arXiv subjects

Suman Das

Publications and source records attributed to Suman Das.

At least 19 recordsLinked to original sources

arXiv2026

Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity

We study symmetry-resolved Krylov complexity in finite-dimensional chaotic quantum many-body systems. When both the Hamiltonian and the initial operator commute with a conserved charge, the operator dynamics decomposes into independent symmetry sectors, each with its own Krylov chain. We show that, after saturation, the unresolved Krylov complexity is additive over symmetry sectors. In the absence of additional Liouvillian degeneracies, the late-time contribution of a sector with Hilbert-space dimension $d_q$ is controlled by $d_q(d_q-1)$, leading to a dimension-weighted equipartition that approaches the simple large-sector scaling $d_q^2/\sum_{q'}d_{q'}^2$. This late-time rule differs from the early-time weighted-average discussed in the literature and is governed instead by the dimensions of the accessible operator spaces. We support the analytic prediction with numerical studies of the real and complex SYK models, a chaotic bosonic spin model, and the mixed-field Ising chain. Our results show that resolving exact symmetries is essential for interpreting the saturation value of Krylov complexity as a diagnostic of chaotic operator growth.

hep-th↗

arXiv2026

Homeostatic Noise Buffering in Biomolecular Condensates Hinges on Phase Multiplicity Modulated by Interfacial and Droplet Size Effects

Specific mixing or demixing of molecular species is a characteristic feature of condensed intracellular membraneless compartments. How sequence patterns of intrinsically disordered proteins (IDPs) fundamentally impact subcompartmentalization of biomolecular condensates and their role in buffering against concentration fluctuations are hereby addressed by modeling liquid-liquid phase separation (LLPS) of polyampholytic sequence pairs using random phase approximation (RPA) polymer theory and molecular dynamics (MD). RPA theory predicts both binary and ternary LLPS in a temperature-sensitive manner. We observe demixing underpinned by ternary LLPS for pairs with dissimilar sequence charge patterns but not for pairs with similar sequence charge patterns. Notably, the predicted behaviors are corroborated by MD when RPA is augmented with interfacial tension and/or a finite-size formalism commensurating with the typical small sizes of MD model systems, supporting our stipulation that RPA theory is a useful sequence-specific modeling tool for biomolecular condensates with larger, more realistic sizes when finite-size effects are much less significant. In principle, when the condensate size is sufficiently large, ternary LLPS is superior to binary LLPS in noise buffering because the IDP compositions of the three coexisting phases in ternary LLPS remain unchanged over an extended two-dimensional concentration regime, whereas the two coexisting phases in binary LLPS are fixed only along a tieline. However, when condensate sizes are sufficiently small, the buffering capacities of ternary versus binary LLPSs are more complex as they are modulated differently by finite-size effects. Biophysical ramifications of this interplay are discussed in view of the size diversity of natural biomolecular condensates.

q-bio.BM↗

arXiv2026

Low-temperature Quantum-corrected Holographic Transport with Momentum Relaxation

We determine the quantum corrections to transport arising from fluctuations of the near-AdS${}_2$ throat of near-extremal black branes in holographic models with momentum relaxation. By computing the shear viscosity and electrical conductivity at both zero and finite chemical potential, we uncover a universal low-temperature enhancement of transport generated by Schwarzian quantum fluctuations. Specifically, transport coefficients extracted from retarded Green's functions increase throughout the regime $C T \ll 1$. For operators with Schwarzian scaling dimension $\Delta >1$, this enhancement is preceded by a universal minimum at a characteristic temperature $T_{\rm min} \propto C^{-1}$, leading to a non-monotonic temperature dependence strikingly similar to that observed in many correlated materials. In contrast, for the case $\Delta =1$, relevant for the electrical conductivity, the transport coefficient evolves monotonically toward a constant value. Our results identify universal signatures of near-horizon quantum gravity in the transport properties of holographic quantum matter.

hep-th↗

arXiv2026

Isoperimetric-type inequalities for pluriharmonic functions on the polydisc

We prove isoperimetric-type inequalities for complex-valued pluriharmonic functions in the unit polydisc $\mathbb{U}^n\subset\mathbb{C}^n$. Denote by $h^p(\mathbb{U}^n)$ and $b^p_{\mathbf q}(\mathbb{U}^n)$, respectively, the pluriharmonic Hardy space and the pluriharmonic weighted Bergman space in $\mathbb{U}^n$, where $\mathbf q=(q_1,\ldots,q_n)>-\mathbf1$. For $m\in\mathbb{N}$, $m\geq2$, write $\mathbf{m-2}=(m-2,\ldots,m-2)$ and let \[ d\mu_{\mathbf{m-2}}(z) =\frac{(m-1)^n}{\pi^n} \prod_{k=1}^n \left[(1-|z_k|^2)^{m-2}\,dx_kdy_k\right], \qquad z_k=x_k+iy_k. \] We prove that if $1 2$, we refine this in the form \[ \|f\|_{b^{mp}_{\mathbf{m-2}}(\mathbb{U}^n)} \leq \left[ \sqrt2\cos\left(\frac{\pi}{4m}\right) \right]^{2n/p} \|f\|_{h^p(\mathbb{U}^n)}. \] Consequently, the obtained constant in the diagonal inclusion tends to $1$ as $p\to\infty$, for fixed $m$ and $n$. When $m=2$ and $n=1$, the latter estimate coincides with best-known planar estimate. Explicit lower bounds at $p=2$, together with the dimension-free upper estimate, show that the optimal diagonal constants converge to $\sqrt2$ as $m\to\infty$, uniformly in the dimension.

math.CV↗

arXiv2026

Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons

Originally proposed by 't Hooft, the brick wall model has recently reemerged as a useful framework for probing quantum aspects of horizon physics, particularly in the context of holography. In this paper, we apply it to asymptotically de Sitter spacetimes. We compute the normal modes of a massless scalar field in pure de Sitter space and in the Schwarzschild-de Sitter black hole, and analyze the resulting single-particle spectra using the level-spacing distribution, the spectral form factor, and Krylov complexity. In pure de Sitter, the spectrum exhibits clear long-range signatures of chaos despite not obeying a conventional Wigner-Dyson level-spacing distribution. The Schwarzschild-de Sitter case is qualitatively richer: in the WKB regime, where tunneling between the two classically allowed regions is exponentially suppressed, the presence of both an event horizon and a cosmological horizon gives rise to two independent near-horizon sectors, so that the full spectrum is the superposition of two subsequences. As a result, the combined level-spacing distribution develops a nonzero value at $s=0$ even when spectral correlations remain. Nevertheless, for sufficiently small stretched-horizon fluctuations, the superposed spectrum still exhibits an approximately linear ramp in the spectral form factor and a pronounced peak in Krylov complexity. Our results show that the absence of strict level repulsion should not, by itself, be taken as evidence against chaos, and that the spectral form factor and Krylov complexity provide sharper diagnostics of the underlying chaotic dynamics.

hep-th↗

arXiv2025

Blackish Holes with Stringy Backreaction

Recent studies have demonstrated that an $\textit{ad hoc}$ Dirichlet boundary condition, placed outside but close to an event horizon, for probe degrees of freedom in an otherwise black hole geometry is capable of capturing non-trivial level-correlations of the corresponding spectrum of the probe sector. Much of the interesting physics stems from a hierarchy of scales that is present in the quantum spectrum, in terms of two quantum numbers that characterize it. In this work, we establish an explicit connection with the hierarchy of these scales with a $\textit{radial localization}$ or the absence of it of the probe scalar WKB-wavefunction. Subsequently, this scale separation can be traced back to the hierarchy between the local red-shift and the classical light-traversing time in a geometry that produces a Rindler-throat. The classical null ray takes a logarithmically divergent time to reach the Dirichlet wall, and interestingly, we explicitly demonstrate that the scalar quantum spectrum arising from the Rindler throat yields a Dip-time of the corresponding spectral form factor, which scales with a universal power of the light traversing time. Armed with these, we further consider a $\textit{dressed effective model}$ where the Dirichlet boundary condition is inserted in a ten-dimensional supergravity geometry, where classical string sources back-react. We demonstrate that, as a result of this backreaction, the quantum-dynamical time-scales, $\textit{e.g.}$ the Dip time of the corresponding spectral form factor can be further enhanced with factors of the string length, thereby making the Dirichlet wall configuration better mimic the true black hole. In the dual field theory, the geometry corresponds to thermal states of a large $N$ gauge theory in the Veneziano limit, where both the number of colour and the flavour degrees of freedom are large.

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

On harmonic quasiregular mappings in Bergman spaces

A classical result of Hardy and Littlewood says that if $f=u+iv$ is analytic in the unit disk $\mathbb{D}$ and $u$ is in the harmonic Bergman space $a^p$ ($0 0$ such that every univalent harmonic function $f$ (and the partial derivatives $f_\theta,\, rf_r$) is of class $a^p$. This result extends nicely to harmonic quasiconformal mappings in $\mathbb{D}$.

math.CV↗

arXiv2025

Note on real and imaginary parts of harmonic quasiregular mappings

If $f=u+iv$ is analytic in the unit disk $\mathbb{D}$, it is known that the integral means $M_p(r,u)$ and $M_p(r,v)$ have the same order of growth. This is false if $f$ is a (complex-valued) harmonic function. However, we prove that the same principle holds if we assume, in addition, that $f$ is $K$-quasiregular in $\mathbb{D}$. The case $0<p<1$ is particularly interesting, and is an extension of the recent Riesz type theorems for harmonic quasiregular mappings by several authors. Further, we proceed to show that the real and imaginary parts of a harmonic quasiregular mapping have the same degree of smoothness on the boundary.

math.CV↗

arXiv2025

Hardy spaces of harmonic quasiconformal mappings and Baernstein's theorem

Let $\mathcal{S}_H^0(K)$, $K\ge 1$, be the class of normalized $K$-quasiconformal harmonic mappings in the unit disk. We obtain Baernstein type extremal results for the analytic and co-analytic parts of functions in the geometric subclasses of $\mathcal{S}_H^0(K)$. We then apply these results to obtain integral means estimates for the respective classes. Furthermore, we find the range of $p>0$ such that these geometric classes of harmonic quasiconformal mappings are contained in the Hardy space $h^p$, thereby refining some earlier results of Nowak.

math.CV↗

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↗

arXiv2025

H\"older continuity and composition operators in pluriharmonic Bloch spaces

We show a H\"older estimate of order $1/n$ for pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n \subset \mathbb{C}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition for the composition operator on the pluriharmonic Bloch space to be bounded below. As a partial converse, we also give a necessary condition for the boundedness below of the composition operator on the Bloch space of holomorphic mappings in $\mathbb{B}^n$.

math.CV↗

arXiv2025

Guaranteeing Out-Of-Distribution Detection in Deep RL via Transition Estimation

An issue concerning the use of deep reinforcement learning (RL) agents is whether they can be trusted to perform reliably when deployed, as training environments may not reflect real-life environments. Anticipating instances outside their training scope, learning-enabled systems are often equipped with out-of-distribution (OOD) detectors that alert when a trained system encounters a state it does not recognize or in which it exhibits uncertainty. There exists limited work conducted on the problem of OOD detection within RL, with prior studies being unable to achieve a consensus on the definition of OOD execution within the context of RL. By framing our problem using a Markov Decision Process, we assume there is a transition distribution mapping each state-action pair to another state with some probability. Based on this, we consider the following definition of OOD execution within RL: A transition is OOD if its probability during real-life deployment differs from the transition distribution encountered during training. As such, we utilize conditional variational autoencoders (CVAE) to approximate the transition dynamics of the training environment and implement a conformity-based detector using reconstruction loss that is able to guarantee OOD detection with a pre-determined confidence level. We evaluate our detector by adapting existing benchmarks and compare it with existing OOD detection models for RL.

cs.LG↗

arXiv2025

Zygmund's theorem for harmonic quasiregular mappings

Given an analytic function $f=u+iv$ in the unit disk $\mathbb{D}$, Zygmund's theorem gives the minimal growth restriction on $u$ which ensures that $v$ is in the Hardy space $h^1$. This need not be true if $f$ is a complex-valued harmonic function. However, we prove that Zygmund's theorem holds if $f$ is a harmonic $K$-quasiregular mapping in $\ID$. Our work makes further progress on the recent Riesz-type theorem of Liu and Zhu (Adv. Math., 2023), and the Kolmogorov-type theorem of Kalaj (J. Math. Anal. Appl., 2025), for harmonic quasiregular mappings. We also obtain a partial converse, thus showing that the proposed growth condition is the best possible. Furthermore, as an application of the classical conjugate function theorems, we establish a harmonic analogue of a well-known result of Hardy and Littlewood.

math.CV↗

arXiv2024

Blackish Holes

Based on previous works, in this article we systematically analyze the implications of the explicit normal modes of a probe scalar sector in a BTZ background with a Dirichlet wall, in an asymptotically AdS-background. This is a Fuzzball-inspired geometric model, at least in an effective sense. We demonstrate explicitly that in the limit when the Dirichlet wall approaches the event horizon, the normal modes condense fast to yield an effective branch cut along the real line in the complex frequency plane. In turn, in this approximation, quasi-normal modes associated to the BTZ black hole emerge and the corresponding two-point function is described by a thermal correlator, associated with the Hawking temperature in the general case and with the right-moving temperature in the extremal limit. We further show, analytically, that the presence of a non-vanishing angular momentum non-perturbatively enhances this condensation. The consequences are manifold: {\it e.g.}~there is an emergent {\it strong thermalization} due to these modes, adding further support to a quantum chaotic nature associated to the spectral form factor. We explicitly demonstrate, by considering a classical collapsing geometry, that the one-loop scalar determinant naturally inherits a Dirichlet boundary condition, as the shell approaches the scale of the event horizon. This provides a plausible dynamical mechanism in the dual CFT through a global quench, that can create an emergent Dirichlet boundary close to the horizon-scale. We offer comments on how this simple model can describe salient features of Fuzzball-geometries, as well as of extremely compact objects. This also provides an explicit realization of how an effective thermal physics emerges from a non-thermal microscopic description, within a semi-classical account of gravity, augmented with an appropriate boundary condition.

hep-th↗

arXiv2024

Brick Wall in AdS-Schwarzschild Black Hole: Normal Modes and Emerging Thermality

This paper investigates the normal modes of a probe scalar field in a five-dimensional AdS-Schwarzschild black hole with the brick wall boundary condition near the horizon. We employ various techniques to compute the spectrum and analyze its properties. Our results reveal a linear dependence of the spectrum on the principal quantum number while demonstrating a non-trivial dependence on the angular momentum quantum number. We compute the Spectral Form Factor (SFF) and find a dip-ramp-plateau structure, with the slope of the ramp approaching unity as the brick wall nears the horizon. We also observe that as the brick wall approaches the horizon, the poles of the retarded Green's function condense on the real line, leading to an emergent thermal behavior in the boundary theory. This work extends previous studies on lower-dimensional black holes to higher dimensions, providing insights into the connection between black hole microstate models and boundary chaos. Our findings contribute to the ongoing discussions on the information paradox and the nature of black hole interiors in the context of AdS/CFT correspondence.

hep-th↗

arXiv2024

Gabriel's problem for harmonic Hardy spaces

We obtain inequalities of the form $$\int_C |f(z)|^p |dz| \leq A(p) \int_{\mathbb{T}} |f(z)|^p |dz|, \quad (p>1)$$ where $f$ is harmonic in the unit disk $\mathbb{D}$, $\mathbb{T}$ is the unit circle, and $C$ is any convex curve in $\mathbb{D}$. Such inequalities were originally studied for analytic functions by R. M. Gabriel [Proc. London Math. Soc. 28(2), 1928]. We show that these results, unlike in the case of analytic functions, cannot be true in general for $0< p \le 1$. Therefore, we produce an inequality of a slightly different type, which deals with the case $0<p<1$. An example is given to show that this result is "best possible", in the sense that an extension to $p=1$ fails. Then we consider the special case when $C$ is a circle, and prove a refined result which surprisingly holds for $p=1$ as well. We conclude with a maximal theorem which has potential applications.

math.CV↗

arXiv2024

Differential Effects of Sequence-Local versus Nonlocal Charge Patterns on Phase Separation and Conformational Dimensions of Polyampholytes as Model Intrinsically Disordered Proteins

Conformational properties of intrinsically disordered proteins (IDPs) are governed by a sequence-ensemble relationship. To differentiate the impact of sequence-local versus sequence-nonlocal features of an IDP's charge pattern on its conformational dimensions and its phase-separation propensity, the charge "blockiness'' $\kappa$ and the nonlocality-weighted sequence charge decoration (SCD) parameters are compared for their correlations with isolated-chain radii of gyration ($R_{\rm g}$s) and upper critical solution temperatures (UCSTs) of polyampholytes modeled by random phase approximation, field-theoretic simulation, and coarse-grained molecular dynamics. SCD is superior to $\kappa$ in predicting $R_{\rm g}$ because SCD accounts for effects of contact order, i.e., nonlocality, on dimensions of isolated chains. In contrast, $\kappa$ and SCD are comparably good, though nonideal, predictors of UCST because frequencies of interchain contacts in the multiple-chain condensed phase are less sensitive to sequence positions than frequencies of intrachain contacts of an isolated chain, as reflected by $\kappa$ correlating better with condensed-phase interaction energy than SCD.

q-bio.BM↗