In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and analyze the relation between the total spread complexity and its decomposition into fixed-charge sectors. After exploring a range of analytical examples and using orthogonal polynomial approach, we identify conditions under which spread complexity exhibits equipartition across sectors. Finally, we discuss quantum speed limits that constrain the growth of complexity in the presence of conserved charges.

Elucidating fundamental limitations inherent in physical systems is a central subject in physics. For important thermodynamic operations such as information erasure, cooling, and copying, resources like time and energetic cost must be expended to achieve the desired outcome within a predetermined error margin. In the context of cooling, the unattainability principle of the third law of thermodynamics asserts that infinite "resources" are needed to reach absolute zero. However, the precise identification of relevant resources and how they jointly constrain achievable error remains unclear within the frameworks of stochastic and quantum thermodynamics. In this work, we introduce the concept of separated states, which consist of fully unoccupied and occupied states, and formulate the corresponding thermokinetic cost and error, thereby establishing a unifying framework for a broad class of thermodynamic operations. We then uncover a three-way trade-off relation between time, cost, and error for thermodynamic operations aimed at creating separated states, simply expressed as $\tau\mathcal{C}\varepsilon_{\tau}\ge 1-\eta$. This fundamental relation is applicable to diverse thermodynamic operations, including information erasure, cooling, and copying. It provides a profound quantification of the unattainability principle in the third law of thermodynamics in a general form. Building upon this relation, we explore the quantitative limitations governing cooling operations, the preparation of separated states, and a no-go theorem for exact classical copying. Furthermore, we extend these findings to the quantum regime, encompassing both Markovian and non-Markovian dynamics. Specifically, within Lindblad dynamics, we derive a similar three-way trade-off relation that quantifies the cost of achieving a pure state with a given error.

Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement, mitigating the bond-dimension bottleneck in TN simulations. In this work, we develop a variational TN framework based on Grassmann tensor networks, which natively encode fermionic statistics while preserving locality. By incorporating locally defined Clifford circuits within the fermionic formalism, we simulate benchmark models including the tight-binding and $t$-$V$ models. Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates. Interestingly, imposing the natural Grassmann-evenness constraint on the Clifford circuits significantly reduces the number of disentangling gates, from 720 to just 32, yielding a far more efficient implementation. These findings highlight the potential of Clifford-augmented Grassmann TNs as a scalable and accurate tool for studying strongly correlated fermionic systems, particularly in higher dimensions.

We study static spherically symmetric black hole solutions with a linearly time-dependent scalar field and discuss their linear stability in the shift- and reflection-symmetric subclass of quadratic degenerate higher-order scalar-tensor (DHOST) theories. We present the explicit forms of the reduced system of background field equations for a generic theory within this subclass. Using the reduced equations of motion, we show that in several cases the solution is forced to be of the Schwarzschild or Schwarzschild-(anti-)de Sitter form. We consider odd-parity perturbations around general static spherically symmetric black hole solutions, and derive the concise criteria for the black holes to be stable. Our analysis also covers the case with a static or constant profile of the scalar field.

The quantum nature of the Schwarzschild black hole interior is investigated through the Wheeler-DeWitt (WDW) equation. The interior of a static, spherically symmetric black hole is described by the Kantowski-Sachs (KS) metric, which represents a homogeneous but anisotropic cosmology. We derive the Hamiltonian for the gravitational system corresponding to the black hole interior and obtain the associated WDW equation. By varying the gravitational constant as a parameter controlling quantum effects, we examine how the solutions of the WDW equation change with respect to this parameter. In the parameter regime where quantum effects are negligible, we find that the wave packet solutions closely follow the classical trajectory of the black hole interior. On the other hand, as quantum effects are enhanced, the wave packet deviates from the classical trajectory and exhibits behavior suggestive of singularity avoidance. To quantify this behavior, we introduce an appropriate "clock" inside the black hole and compute the time to singularity formation with respect to this clock. The results show that stronger quantum effects lead to a longer formation time, suggesting a tendency toward the avoidance of singularity formation due to quantum gravity effects.

Cold dark matter (CDM) can be thought of as a 2D (or 3D) sheet of particles in 4D (or 6D) phase-space due to its negligible velocity dispersion. The large-scale structure, also called the cosmic web, is thus a result of the topology of the CDM manifold. Initial crossing of particle trajectories occurs at the critical points of this manifold, forming singularities that seed most of the collapsed structures. The cosmic web can thus be characterized using the points of singularities. In this context, we employ catastrophe theory in 2D to study the motion around such singularities and analytically model the shape of the emerging structures, particularly the pancakes, which later evolve into halos and filaments-the building blocks of the 2D web. We compute higher-order corrections to the shape of the pancakes, including properties such as the curvature and the scale of transition from their C to S shape. Using Gaussian statistics (with the assumption of Zeldovich flow) for our model parameters, we also compute the distributions of observable features related to the shape of pancakes and their variation across halo and filament populations in 2D cosmologies. We find that a larger fraction of pancakes evolve into filaments, they are more curved if they are to evolve into halos, are dominantly C-shaped, and the nature of shell-crossing is highly anisotropic. Extending this work to 3D will allow testing of predictions against actual observations of the cosmic web and searching for signatures of non-Gaussianity at corresponding scales.

The Berry phase is a fundamental quantity in the classification of topological phases of matter. In this paper, we present a new quantum algorithm and several complexity-theoretical results for the Berry phase estimation (BPE) problems. Our new quantum algorithm achieves BPE in a more general setting than previously known quantum algorithms, with a theoretical guarantee. For the complexity-theoretic results, we consider three cases. First, we prove $\mathsf{BQP}$-completeness when we are given a guiding state that has a large overlap with the ground state. This result establishes an exponential quantum speedup for estimating the Berry phase. Second, we prove $\mathsf{dUQMA}$-completeness when we have \textit{a priori} bound for ground state energy. Here, $\mathsf{dUQMA}$ is a variant of the unique witness version of $\mathsf{QMA}$ (i.e., $\mathsf{UQMA}$), which we introduce in this paper, and this class precisely captures the complexity of BPE without the known guiding state. Remarkably, this problem turned out to be the first natural problem contained in both $\mathsf{UQMA}$ and $\mathsf{co}$-$\mathsf{UQMA}$. Third, we show $\mathsf{P}^{\mathsf{dUQMA[log]}}$-hardness and containment in $\mathsf{P}^{\mathsf{PGQMA[log]}}$ when we have no additional assumption. These results advance the role of quantum computing in the study of topological phases of matter and provide a pathway for clarifying the connection between topological phases of matter and computational complexity.

In this paper, we discuss the concept of bulk reconstruction, which involves mapping bulk operators into CFT operators to understand the emergence of spacetime and gravity. We argue that the $N=\infty$ approximation fails to capture crucial aspects of gravity, as it does not respect gauge invariance and lacks direct connections between energy and boundary metrics. Key concepts such as entanglement wedge reconstruction and holographic error correction codes, which are based on the $N=\infty$ theory, may be incorrect or require significant revision when finite $N$ effects are considered. We present explicit examples demonstrating discrepancies in bulk reconstructions and suggest that a gauge-invariant approach is necessary for an accurate understanding.

Dark matter fermions interacting via attractive fifth forces mediated by a light mediator can form dark matter halos in the very early universe. We show that bound systems composed of these halos are capable of generating gravitational wave (GW) signals detectable today, even when the individual halos are very light. The Yukawa force dominates the dynamics of these halo binaries, rather than gravity. As a result, large GW signals can be produced at initially extremely high frequencies, which are then redshifted to frequency bands accessible to current or future GW observatories. In addition, the resulting GW signals carry distinctive features that enable future observations to distinguish them from conventional ones. Notably, even if only a tiny fraction of dark matter experiences strong fifth-force interactions, such effects provide a new avenue to discover self-interacting dark matter through GW observations.

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.

We present a novel search for dark photon dark matter (DM) using terrestrial magnetic field measurements at frequencies below 100 Hz. Coherently oscillating dark photon DM can induce a monochromatic magnetic field via kinetic mixing with ordinary photons. Notably, for dark photon masses $m_{A'}$ around $3 \times 10^{-14}$ eV, the signal can be resonantly amplified within a cavity formed by the Earth's surface and the ionosphere. We compute the expected signal incorporating the effect of atmospheric conductivity, and derive new upper limits on the kinetic mixing parameter $\varepsilon$ from long-term geomagnetic data. These limits improve upon previous ground-based constraints in the mass range of $1 \times 10^{-15}$ eV $\lesssim m_{A'} \lesssim 2 \times 10^{-13}$ eV.

We provide a concrete link between celestial amplitudes and cosmological correlators. We first construct a map from quantum field theories (QFTs) in $(D+2)$-dimensional Euclidean space to theories on the $(D+1)$-dimensional sphere, through a Weyl rescaling and a Fourier transformation. An analytic continuation extends this map to a relation between QFTs in Minkowski spacetime $\text{M}_{D+2}$ and in de Sitter spacetime $\text{dS}_{D+1}$ with the Bunch-Davies vacuum. Combining this relation with celestial holography, we show that the extrapolated operators in de Sitter space can be represented by operators on the celestial sphere $S^{D}$. Our framework offers a systematic route to transfer computational techniques and physical insights between celestial holography and the dS/CFT correspondence.

In scalar-tensor theories we revisit the issue of strong coupling of perturbations around stealth solutions, i.e.\ backgrounds with the same forms of the metric as in General Relativity but with non-trivial configurations of the scalar field. The simplest among them is a stealth Minkowski (or de Sitter) solution with a constant, timelike derivative of the scalar field, i.e.\ ghost condensation. In the decoupling limit the effective field theory (EFT) describing perturbations around the stealth Minkowski (or de Sitter) solution shows the universal dispersion relation of the form $\omega^2 = \alpha k^4/M^2$, where$M$ is a mass scale characterizing the background scalar field and $\alpha$ is a dimensionless constant. Provided that $\alpha$ is positive and of order unity, a simple scaling argument shows that the EFT is weakly coupled all the way up to $M$. On the other hand, if the structure of the underlining theory forces the perturbations to follow second-order equations of motion then $\alpha=0$ and the dispersion relation loses dependence on the spatial momentum. This not only explains the origin of the strong coupling problem that was recently pointed out in a class of degenerate theories but also provides a hint for a possible solution of the problem. We then argue that a controlled detuning of the degeneracy condition, which we call scordatura, renders the perturbations weakly coupled without changing the properties of the stealth solutions of degenerate theories at astrophysical scales.

We find various exact black hole solutions in the shift-symmetric subclass of the quadratic degenerate higher-order scalar-tensor (DHOST) theories with linearly time dependent scalar field whose kinetic term is constant. The exact solutions are the Schwarzschild and Schwarzschild-(anti-)de Sitter solutions, and the Schwarzschild-type solution with a deficit solid angle, which are accompanied by nontrivial scalar field regular at the black hole event horizon. We derive the conditions for the coupling functions in the DHOST Lagrangian that allow the exact solutions, clarify their compatibility with the degeneracy conditions, and provide general form of coupling functions as well as simple models that satisfy the conditions.