The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition invariants in generalized Brillouin zone. resultant phase diagrams dramatically differ from usual Bloch theory. Specifically, we obtain diagram Su-Schrieffer-Heeger model, whose zero modes are determined by non-Bloch winding number instead Bloch-Hamiltonian-based number. Our work settles issue breakdown...

The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example bulk-boundary correspondence. We show that the are not strictly tied to defined by non-Hermitian Bloch Hamiltonian. This breakdown conventional correspondence stems from non-Bloch-wave behavior eigenstates (non-Hermitian skin effect), which generates pronounced deviations phase diagrams theory. introduce non-Bloch faithfully predict modes. theory backed up open-boundary energy...

One of the unique features non-Hermitian Hamiltonians is skin effect, namely, that eigenstates are exponentially localized at boundary system. For open quantum systems, a short-time evolution can often be well described by effective Hamiltonians, while long-time dynamics calls for Lindblad master equations, in which Liouvillian superoperators generate time evolution. In this Letter, we find exhibit and uncover its unexpected physical consequences. It shown effect dramatically shapes...

The topology of non-Hermitian systems is drastically shaped by the skin effect, which leads to generalized bulk-boundary correspondence and non-Bloch band theory. essential part in formulations a general computable definition topological invariants. In this Letter, we introduce construction invariants based directly on real-space wave functions, provides straightforward approach for determining topology. As an illustration, apply formulation several representative models systems, efficiently...

Language models are increasingly being deployed for general problem solving across a wide range of tasks, but still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play pivotal role. To surmount these challenges, we introduce new framework language model inference, Tree Thoughts (ToT), which generalizes over the popular Chain Thought approach...

While large language models (LLMs) have demonstrated impressive capabilities across tasks in understanding and interactive decision making, their abilities for reasoning (e.g. chain-of-thought prompting) acting action plan generation) primarily been studied as separate topics. In this paper, we explore the use of LLMs to generate both traces task-specific actions an interleaved manner, allowing greater synergy between two: help model induce, track, update plans well handle exceptions, while...

A bstract After averaging over fermion couplings, SYK has a collective field description that sometimes “wormhole” solutions. We study the fate of these wormholes when couplings are fixed. Working mainly in simple model, we find wormhole saddles persist, but new also appear elsewhere integration space — “half-wormholes.” The contributions depend only weakly on specific choice while half-wormhole strongly sensitive. half-wormholes crucial for factorization decoupled systems with fixed they...

A bstract We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on group SU q (1 , 1). construct its left-and right-regular representations, and representation matrices reproduce two-sided wavefunctions correlation functions DSSYK. then dynamical action path integral for 1), whose quantization reproduces aforementioned theory. By imposing boundary conditions or constraining system we find -analog Schwarzian Liouville descriptions. This...

Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) formulation topological invariants based on cooperation topology symmetries. Topological are constructed for ten symmetry classes all spatial dimensions, both homogeneous (Floquet insulators superconductors) defects. Meanwhile, useful representative Dirac Hamiltonians obtained studied. (ii) A general...

A bstract Haar integrals over the unitary group contain subleading terms that are needed for unitarity. We study analogous effects in time evolution operators of JT gravity and Brownian SYK. In with bulk matter we find an explanation first sub-leading terms, SYK configurations can explain full series. An important role is played by slightly off-shell modes exponentially amplified chaos.

As has been known since the 90s, there is an integrable structure underlying two-dimensional gravity theories. Recently, theories have regained enormous amount of attention, but now in relation with quantum chaos - superficially nothing like integrability. In this paper, we return to roots and exploit dilaton study a late time, large $e^{S_\text{BH}}$ double scaled limit spectral form factor. limit, novel cancellation due ensures that at each genus $g$ factor grows $T^{2g+1}$, sum over...

A bstract In AdS/CFT partition functions of decoupled copies the CFT factorize. bulk computations such quantities contributions from spacetime wormholes which link separate asymptotic boundaries threaten to spoil this property, leading a “factorization puzzle.” Certain simple models like JT gravity have wormholes, but in them correspond averages over an ensemble boundary systems. These need not We can formulate toy version factorization puzzle by focusing on specific member where will again...

A bstract We conjecture a formula for the spectral form factor of double-scaled matrix integral in limit large time, density states, and fixed temperature. The has genus expansion with nonzero radius convergence. To understand origin this series, we compare to semiclassical theory “encounters” periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond portions moduli space that mutually cancel (in orientable case) but individually grow at low energies. At one show how full...

After averaging over fermion couplings, SYK has a collective field description that sometimes "wormhole" solutions. We study the fate of these wormholes when couplings are fixed. Working mainly in simple model, we find wormhole saddles persist, but new also appear elsewhere integration space -- "half-wormholes." The contributions depend only weakly on specific choice while half-wormhole strongly sensitive. half-wormholes crucial for factorization decoupled systems with fixed they vanish...

Existing benchmarks for grounding language in interactive environments either lack real-world linguistic elements, or prove difficult to scale up due substantial human involvement the collection of data feedback signals. To bridge this gap, we develop WebShop -- a simulated e-commerce website environment with $1.18$ million products and $12,087$ crowd-sourced text instructions. Given instruction specifying product requirement, an agent needs navigate multiple types webpages issue diverse...

A bstract We present a new holographic duality between q-Schwarzian quantum mechanics and Liouville gravity. The is one parameter deformation of the Schwarzian, which dual to JT gravity describes low energy sector SYK. show that in turn sinh dilaton This can be rewritten as match thermodynamics classical two point function further prove on level by rewriting topological gauge theory, showing latter equals q-Schwarzian. As quantized exactly, this viewed an exact solution disk topology. For...

In AdS/CFT partition functions of decoupled copies the CFT factorize. bulk computations such quantities contributions from spacetime wormholes which link separate asymptotic boundaries threaten to spoil this property, leading a "factorization puzzle." Certain simple models like JT gravity have wormholes, but in them correspond averages over an ensemble boundary systems. These need not We can formulate toy version factorization puzzle by focusing on specific member where will again As Coleman...

A bstract As shown by Louko and Sorkin in 1995, topology change Lorentzian signature involves spacetimes with singular points, which they called crotches. We modify their construction to obtain semiclassical wormholes asymptotically AdS. These solutions are obtained inserting crotches on known saddles, like the double-cone or multiple copies of black hole. The implement swap-identifications, classically located near an extremal surface. resulting have instanton action equal area, is...

The study of language emergence aims to understand how human languages are shaped by perceptual grounding and communicative intent. Computational approaches emergent communication (EC) predominantly consider referential games in limited domains analyze the learned protocol within game framework. As a result, it remains unclear from these settings connect natural or provide benefits real-world processing tasks, where statistical models trained on large text corpora dominate. In this work, we...

Text adventure games present unique challenges to reinforcement learning methods due their combinatorially large action spaces and sparse rewards. The interplay of these two factors is particularly demanding because require extensive exploration, while rewards provide limited feedback. This work proposes tackle the explore-vs-exploit dilemma using a multi-stage approach that explicitly disentangles strategies within each episode. Our algorithm, called eXploit-Then-eXplore (XTX), begins...

We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on group SU$_q(1,1)$. construct its left-and right-regular representations, and representation matrices reproduce two-sided wavefunctions correlation functions DSSYK. then dynamical action path integral for SU$_q(1,1)$, whose quantization reproduces aforementioned theory. By imposing boundary conditions or constraining system we find $q$-analog Schwarzian Liouville descriptions. This...

We present a new holographic duality between q-Schwarzian quantum mechanics and Liouville gravity. The is one parameter deformation of the Schwarzian, which dual to JT gravity describes low energy sector SYK. show that in turn sinh dilaton This can be rewritten as match thermodynamics classical two point function further prove on level by rewriting topological gauge theory, showing latter equals q-Schwarzian. As quantized exactly, this viewed an exact solution disk topology. For real q,...

A new structure with InGaN/AlInN/InGaN composition-graded barriers for a nitride-based light-emitting diode (LED) has been proposed and analyzed numerically. The energy band diagrams, the electrostatic fields, carrier concentrations in quantum well, light output power internal efficiency are investigated. Numerical simulation results suggest that contributes to more uniform concentration distribution, smaller polarization field effective confinement of electrons active region. As result,...