arXiv subjects

Jeff Murugan

Publications and source records attributed to Jeff Murugan.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Information in SYK Model

We investigate the bulk-boundary correspondence in the SYK model from a quantum information perspective. The SYK model describes a system of Majorana fermions with random all-to-all interactions, whose disorder average-typically taken over a Gaussian ensemble-admits a dual description in terms of JT gravity in the large-$N$, low-energy limit. This framework provides a minimal setting for exploring holography and emergent spacetime in nearly AdS$_2$. We probe the holographic principle through diagnostics of quantum chaos and entanglement. In the early-time regime, the SYK model saturates the universal bound on the Lyapunov exponent, signaling maximal chaos consistent with semiclassical black hole dynamics. In the late-time regime, its spectral statistics are governed by random matrix theory, reflecting universal features of strongly chaotic quantum systems. These dynamical properties establish a concrete link between boundary quantum chaos and bulk semiclassical gravity. In parallel, we analyze quantum entanglement and the structure of operator algebras to investigate transitions in the associated von Neumann algebras and their implications for emergent geometry. To explore the robustness of these phenomena, we consider deformations of the SYK model through modified matter couplings and alternative random distributions. Our results clarify how quantum information-theoretic structures encode bulk gravitational dynamics and provide insight into the mechanism of spacetime emergence.

hep-th↗

arXiv2026

Spectral Topology and Universal Krylov Dynamics

The leading asymptotic growth of Lanczos coefficients is controlled by spectral tails and furnishes a coarse classification of Krylov dynamics. We show that the \textit{global topology} of the spectral measure, specifically the number of connected components, the gap structure, and the behaviour at gap-closing transitions, encodes a finer hierarchy of dynamical invariants invisible to tail-based arguments. Using the Riemann-Hilbert formulation of orthogonal polynomials and Deift-Zhou steepest descent, we recover the Freud growth laws $b_n\sim n^{1/\beta}$ for single-cut measures and determine their sub-leading corrections from endpoint data. Gapped spectra produce quasiperiodic Lanczos oscillations at a frequency fixed by the filling fraction of the spectral bands alone, and hence predictable from the band edges. We verify this in the SSH chain and its next-nearest-neighbour deformation. At a gap-closing transition the oscillation amplitude is governed by the Hastings-McLeod solution of Painlev\'e II, decaying as $n^{-1/3}$ at criticality and interpolating between the gapped and merged phases, so that the topology change of the spectral curve is realised as a Krylov phase transition. We also demonstrate that, while in the conformal limit of SYK the operator scaling dimension is invisible in the leading rate $\alpha = \pi T$, it can be extracted from the subleading offset $b_0 = \pi T(\Delta - \frac{1}{2})$. These results establish a refined notion of universality in operator growth, classified by spectral topology rather than spectral tails alone.

hep-th↗

arXiv2026

Spacetime Duality Beyond Conformality

We extend the spacetime duality programme of Burgess \textit{et.al.} to massive theories in 1+1 dimensions. For the massive scalar, a heat-kernel computation tracking three contributions to the conformal-mode effective action reveals that the naive leading correction $\sim m^2(e^{\phi} -1)$ to the Liouville action cancels exactly, with the genuine leading deformation being $-\frac{m^2}{16\pi}(e^{\phi}-1)^{2}$. This breaks self-duality and renders the dual theory for the Lagrange multiplier field $\Lambda$ non-local. For the massive Dirac fermion, two independent derivations establish that the fermion mass dresses under conformal scaling as $m \to m\, e^{\phi/2}$, reflecting the Weyl weight $\frac{1}{2}$ of the two-dimensional spinor. Via the Coleman-Mandelstam bosonisation, this transfers to the mass bilinear as $\mu\cos(\beta\vartheta) \to \mu e^{\phi/2}\cos(\beta\vartheta)$, producing a coupled Liouville-sine-Gordon system as the natural starting point for the fermionic construction. Both results are interpreted in terms of the determinant line bundle over Met($\Sigma$)/Diff($\Sigma$).

hep-th↗

arXiv2026

On the Universality of Probe Complexity in $\mathcal{N}=4$ SYM

We investigate Krylov complexity for single-trace operators dual to open strings attached to giant gravitons in planar $\mathcal{N}=4$ super Yang-Mills theory. We show that in protected and few-body sectors, Krylov dynamics is governed by orthogonal polynomial theory associated to the seed spectral measure, leading to bounded Lanczos coefficients determined solely by spectral support. In particular, for fixed magnon number $M$ and open-string length $L\rightarrow\infty$, we derive $a_n=2Mg$ and $b_n\rightarrow Mg$, demonstrating integrable, band-limited dynamics. This establishes that such sectors are insufficient to test recently proposed gravity-side universality of operator complexity growth. We therefore formulate a finite-density program in which magnons scale with system size, and propose a concrete universality test: whether the leading Krylov growth depends only on coarse thermodynamic data $(\rho,\varepsilon)$ and not on microscopic probe structure. This provides a precise boundary-field-theory framework for testing gravitational universality conjectures.

hep-th↗

arXiv2026

Krylov complexity from a simple quantum mechanical model for a radiating black hole

We investigate Krylov complexity in a simple quantum mechanical model describing a black hole coupled to its radiation. The model is constructed as a simplified ``mini-BMN" matrix system inspired by a recent proposal of Maldacena. Our aim is not to reproduce the full dynamics of the BMN matrix model, but rather to isolate a tractable setting in which the information-theoretic behaviour of a radiating black hole can be studied explicitly. We analyze both the early- and late-time behaviour of Krylov complexity and the associated Krylov entropy. At early times, perturbative and numerical analyses reveal the expected growth characteristic of chaotic quantum dynamics. At late times, however, the dynamics saturates to a plateau, consistent with equilibration between the black hole and its radiation and with general expectations from finite-entropy quantum systems. We argue that this plateau behaviour admits a semiclassical interpretation in terms of Euclidean instanton contributions in an effective path-integral. The toy model studied here offers a controlled framework in which these features can be investigated analytically and numerically.

hep-th↗

arXiv2026

Stochastic Krylov Dynamics: Revisiting Operator Growth in Open Quantum Systems

In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture survives, albeit in a fundamentally altered form, once the system is coupled to an environment.Using a Schwinger-Keldysh formulation of the full counting statistics of the Krylov position, we derive an effective action for operator growth under Lindblad dynamics. Even for the minimal case of dephasing, the phase-space dynamics ceases to be Hamiltonian; environmental coupling generates diffusion in the variable conjugate to Krylov depth, converting deterministic trajectories in to stochastic ones. The hyperbolic mechanism underlying exponential complexity growth is therefore broadened and, beyond a parametrically controlled scale, destroyed.This identifies dissipation as a relevant perturbation of the chaotic Krylov fixed point and reveals operator growth in open systems as a problem of stochastic dynamics in an emergent phase space.

hep-th↗

arXiv2026

More on OTOCs and Chaos in Quantum Mechanics -- Magnetic Fields

We revisit thermal out-of-time-order correlators (OTOCs) in single-particle quantum systems, focusing on magnetic billiards. Using the stadium billiard as a testbed, we compute the thermal OTOC $C_T(t) = -\langle [x(t), p]^2 \rangle_\beta$ and extract Lyapunov-like exponents $\lambda_L$ that quantify early-time growth. We map out $\lambda_L(T, B)$, revealing a crossover from quantum chaos to magnetic rigidity. In parallel, we compute an alternative OTOC built from guiding-center operators, which exhibits qualitatively distinct dynamics and no exponential growth. Our results offer a controlled framework for probing scrambling, temperature dependence, and the interplay of geometry and magnetic fields in quantum systems.

hep-th↗

arXiv2026

A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics

In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an emergent phase-space description in which the Lanczos coefficients define an effective Hamiltonian governing operator motion along the Krylov chain. In the semiclassical limit, exponential complexity growth arises from hyperbolic trajectories, and asymptotically linear Lanczos growth appears as a universal chaotic fixed point, with sub-leading deformations classified as irrelevant, marginal or relevant. Going beyond the saddle, the Schwinger-Keldysh framework provides controlled access to fluctuations and large deviations of Krylov complexity, revealing sharp signatures of integrability-chaos crossovers that are invisible at the level of the mean. This formulation reorganises Krylov complexity into a dynamical field-theoretic framework and identifies new fluctuation diagnostics of operator growth in closed quantum systems.

quant-ph↗

arXiv2026

Superadditivity of Krylov Complexity for Tensor Products

We study Krylov complexity for quantum systems whose Hamiltonians factorise as tensor products. We prove that complexity is superadditive under tensor products, $C_{12}\ge C_1+C_2$, and identify a positive operator that quantifies the resulting excess complexity. The underlying mechanism is made transparent by introducing a Krylov graph representation in which tensor products generate a higher-dimensional lattice whose diagonal shells encode operator growth and binomial path multiplicities. In the continuum limit, Krylov dynamics reduces to diffusion on this graph, with superadditivity arising from geometric broadening across shells. Explicit examples illustrate how deviations from synchronous evolution generate bounded, oscillatory excess complexity.

hep-th↗

arXiv2025

Misinformation Dynamics in Social Networks

Information transmitted across modern communication platforms is degraded not only by intentional manipulation (disinformation) but also by intrinsic cognitive decay and topology-dependent social averaging (misinformation). We develop a continuous-fidelity field theory on multiplex networks with distinct layers representing private chats, group interactions, and broadcast channels. Our analytic solutions reveal three universal mechanisms controlling information quality: (i) groupthink blending, where dense group coupling drives fidelity to the initial group mean; (ii) bridge-node bottlenecks, where cross-community flow produces irreversible dilution; and (iii) a network-wide fidelity landscape set by a competition between broadcast truth-injection and structural degradation pathways. These results demonstrate that connectivity can reduce information integrity and establish quantitative control strategies to enhance fidelity in large-scale communication systems.

physics.soc-ph↗

arXiv2025

On-Shell Methods for Quantum Matter: Strongly correlated Dirac materials

We propose a framework for applying on-shell scattering amplitude methods to emergent relativistic phases of quantum matter. Many strongly correlated systems, from Dirac and Weyl semimetals to topological-insulator surfaces, exhibit low-energy excitations that are effectively massless relativistic spinors. We show that physical observables such as nonlinear optical and Hall responses can be obtained from compact on-shell amplitudes, bypassing the complexity of Feynman diagrams. As a concrete demonstration, we derive the nonlinear Hall conductivity of a Dirac semimetal from a single parity-odd three-photon amplitude, highlighting the analytic and conceptual power of amplitude-based approaches for strongly correlated condensed-matter systems.

cond-mat.str-el↗

arXiv2025

(A)Symmetric Complexity and the Quantum Mpemba Effect

The Quantum Mpemba Effect (QME) -- the counter-intuitive phenomenon where states further from equilibrium can relax faster than those closer to it -- challenges standard expectations of quantum thermalization. In this work, we introduce Krylov complexity as a sensitive diagnostic for the QME. We show that Krylov spread complexity encodes the asymmetry essential to the effect, and we define a new class of projective (a)symmetric complexities that sharpen this connection. Strikingly, the structure of these projective complexities at the initial moment ($t=0$) already carries predictive power for the onset of Mpemba-like inversions, obviating the need for explicit time evolution. Our results suggest that the geometry of states in Krylov space captures deep information about non-monotonic relaxation and provides a powerful framework for diagnosing and anticipating anomalous thermalization phenomena in quantum systems.

hep-th↗

arXiv2025

Krylov complexity, path integrals, and instantons

Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at large times, for classical chaotic systems with at least two minima of the potential, that have a plateau for $K(t)$, the value of the plateau is described by quantum mechanical instantons, as is the case for standard transition amplitudes. We explain and test these ideas in a simple toy model.

hep-th↗

arXiv2025

Matter Coupling of Dirac Matter in the Context of the SYK Model: Non-Gaussian Random Couplings and Bulk Mass Deformations

We elaborate further on the matter coupling of Dirac matter in the SYK framework, incorporating non-Gaussian coupling distributions and bulk fermion mass effects. Our study analyzes quartic matter couplings generated by a non-Gaussian distribution as an illustrative example. The introduction of bulk-fermion mass alters the boundary coupling between the Dirac and Majorana fermions. The averaged adjacent gap ratio is sensitive to the distribution of random couplings, which remains independent of the Hamiltonian's symmetry. The generalization of the SYK model to non-Gaussian distributions and the inclusion of bulk fermion mass remain qualitatively similar to the Gaussian and massless cases. Key deviations are observed only in the time scales for the linear ramp in the spectral form factor and the saturation of entanglement entropy.

hep-th↗

arXiv2025

Astrophysical Quantum Matter Revisited: Flat-Band Topological States on a Zero-Flux Dipole Sphere

We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly degenerate manifold of normalizable zero modes, with degeneracy proportional to the total absolute flux. We introduce a non-Abelian spin gauge field near the equator to hybridize the north and south domain-confined modes, forming a global flat band. Projecting interactions into this band yields Laughlin-type correlated states. The entanglement spectrum shows a chiral tower consistent with a virtual edge, demonstrating bulk-edge correspondence in a closed geometry. This generalizes the zero-flux flat-band construction of \cite{Parhizkar:2024som} to curved backgrounds, with potential applications to synthetic and astrophysical systems.

cond-mat.str-el↗

arXiv2025

A Quantum Computational Perspective on Spread Complexity

We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations: time-evolution and superposition. Our approach leverages a computational setup where unitary gates and beam-splitting operations generate target states, with the minimal cost of synthesis yielding a complexity measure that converges to spread complexity in the infinitesimal time-evolution limit. This perspective not only provides a physical interpretation of spread complexity but also offers computational advantages, particularly in scenarios where traditional methods like the Lanczos algorithm fail. We illustrate our framework with an explicit SU(2) example and discuss broader applications, including cases where return amplitudes are non-perturbative or divergent

hep-th↗

arXiv2025

Spinning Billiards and Chaos

We investigate the impact of internal spin on chaos in billiard systems. Extending the standard point-particle billiard by coupling translational and rotational degrees of freedom through a dimensionless spin parameter $\alpha = I/(mr^2) \in [0,1]$, we find that spin reduces chaos monotonically but does not eliminate it. In the Bunimovich stadium and Sinai billiard, the Lyapunov exponent decreases with $\alpha$ but remains positive throughout the physical range, while the circle and rectangle remain integrable. Finite-time Lyapunov exponent distributions reveal a mixed phase space in which spin creates islands of regularity while the majority of trajectories remain chaotic. The mechanism is a conserved quantity $Q = v_\parallel - \alpha u$ preserved through each collision, which constrains the dynamics on sequences of same-orientation wall collisions and explains why spin suppresses chaos more effectively in geometries with longer flat sections. We further show that the Datseris--Hupe--Fleischmann scaling $\lambda \propto 1/f_{\rm chaotic}$ fails for spinning billiards: spin reduces the intensity of chaos, not merely the fraction of chaotic trajectories.

nlin.CD↗

arXiv2024

The SYK charging advantage as a random walk on graphs

We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size $N$ and the facilitation of operator delocalization by specific graph structures. A novel graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.

quant-ph↗