arXiv subjects

Rathindra Nath Das

Publications and source records attributed to Rathindra Nath Das.

16 recordsLinked to original sources

arXiv2026

Probing weak chaos in $\mathcal N=4$ super Yang-Mills and long-range spin chains

We study signatures of quantum chaos in finite-loop truncations of the planar dilatation operator in the $\mathfrak{su}(2)$ sector of $\mathcal N=4$ super Yang-Mills and its $β$-deformation. These truncations define holographically motivated long-range deformations of the nearest-neighbour XXX spin chain. At one-loop the model is integrable, while the all-loop planar theory is expected to again be integrable. Finite-loop truncations therefore provide a natural setting for investigating how chaotic behaviour emerges between these two integrable limits. We analyse this question using spectral statistics, eigenvector diagnostics and spread complexity. We find that the two- and four-loop truncations develop GOE-like level statistics at sufficiently large coupling but with features characteristic of weak integrability breaking. The integrability breaking at four-loops is weaker than at two-loops and the critical coupling at which chaos occurs is larger, at least for long spin chains. The three-loop truncation does not show the same onset of chaos in the range studied. Eigenvector diagnostics show that the corresponding eigenstates remain less random than GOE vectors, indicating weak ergodicity and multifractality. Finally, we can identify signatures of the eigenvalue and eigenvector chaos in the Krylov-space data. Namely, we demonstrate a correlation of the level spacing statistics with the peak of spread complexity and disorder on the Krylov chain. The delocalisation of the initial state in the Hamiltonian eigenbasis is shown to strongly affect the saturation of complexity. Our results suggest that finite-loop dilatation operators are not generic long-range spin chain Hamiltonians, but already display patterns consistent with the restoration of integrability in the all-loop planar theory.

hep-th↗

arXiv2026

Experimental observation of hyperbolic spacetime dynamics

Understanding quantum dynamics in curved spacetime is a central challenge at the intersection of quantum mechanics and gravity. Anti-de-Sitter (AdS) spacetime plays a pivotal role in the context of the AdS/CFT correspondence, which relates gravitational dynamics in the AdS bulk to a conformal field theory (CFT) living on its boundary. Despite its foundational importance, direct experimental access to dynamical quantum phenomena in Lorentzian AdS spacetime has so far remained out of reach. Here, we report the first experimental emulation of fermionic wave packet dynamics in Lorentzian AdS spacetime using a photonic platform. By mapping the Dirac equation in curved spacetime onto the propagation of light in engineered wave\-guide arrays, we directly observe gravitational confinement of relativistic wave packets and resolve their center-of-mass motion in real time. We identify a characteristic superposition of slow geodesic oscillations governed solely by spacetime curvature and fast Zitterbewegung arising from relativistic particle--antiparticle interference. While the geodesic frequency is independent of fermion mass, the Zitterbewegung frequency exhibits a distinct joint dependence on mass and curvature, revealing a curvature-induced modification of relativistic quantum dynamics. Our results provide the first quantitative experimental access to fermionic bulk dynamics in emulated AdS$_2$ spacetime with Lorentzian signature. This establishes a scalable analog platform that may potentially be used for exploring dynamical aspects of holography.

physics.optics↗

arXiv2026

Probing the Chaos to Integrability Transition in Double-Scaled SYK

We investigate how a thermodynamical first-order phase transition affects the dynamical chaotic behaviour of a given model. To this effect, we analyze the model of Berkooz, Brukner, Jia and Mamroud that interpolates between the double-scaled SYK model and an integrable chord Hamiltonian. This model exhibits a first-order transition, characterized by a kink in the free energy, between the chaotic and quasi-integrable phases, with the branch of subdominant saddles interpolating between them. We characterize the dynamical behavior across the phase diagram using the chord number, Krylov complexity, and operator size. The chord number, which is proportional to the Krylov state complexity in the classical limit, exhibits a discontinuous transition from linear to quadratic growth at the transition point. Similarly, the Krylov operator complexity and the operator size, as scrambling diagnostics, exhibit discontinuous transitions from exponential to quadratic growth. We also discuss a possible holographic interpretation of the model.

hep-th↗

arXiv2026

Integrability breaking in semiclassical strings in Koopman-Krylov space

While very powerful, integrability in semiclassical string solutions is known to be a rare property. Motivated by the need to understand and characterise the large landscape of non-integrable string dynamics, we extend Krylov methods for probing chaos to classical systems. We introduce a Koopman-Krylov framework, formulated in the Koopman-von Neumann description of classical mechanics and implemented via a generator extended dynamic mode decomposition (gEDMD) approximation of the Koopman generator acting on observables. Using this framework, we study how integrability-breaking deformations of integrable string dynamics induce characteristic redistributions of spectral weight, leading to observable-dependent delocalisation and spreading in Krylov space. We illustrate the Koopman-Krylov diagnostics across three classes of non-integrable semiclassical string solutions.

hep-th↗

arXiv2026

Complexity and the Hilbert space dimension of 3D gravity

A central problem in formulating a theory of quantum gravity is to determine the size and structure of the Hilbert space of black holes. Here we use a quantum dynamical Krylov complexity approach to calculate the Hilbert space dimension of a black hole in 2+1-dimensional Anti-de Sitter space. We achieve this by obtaining the spread of an initial thermofield double state over the Krylov basis. The associated Lanczos coefficients match those for chaotic motion on the $SL(2,\mathbb{R})$ group. By including non-perturbative effects in the path integral, which computes coarse-grained ensemble averages, we find that the complexity saturates at late times. The saturation value is given by the exponential of the Bekenstein-Hawking entropy. Our results introduce a new way to compute the Hilbert space dimension of complex interacting systems from the saturating value of spread complexity.

hep-th↗

arXiv2026

Timelike Entanglement Signatures of Ergodicity and Spectral Chaos

We investigate timelike entanglement measures derived from the spacetime density kernel in the Rosenzweig-Porter model and show that they sharply diagnose both eigenvector ergodicity and spectral chaos. For several Hilbert-space bipartitions, we compute the second Tsallis entropy, the entanglement imagitivity that quantifies non-Hermiticity, and Schatten-norm diagnostics of the kernel. The imagitivity and Frobenius norm exhibit rapid growth and high late-time plateaus in the ergodic regime, are suppressed in the localized regime, and show intermediate behavior in the fractal phase. The real part of the second Tsallis entropy displays a spectral form factor-like dip-ramp-plateau throughout the chaotic window and a suppressed ramp in the localized regime. We further introduce a kernel negativity, defined as the negative spectral weight of the Hermitian part of the kernel. This negativity equals the trace-norm distance to the set of positive semidefinite operators and the maximal witnessable negative quasiprobability, and its time-averaged value decreases across the ergodic-fractal-localized crossover in close correspondence with the fractal dimension.

hep-th↗

arXiv2026

Krylov complexity of purification

In quantum systems, purification can map mixed states into pure states and a non-unitary evolution into a unitary one by enlarging the Hilbert space. We establish a connection between the complexities of mixed quantum states and their purification, proposing new inequalities among these complexities. By examining single qubits, two-qubit Werner states, eight-dimensional Gaussian random unitary ensembles, and infinite-dimensional systems, we demonstrate how these relationships manifest across a broad class of systems. We find that the spread complexity of purification of a vacuum state evolving into a thermal state equals the average number of Rindler particles. This complexity is also shown to adhere to the Lloyd-like bound, indicating a further relation to the quantum speed limit. Finally, using mutual Krylov complexity, we observe subadditivity of the Krylov complexities, which contrasts with known results from holographic volume complexity. We put forward Krylov mutual complexity as a diagnosis of a potential gravity dual of Krylov complexities.

hep-th↗

arXiv2025

Temporal correlations and chaos from spacetime kernel

We develop a finite-dimensional formulation of the recently introduced notion of ``timelike entanglement'', defined in terms of two-point functions between operators supported on different Cauchy slices. Using a local orthonormal operator basis, we recast this construction in terms of a generalized response tensor. Building on this, we introduce a generalized spacetime density kernel (GSDK) corresponding to higher-point correlation functions, including time-ordered as well as out-of-time-ordered correlators. We show that the Haar-averaged $(2N)$-point function yields the $(2N)$-th moment of the spectral form factor (SFF), evaluated at an $N$-enhanced effective temperature. The correlation functions of the GSDK operators also yield the SFF, with an effective $(1/N)$-reduction of the physical time-scales. The GSDK places both scrambling diagnostics and spectral statistics on a similar footing and clarifies how higher-point correlators and non-trivial time ordering capture fine-grained dynamical information of a quantum system.

hep-th↗

arXiv2024

Chaos and integrability in triangular billiards

We characterize quantum dynamics in triangular billiards in terms of five properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC), (3) Lanczos coefficient variance, (4) energy eigenstate localisation in the Krylov basis, and (5) dynamical growth of spread complexity. The billiards we study are classified as integrable, pseudointegrable or non-integrable, depending on their internal angles which determine properties of classical trajectories and associated quantum spectral statistics. A consistent picture emerges when transitioning from integrable to non-integrable triangles: (1) LSRs increase; (2) spectral complexity growth slows down; (3) Lanczos coefficient variances decrease; (4) energy eigenstates delocalize in the Krylov basis; and (5) spread complexity increases, displaying a peak prior to a plateau instead of recurrences. Pseudo-integrable triangles deviate by a small amount in these charactertistics from non-integrable ones, which in turn approximate models from the Gaussian Orthogonal Ensemble (GOE). Isosceles pseudointegrable and non-integrable triangles have independent sectors that are symmetric and antisymmetric under a reflection symmetry. These sectors separately reproduce characteristics of the GOE, even though the combined system approximates characteristics expected from integrable theories with Poisson distributed spectra.

hep-th↗

arXiv2024

Spread complexity and localization in $\mathcal{PT}$-symmetric systems

We present a framework for investigating wave function spreading in $\mathcal{PT}$-symmetric quantum systems using spread complexity and spread entropy. We consider a tight-binding chain with complex on-site potentials at the boundary sites. In the $\mathcal{PT}$-unbroken phase, the wave function is delocalized. We find that in the $\mathcal{PT}$-broken phase, it becomes localized on one edge of the tight-binding lattice. This localization is a realization of the non-Hermitian skin effect. Localization in the $\mathcal{PT}$-broken phase is observed both in the lattice chain basis and the Krylov basis. Spread entropy, entropic complexity, and a further measure that we term the Krylov inverse participation ratio probe the dynamics of wave function spreading and quantify the strength of localization probed in the Krylov basis. The number of Krylov basis vectors required to store the information of the state reduces with the strength of localization. Our results demonstrate how measures in Krylov space can be used to characterize the non-hermitian skin effect and its localization phase transition.

hep-th↗

arXiv2024

Late time dynamics in SUSY saddle-dominated scrambling through higher-point OTOC

In this article, we study the scrambling dynamics in supersymmetric quantum mechanical systems. The eigenstate representation of such supersymmetric systems allows us to present an explicit form of the $2N$-point out-of-time-order correlator (OTOC) using two equivalent formalisms viz. "Tensor Product formalism" and "Partner Hamiltonian formalism". We analytically compute the $2N$-point OTOC for the supersymmetric 1D harmonic oscillator and find that the result is in exact agreement with that of the OTOC of the 1D bosonic harmonic oscillator system. The higher-point OTOC is a more sensitive measure of scrambling than the usual 4-point OTOC. To demonstrate this feature, we consider a supersymmetric sextic 1D oscillator for which the bosonic partner system has an unstable saddle in the phase space, which is absent in the fermionic counterpart. For such a system we show that the bosonic, the fermionic as well as the supersymmetric OTOC exhibit similar dynamics due to supersymmetry constraints. Finally, we illustrate the late-time oscillatory behaviour of higher-point OTOC for saddle-dominated scrambling and anharmonic oscillator systems and propose it to be a probe of late-time dynamics in non-chaotic systems that exhibit fast early-time scrambling.

quant-ph↗

arXiv2024

Spread complexity for measurement-induced non-unitary dynamics and Zeno effect

Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution.

hep-th↗

arXiv2023

Aperiodic spin chains at the boundary of hyperbolic tilings

In view of making progress towards establishing a holographic duality for theories defined on a discrete tiling of the hyperbolic plane, we consider a recently proposed boundary spin chain Hamiltonian with aperiodic couplings that are chosen such as to reflect the inflation rule, i.e. the construction principle, of the bulk tiling. As a remnant of conformal symmetry, the spin degrees of freedom are arranged in multiplets of the dihedral group under which the bulk lattice is invariant. For the boundary Hamiltonian, we use strong-disorder RG techniques and evaluate correlation functions, the entanglement entropy and mutual information for the case that the ground state is in an aperiodic singlet phase. We find that two-point functions decay as a power-law with exponent equal to one. Furthermore, we consider the case that the spin variables transform in the fundamental representation of $SO(N)$, leading to a gapless system, and find that the effective central charge obtained from the entanglement entropy scales as $\ln N$, reflecting the number of local degrees of freedom. We also determine the dependence of this central charge on the parameters specifying the bulk tiling. Moreover, we obtain an analytical expression for the mutual information, according to which there is no phase transition at any finite value of the distance between the two intervals involved.

hep-th↗

arXiv2023

Geometric Quantum Discord Signals Non-Factorization

We propose the information-theoretic quantity of geometric quantum discord (GQD) as an indicator of the factorization properties of a given quantum system. In particular, we show how non-vanishing discord implies that the corresponding partition function does not factorize, both for generic pure states and the thermofield double state as a state with a known geometric dual in light of the AdS/CFT correspondence. Via this analysis, we give a novel interpretation to the thermomixed double state as the best purely classical approximation of the Einstein-Rosen bridge. We connect the non-vanishing of GQD with the existence of wormhole microstates.

hep-th↗

arXiv2022

Indirect detection of Cosmological Constant from interacting open quantum system

We study the indirect detection of Cosmological Constant from an open quantum system of interacting spins, weakly interacting with a thermal bath, a massless scalar field minimally coupled with the static de Sitter background, by computing the spectroscopic shifts. By assuming pairwise interaction between spins, we construct states using a generalisation of the superposition principle. The corresponding spectroscopic shifts, caused by the effective Hamiltonian of the system due to Casimir Polder interaction, are seen to play a crucial role in predicting a very tiny value of the Cosmological Constant, in the static patch of de Sitter space, which is consistent with the observed value from the Planck measurements of the cosmic microwave background (CMB) anisotropies.

hep-th↗

arXiv2020

Coherence and path indistinguishability for the interference of multiple single-mode fields

A well known result for the interference of two single-mode fields is that the degree of coherence and the degree of indistinguishablity are same when we consider the detection of a single photon. In this article we present the relation between degree of coherence, path indistinguishability and the fringe visibility considering interference of multiple number of single-mode fields while being interested in the detection of a single photon only . We will also mention how Born's rule of interference for multiple sources is reflected in these results.

quant-ph↗