formalism to calculate the effective potential. While the free energy diverges due to the presence of the Rindler horizon, the effective potential, which is a local function of space, is finite after the necessary renormalization procedure. We apply the results of our formalism to understand the restoration of spontaneously broken $\mathbb{Z}_2$ symmetry in three and four dimensions.

hep-th↗

arXiv2023

On Aspects of Spontaneous Symmetry Breaking in Rindler and Anti-de Sitter spacetimes for the $O(N)$ Linear Sigma Model

We investigate aspects of spontaneous breakdown of symmetry for $O(N)$ symmetric linear sigma model in the background of Rindler and Anti-de Sitter spacetimes respectively. In the large $N$ limit, by computing the one-loop effective action, we report that in three dimensional Rindler space, there is a phase transition from the disordered phase to an ordered phase past a certain critical Rindler acceleration parameter `$a$'. Connections with finite temperature field theory results are established, thereby further reinforcing the idea that Rindler space can indeed be a proxy for Minkowski spacetime with finite temperature. We extend our calculations to Anti-de Sitter space in various dimensions and observe that symmetry is broken in three dimensions, but not in four dimensions. We discuss the implications of our results.

hep-th↗

arXiv2022

Machine learning of Ising criticality with spin-shuffling

We investigate the performance of neural networks in identifying critical behaviour in the 2D Ising model with next-to-nearest neighbour interactions. We train DNN and CNN based classifiers on the Ising model configurations with nearest neighbour interactions and test the ability of our models to identify the critical (cross-over) region, as well as the phases in the presence of next-to-nearest neighbour interactions. Our main objective is to investigate whether our models can learn the notion of criticality and universality, in contrast to merely identifying the phases by simply learning the value of the order parameter, magnetization in this case. We design a simple adversarial training process which forces our models to ignore learning about the order parameter while training. We find that such models are able to identify critical region with reasonable success, implying that it has learned to identify the structure of spin-spin correlations near criticality.

cond-mat.stat-mech↗

arXiv2021

Incomplete RG: Hawking-Page transition, C-theorem and relevant scalar deformations of global AdS

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS$_4$ with its spatially compact boundary $S^2$. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with $m^2 = -2$. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant ($\Lambda$) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

hep-th↗

arXiv2020

Amortized Probabilistic Detection of Communities in Graphs

Learning community structures in graphs has broad applications across scientific domains. While graph neural networks (GNNs) have been successful in encoding graph structures, existing GNN-based methods for community detection are limited by requiring knowledge of the number of communities in advance, in addition to lacking a proper probabilistic formulation to handle uncertainty. We propose a simple framework for amortized community detection, which addresses both of these issues by combining the expressive power of GNNs with recent methods for amortized clustering. Our models consist of a graph representation backbone that extracts structural information and an amortized clustering network that naturally handles variable numbers of clusters. Both components combine into well-defined models of the posterior distribution of graph communities and are jointly optimized given labeled graphs. At inference time, the models yield parallel samples from the posterior of community labels, quantifying uncertainty in a principled way. We evaluate several models from our framework on synthetic and real datasets, and demonstrate improved performance compared to previous methods. As a separate contribution, we extend recent amortized probabilistic clustering architectures by adding attention modules, which yield further improvements on community detection tasks.

stat.ML↗

arXiv2019

A holographic superconductor forced through interactions

We propose a novel mechanism to achieve superconductivity at zero chemical potential, within the holographic framework. Extending previous construction of the holographic superconductors, we consider an Einstein-Maxwell system coupled with two interacting scalars in Anti-de Sitter space. One of the scalar fields is charged and therefore, interacts non-trivially with the gauge field, while the other is uncharged. We find that, if we turn on a boundary source for the uncharged scalar field, it forces the condensation of the charged scalar, leading to a superconducting phase in the dual boundary theory. The condensation occurs at a certain critical value of the source, depending on the value of the chemical potential, which can even be zero. We work out the complete phase diagram of this scenario. We further corroborate the existence of superconductivity at zero chemical potential, through a fluctuation analysis on our solution. Notably, the conductivity of the system, as a function of probing frequency, exhibits characteristics of usual holographic superconductors. We also investigate how these properties of the system changes, as we vary the interaction strength between the scalar fields. Our results indicate a controlled mechanism to manipulate the phase transition temperature of superconductors with strongly coupled microscopics.

hep-th↗

arXiv2018

Anticipation: an effective evolutionary strategy for a sub-optimal population in a cyclic environment

We built a two-state model of an asexually reproducing organism in a periodic environment endowed with the capability to anticipate an upcoming environmental change and undergo pre-emptive switching. By virtue of these anticipatory transitions, the organism oscillates between its two states that is a time $\theta$ out of sync with the environmental oscillation. We show that an anticipation-capable organism increases its long-term fitness over an organism that oscillates in-sync with the environment, provided $\theta$ does not exceed a threshold. We also show that the long-term fitness is maximized for an optimal anticipation time that decreases approximately as $1/n$, $n$ being the number of cell divisions in time $T$. Furthermore, we demonstrate that optimal "anticipators" outperforms "bet-hedgers" in the range of parameters considered. For a sub-optimal ensemble of anticipators, anticipation performs better to bet-hedging only when the variance in anticipation is small compared to the mean and the rate of pre-emptive transition is high. Taken together, our work suggests that anticipation increases overall fitness of an organism in a periodic environment and it is a viable alternative to bet-hedging provided the error in anticipation is small.

q-bio.PE↗

arXiv2018

Higher point OTOCs and the bound on chaos

By extending methods of arXiv:1503.01409, we investigate the bound on the growth of higher point OTOCs by studying their complex analytical properties. We explore some subtleties in our mathematical investigation, and carefully examine the physical interpretation of our result. We also touch upon the possibility of the saturation of the bound in a physical system. Finally, we consider few known examples of higher point OTOCs. For the simplest case of $2n$-point Tremolo correlators the bound on the exponent is proportional to $n$.

hep-th↗

arXiv2018

Complex Langevin Dynamics in Large $N$ Unitary Matrix Models

Using complex Langevin dynamics we examine the phase structure of complex unitary matrix models and compare the numerical results with analytic results found at large $N$. The actions we consider are manifestly complex, and thus the dominant contribution to the path integral comes from the space of complexified gauge field configuration. For this reason, the eigenvalues of unitary matrix lie off the unit circle and venture out in the complex plane. One example of a complex unitary matrix model, with Polyakov line as the unitary matrix, is an effective description of a QCD at finite density and temperature with $N$ number of colors and $N_f$ number of quark flavors defined on the manifold $S^1 \times S^3$. A distinct feature of this model, the occurrence of a series of Gross-Witten-Wadia transitions, as a function of the quark chemical potential, is reproduced using complex Langevin simulations. We simulate several other observables including Polyakov lines and quark number density, for large $N$ and $N_f$ and found excellent match with the analytic results.

hep-th↗

arXiv2017

Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential

In this paper, we study the finite-temperature matrix quantum mechanics with chemical potential term linear in the single trace of U(N) matrices, via Monte Carlo simulation. In the bosonic case, we exhibit the existence of the Gross-Witten-Wadia (GWW) type third-order phase transition. We also extend our studies to the model with the fermionic degrees of freedom employing the non-lattice simulation via Fourier expansion, and explore the possibilities that there is a phase transition between the gapped and ungapped phase both in the absence and presence of the chemical potential term. We make a comparison of the phase diagram between the bosonic and fermionic cases.

hep-th↗

arXiv2017

On thermality of CFT eigenstates

The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operators in (1+1)-$d$ conformal field theories, consisting of quasi-primaries of the identity module, which satisfy the hypothesis only at the leading order in large central charge. In the context of subsystem ETH, this plays a role in the deviation of the reduced density matrices, corresponding to a finite energy density eigenstate from its hypothesized thermal approximation. The universal deviation in terms of the square of the trace-square distance goes as the 8th power of the subsystem fraction and is suppressed by powers of inverse central charge ($c$). Furthermore, the non-universal deviations from subsystem ETH are found to be proportional to the heavy-light-heavy structure constants which are typically exponentially suppressed in $\sqrt{h/c}$, where $h$ is the conformal scaling dimension of the finite energy density state. We also examine the effects of the leading finite size corrections.

hep-th↗

arXiv2016

Hairy Black Holes in a Box

We do a systematic study of the phases of gravity coupled to an electromagnetic field and charged scalar in flat space, with box boundary conditions. The scalar-less box has previously been investigated by Braden, Brown, Whiting and York (and others) before AdS/CFT and we elaborate and extend their results in a language more familiar from holography. The phase diagram of the system is analogous to that of AdS black holes, but we emphasize the differences and explain their origin. Once the scalar is added, we show that the system admits both boson stars as well as hairy black holes as solutions, providing yet another way to evade flat space no-hair theorems. Furthermore both these solutions can exist as stable phases in regions of the phase diagram. The final picture of the phases that emerges is strikingly similar to that found recently for holographic superconductors in global AdS, arXiv: 1602.07211. Our construction lays bare certain previously unnoticed subtleties associated to the definition quasi-local charges for gravitating scalar fields in finite regions.

hep-th↗

arXiv2016

Chaotic dynamics of strings in charged black hole backgrounds

We study the motion of a string in the background of Reissner-Nordstrom black hole, in both AdS as well as asymptotically flat spacetimes. We describe the phase space of this dynamical system through largest Lyapunov exponent, Poincare sections and basins of attractions. We observe that string motion in these settings is particularly chaotic and comment on its characteristics.

hep-th↗

arXiv2016

Phases of Global AdS Black Holes

We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime ($AdS_4$) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.

hep-th↗

arXiv2015

$ε$-Expansions Near Three Dimensions from Conformal Field Theory

We formally extend the CFT techniques introduced in arXiv:1505.00963, to $ϕ^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-ε$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a similar analysis of the $O(N)$ model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the $ϕ^3$ theory in $d_0=6$ is qualitatively different.

hep-th↗