arXiv subjects

Mohsen Alishahiha

Publications and source records attributed to Mohsen Alishahiha.

At least 19 recordsLinked to original sources

arXiv2026

Timelike Holographic Complexity

Motivated by the pseudo-entropy program, we study timelike subregion complexity within the holographic Complexity=Volume framework, extending previous spatial constructions to Lorentzian boundary intervals. For hyperbolic timelike regions in pure AdS, we compute the enclosed bulk volume and show that, despite the Lorentzian embedding, the resulting complexity is purely real under the stated volume prescription. We generalize the analysis to AdS black brane geometries, where the extremal-surface configurations considered may either remain outside the horizon or penetrate it, with the horizon-to-turning-point segment being timelike in the exterior case and spacelike in the interior case. In both configurations, the complexity exhibits the same leading UV-divergence structure as the spacelike case and receives no imaginary contribution when the horizon terms are combined with a common regulator. This reality contrasts with the potentially complex-valued pseudo-entropy and reflects the chosen Lorentzian volume prescription, while a precise boundary interpretation of the proposed complexity remains conjectural.

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arXiv2026

Coherent Release Fronts in Krylov Chains and Thermal AdS$_2$ Response

We study coherent release from a finite serial Krylov sector into an exact conformal tail with asymptotically linear Lanczos coefficients. We derive an exact finite-cut occupation kernel and its locally uniform moving-cut limit, whose derivative is the squared modulus of a filtered boundary-emission amplitude. The tail sets the filtering kernel and logarithmic transit scale, while the release profile also depends on the finite sector. Its early edge records the number of serial steps before emission, whereas its late edge reflects slow resonances, interference, and logarithmic enhancements from merged poles. A one- and two-site family can share the same leading continued-fraction pole while exhibiting inequivalent profiles. We further consider a thermal AdS$_2$ realization in which, in the weak-coupling limit, the dressed oscillator measure approaches a two-site shallow sector followed by the conformal tail, with the leading complex pole reproduced through second order.

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arXiv2026

Krylov-Space Memory Cores

We introduce Krylov-space memory cores as stationary, depth-resolved structures that reveal how anomalous initial-state memory is organized inside the Krylov space of otherwise thermalizing nonintegrable systems. The stationary occupation profile identifies where late-time probability is concentrated along the Krylov chain, while complementary diagnostics of residual equilibration fluctuations, deviation from the Gibbs reference, and long-time Krylov-current fluctuations determine the physical character of that region. Across weak thermalization, confinement-induced anomalous dynamics, and many-body scarring, anomalous initial states develop compact low-depth memory cores that carry appreciable residual fluctuations, Gibbs mismatch, and persistent current-fluctuation activity. These cores are often embedded within substantially broader stationary occupation halos. The reference states considered, by contrast, do not exhibit a comparable combination of signal strength and spatial compactness. An auxiliary integrable comparison further shows that compact Krylov memory is state selective rather than a generic consequence of integrability. Krylov-space memory cores therefore provide a stationary framework for identifying where structured quantum memory resides and how it remains dynamically encoded.

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arXiv2026

Krylov Distribution and Spectral Convergence of Quantum Fisher Information

We establish a direct correspondence between the Krylov hierarchy of quantum Fisher information (QFI) and a Krylov-resolved decomposition of the symmetric logarithmic derivative (SLD). Building on the existing Krylov formulation of QFI, we show that the metrological information resolved at each Krylov level is exactly encoded in the incremental gain of the Lanczos hierarchy, giving the Krylov distribution a direct information-theoretic interpretation. A dual spectral formulation distinguishes the Hilbert--Schmidt geometry used to construct the computational Lanczos hierarchy from the state-dependent geometry in which the SLD and QFI are naturally defined, and relates their associated Liouville measures. This distinction clarifies the origin of different convergence regimes: we recover exponential convergence for gapped spectra and derive an exact algebraic hard-edge convergence law for the Jacobi class, including the exact finite-order error and the marginal case separating finite from divergent QFI.

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arXiv2026

Eigenstate Thermalization Hypothesis: A Primer

How does an isolated quantum system evolve toward thermal equilibrium from a far-from-equilibrium initial state-for instance, one prepared by a global quantum quench? This question has attracted significant interest in recent years. The Eigenstate Thermalization Hypothesis (ETH) provides a compelling framework for addressing it, with far-reaching implications from high-energy physics to condensed matter. This primer offers a pedagogical introduction to quantum equilibrium and ETH for a broad physics audience, particularly high-energy physicists seeking a comprehensive understanding of these topics. We assume only basic knowledge of quantum mechanics and statistical mechanics.

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arXiv2026

Krylov Distribution

We introduce the Krylov distribution $\mathcal{D}(ξ)$, a static Krylov-space diagnostic that characterizes how inverse-energy response is organized in Hilbert space. The central object is the resolvent-dressed state $(H-ξ)^{-1}|ψ_0\rangle$, whose decomposition in the Krylov basis generated from a reference state defines a normalized distribution over Krylov levels. Unlike conventional spectral functions, which resolve response solely along the energy axis, the Krylov distribution captures how the resolvent explores the dynamically accessible subspace as the spectral parameter $ξ$ is varied. Using asymptotic analysis, exact results in solvable models, and numerical studies of an interacting spin chain, we identify three universal regimes: saturation outside the spectral support, extensive growth within continuous spectra, and sublinear or logarithmic scaling near spectral edges and quantum critical points. We further show that fidelity susceptibility and the quantum geometric tensor admit natural decompositions in terms of Krylov-resolved resolvent amplitudes.

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arXiv2026

The Exact Uncertainty Relation and Geometric Speed Limits in Krylov Space

We show that Hall's exact uncertainty relation acquires a simple geometric form in the Krylov basis generated by the Liouvillian. In this canonical operator frame, the uncertainty equality implies that the operator amplitude vector evolves on the unit Krylov sphere with constant speed fixed solely by the first Lanczos coefficient. This yields an exact linear bound on geometric operator evolution, independent of higher Lanczos coefficients and valid for arbitrary Hamiltonians, integrable or chaotic. Our results provide the first unified geometric interpretation of exact quantum speed limits and operator growth, identifying the first Lanczos coefficient as the intrinsic speed scale of quantum dynamics.

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arXiv2025

On Krylov Complexity as a Probe of the Quantum Mpemba Effect

We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional diagnostics such as the trace distance, while offering a complementary interpretation in terms of Hilbert-space exploration and dynamical delocalization. In $U(1)$-symmetric systems, we confirm that the recently proposed symmetric component of Krylov complexity serves as a robust and reliable indicator of the QME, capturing anomalous relaxation even in cases where the total complexity fails to do so.

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arXiv2025

Krylov Complexity as a Probe for Chaos

In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner in which complexity saturates reveals the chaotic nature of the system. In particular, we show that the dynamics towards saturation precisely distinguish between chaotic and integrable systems. For chaotic models, the saturation value of complexity reaches its infinite time average at a finite saturation time. In this case, depending on the initial state, it may also exhibit a peak before saturation. In contrast, in integrable models, complexity approaches the infinite time average value from below at a much longer timescale. We confirm this distinction using numerical results for specific spin models.

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arXiv2025

On JT gravity path integrals and the tunneling process

The Jackiw-Teitelboim (JT) gravity path integral of the trumpet can be interpreted as a transition amplitude from an older black hole to a younger one, accompanied by the emission of a baby universe, represented by the geodesic boundary of the trumpet. However, this interpretation becomes less straightforward for geometries with higher genus and multiple geodesic boundaries. In this paper, we examine the path integral for these more complex geometries and find that maintaining this interpretation requires accounting for a portion of the moduli space.

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arXiv2025

Thermalization in Krylov Basis

We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix are exponentially small, reminiscent of the eigenstate thermalization hypothesis. Within this framework, we propose that the nature of thermalization, whether weak or strong, can be examined by the infinite time average of the Krylov complexity. Moreover, we analyze the variance of Lanczos coefficients as another probe for the nature of thermalization. One observes that although the variance of Lanczos coefficients may capture certain features of thermalization, it is not as effective as the infinite time average of complexity.

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arXiv2023

On Quantum Complexity

The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a particular condition on its matrix elements in the energy eigenstate basis so that the corresponding quantity exhibit linear growth at late times. The condition is to do with a possible pole structure the corresponding matrix elements may have. Based on the general expectation of complexity one may want to think of this quantity as a possible candidate for the quantum complexity. We note, however, that for the explicit examples we have considered in this paper, there are infinitely many quantities exhibiting similar behavior.

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arXiv2023

A universal approach to Krylov State and Operator complexities

We present a general framework in which both Krylov state and operator complexities can be put on the same footing. In our formalism, the Krylov complexity is defined in terms of the density matrix of the associated state which, for the operator complexity, lives on a doubled Hilbert space obtained through the channel-state map. This unified definition of complexity in terms of the density matrices enables us to extend the notion of Krylov complexity, to subregion or mixed state complexities and also naturally to the Krylov mutual complexity. We show that this framework also encompasses nicely the holographic notions of complexity.

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arXiv2022

On the saturation of late-time growth of complexity in supersymmetric JT gravity

In this work we use the modified replica trick, proposed in arXiv:2205.01150, to compute the late time behaviour of complexity for JT gravity with ${\cal N} = 1$ and ${\cal N} = 2$ supersymmetries. For the ${\cal N} = 1$ theory, we compute the late time behaviour of complexity defined by the ``quenched geodesic length" and obtain the expected saturation of complexity at time $t \sim e^{S_0}$, to a constant value with time-independent variance. For the ${\cal N} = 2$ theory, we explicitly compute complexity at the disk level which yields the late-time linear growth of complexity. However, we comment on the expectation of the late-time saturation by speculating the trumpet partition function and the non-perturbative corrections to the spectral correlation, relevant for the late-time behaviour of complexity. Furthermore, we compute the matter correlation functions for both the theories.

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arXiv2022

Complexity via Replica Trick

We consider the complexity of a single-sided AdS black hole as modelled by an end-of-the-world brane. In addition, we present multi-boundary partition functions and matter correlation functions for such a setting. We compute the complexity using a modified replica trick corresponding to the "quenched geodesic length" in JT gravity. The late-time behaviour of complexity shows a saturation to a constant value of order $e^{S_0}$ following a period of linear growth. Furthermore, we show that our approach leads to an improved result for the variance of complexity, namely it being time-independent at late times. We conclude by commenting on the introduction of dynamical end-of-the-world branes.

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arXiv2022

Complexity as a holographic probe of strong cosmic censorship

Based on reasonable assumptions, we propose a new expression for Lloyd's bound, which confines the complexity growth of charged black holes. We then revisit holographic complexity for charged black branes in the presence of a finite cutoff. Using the proposed Lloyd's bound we find a relation between the UV and the behind the horizon cutoff. This is found to be consistent with the factorization of the partition function at leading order in large N. We argue that the result may be thought of as a holographic realization of strong cosmic censorship.

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arXiv2021

Island in the Presence of Higher Derivative Terms

Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.

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arXiv2021

On Free Energy for Deformed JT Gravity

In this paper, we study a particular deformation of the Jackiw-Teitelboim gravity recently considered by Maxfield, Turiaci and independently by Witten. We will compute the partition function of this model as well as its higher order correlators to all orders in genus expansion in the low temperature limit for small perturbations. In this limit, the results match with those obtained from the Airy limit of a Hermitian random matrix ensemble. Using this result, we will also study the free energy of the model. One observes that although the annealed free energy has pathological behaviors, under certain assumptions, the quenched free energy evaluated by replica trick exhibits the desired properties at low temperatures.

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