arXiv subjects

Anees Ahmed

Publications and source records attributed to Anees Ahmed.

14 recordsLinked to original sources

arXiv2026

Effects of super-Gaussian pulse shape and relative phase on dynamically assisted pair production in spatially inhomogeneous electric fields with frequency chirping

We investigate the effects of super-Gaussian pulse shapes on dynamically assisted pair production in spatially inhomogeneous electric fields with frequency chirping within the framework of the (1+1)-dimensional Dirac-Heisenberg-Wigner formalism. The analysis is carried out for both single-color fields and dynamically assisted two-color combined fields by varying the chirp parameter, super-Gaussian pulse shape, and the spatial scale of the external field. Our results are presented in terms of the reduced momentum distribution and the total particle yield, revealing that the interplay between pulse shaping, spatial inhomogeneity, frequency chirping, and dynamical assistance can significantly modify the pair-production dynamics. In particular, chirping substantially enhances the absolute pair-production yield and reshapes the momentum spectrum, with chirping of the weak component being particularly effective, while simultaneous chirping of both components produces the largest yields. The super-Gaussian order has a relatively modest influence on strong-field production, while increasing the flat-top character of the pulse enhances spectral structures and momentum redistribution in the weak and dynamically assisted regimes, particularly under chirping. Finally, we show that the relative phase between the two field components provides an additional control parameter, with its influence becoming more pronounced for larger spatial scales leading to significant changes in the momentum-space structure. Overall, our results provide a useful reference for optimal control of dynamically assisted pair production in space- and time-dependent electric fields within a prescribed range of field parameters.

hep-ph↗

arXiv2026

Dynamically assisted Schwinger pair production in differently polarized electric fields with the frequency chirping

We investigate the enhanced dynamically assisted electron-positron pair production in differently polarized electric fields with frequency chirps within the real-time Dirac-Heisenberg-Wigner formalism. The combined influence of the chirp strength and the field polarization on the momentum distribution and the total number density of the created pairs is studied in detail for one-color fields as well as dynamically assisted two-color combined fields. Frequency chirps, applied in different field configurations, strongly reshape the momentum spectra by modifying the interference patterns and enhancing the peak momentum distribution. In the dynamically assisted case, the total number density can be enhanced significantly over $2-3$ orders when large chirps are applied to both strong and weak fields. Furthermore, we observe that sensitivity of the number density to field polarization progressively diminishes as the chirp strength increases, a trend that holds for both one-color field and the assisted two-color combined fields. A comparison of different chirping scenarios shows that chirping only the weak field produces nearly the same enhancement in the pair yield as chirping both fields simultaneously, demonstrating that the weak-field chirp plays the dominant role in the chirp-induced enhancement of the dynamically assisted Schwinger mechanism. We also find the enhancement factor to be the largest near circular polarization in the chirp-free and weakly chirped regimes, but is strongly suppressed with increasing weak-field chirp despite the continued growth of the absolute pair yield. These results provide new insight into the interplay among chirp, polarization, and dynamical assistance in strong-field quantum electrodynamics.

hep-ph↗

arXiv2026

Carrier-envelope phase and pulse shape effects on vacuum pair production in asymmetric electric fields with bell-shaped envelopes

We investigate the combined effects of carrier-envelope phase and laser pulse shape on electron-positron pair production in the presence of an external time-dependent asymmetric electric field by solving the quantum Vlasov equation. We analyze how the pulse asymmetry, the envelope type (Gaussian, Lorentzian and Sauter), and the carrier-envelope phase jointly influence the momentum distribution and the total number of produced pairs per unit volume. Our results show that pair production exhibits extreme sensitivity to both the degree of temporal asymmetry and the steepness of the envelope on either side of the pulse. These effects are qualitatively explained through a turning-point analysis for the non-analytic electric field using a regularization scheme. We observe that multiphoton pair production dominates the Schwinger mechanism in the case of a long falling-pulse asymmetry. For a short falling pulse with a flat-topped profile, pair production is further facilitated. We demonstrate that the density of produced pairs can be enhanced by two to three orders of magnitude by choosing certain field parameters.

hep-ph↗

arXiv2026

Spectral and Phase Structure of a Unitary Matrix Model with Fisher-Hartwig Singularities

We investigate a unitary matrix model with a complex potential with Fisher-Hartwig singularities. We show that the model exhibits finite-$N$ phase transitions. The order of the phase transition is coupling-dependent. At large-$N$, these transitions are replaced by third-order Gross-Witten-Wadia transitions between multiple ungapped phases and a single gapped phase, with transitions between ungapped phases forbidden. At both finite and large $N$, the phases are characterized by the locations of the Fisher-Hartwig singularities in the complex plane.

hep-th↗

arXiv2026

Carrier envelope phase and laser pulse shape effects on Schwinger vacuum pair production in super-Gaussian asymmetric electric fields

We investigate the combined effects of carrier envelope phase and laser pulse shape on electron-positron pair production in the presence of an external asymmetric super-Gaussian electric field by solving the quantum Vlasov equation. By varying the field asymmetry, the pulse shape from Gaussian to super-Gaussian, and the carrier envelope phase, we show the momentum distribution and the number density of created pairs to exhibit extreme sensitivity to these field characteristics. The effects are also qualitatively explained by analyzing the turning-point structures within the WKB formalism. We observed that multiphoton pair production dominates in the case of long falling-pulse asymmetry. For a short falling pulse with a flat-top super-Gaussian laser profile, pair production is further facilitated. For certain field parameters, we demonstrate that the number density can be enhanced by two to three orders of magnitude.

physics.plasm-ph↗

arXiv2025

Gotta Hash 'Em All! Speeding Up Hash Functions for Zero-Knowledge Proof Applications

Collision-resistant cryptographic hash functions (CRHs) are crucial for security, particularly for message authentication in Zero-knowledge Proof (ZKP) applications. However, traditional CRHs like SHA-2 or SHA-3, while optimized for CPUs, generate large circuits, rendering them inefficient in the ZK domain. Conversely, ZK-friendly hashes are designed for circuit efficiency but struggle on conventional hardware, often orders of magnitude slower than standard hashes due to their reliance on expensive finite field arithmetic. To bridge this performance gap, we present HashEmAll, a novel collection of FPGA-based realizations for three prominent ZK-friendly hashes: Griffin, Rescue-Prime, and Reinforced Concrete. Each offers distinct optimization profiles, with both area-optimized and latency-optimized variants available, allowing users to tailor hardware selection to specific application constraints regarding resource utilization and performance. Our extensive evaluation shows that latency-optimized HashEmAll designs outperform CPU implementations by at least $10 \times$, with the leading design achieving a $23 \times$ speedup. These gains are coupled with lower power consumption and compatibility with accessible FPGAs. Importantly, the highly parallel and pipelined architecture of HashEmAll enables significantly better practical scaling than CPU-based approaches towards building real-world ZKP applications, such as data commitments with Merkle Trees, by mitigating the hashing bottleneck for large trees. This highlights the suitability of HashEmAll for real-world ZKP applications involving large-scale data authentication. We also highlight the ability to translate the HashEmAll methodology to various ZK-friendly hash functions and different field sizes.

cs.CR↗

arXiv2025

Zero-Knowledge Proof Frameworks: A Systematic Survey

Zero-Knowledge Proofs (ZKPs) are a cryptographic primitive that allows a prover to demonstrate knowledge of a secret value to a verifier without revealing anything about the secret itself. ZKPs have shown to be an extremely powerful tool, as evidenced in both industry and academic settings. In recent years, the utilization of user data in practical applications has necessitated the rapid development of privacy-preserving techniques, including ZKPs. This has led to the creation of several robust open-source ZKP frameworks. However, there remains a significant gap in understanding the capabilities and real-world applications of these frameworks. Furthermore, identifying the most suitable frameworks for the developers' specific applications and settings is a challenge, given the variety of options available. The primary goal of our work is to lower the barrier to entry for understanding and building applications with open-source ZKP frameworks. In this work, we survey and evaluate 25 general-purpose, prominent ZKP frameworks. Recognizing that ZKPs have various constructions and underlying arithmetic schemes, our survey aims to provide a comprehensive overview of the ZKP landscape. These systems are assessed based on their usability and performance in SHA-256 and matrix multiplication experiments. Acknowledging that setting up a functional development environment can be challenging for these frameworks, we offer a fully open-source collection of Docker containers. These containers include a working development environment and are accompanied by documented code from our experiments. We conclude our work with a thorough analysis of the practical applications of ZKPs, recommendations for ZKP settings in different application scenarios, and a discussion on the future development of ZKP frameworks.

cs.CR↗

arXiv2024

Quantum Annealing based Hybrid Strategies for Real Time Route Optimization

One of the most well-known problems in transportation and logistics is the Capacitated Vehicle Routing Problem (CVRP). It involves optimizing a set of truck routes to service a set of customers, subject to limits on truck capacity, to reduce travel costs. The biggest challenge faced whilst attempting to solve the issue is that the time complexity of the issue grows exponentially with the number of customers and trucks, rendering it virtually intractable to traditional computers and algorithms. In this paper, we propose a method to circumvent this limitation, employing quantum computers to aid classical computers in solving problems faster while reducing complexity. To obtain our results, we employ two algorithms: Hybrid Two Step (H2S) and Hybrid Three Step (H3S). Both algorithms involve two phases: clustering and routing. It has been observed that both algorithms produce promising results, both in terms of solution time and solution cost.

quant-ph↗

arXiv2024

AMAZE: Accelerated MiMC Hardware Architecture for Zero-Knowledge Applications on the Edge

Collision-resistant, cryptographic hash (CRH) functions have long been an integral part of providing security and privacy in modern systems. Certain constructions of zero-knowledge proof (ZKP) protocols aim to utilize CRH functions to perform cryptographic hashing. Standard CRH functions, such as SHA2, are inefficient when employed in the ZKP domain, thus calling for ZK-friendly hashes, which are CRH functions built with ZKP efficiency in mind. The most mature ZK-friendly hash, MiMC, presents a block cipher and hash function with a simple algebraic structure that is well-suited, due to its achieved security and low complexity, for ZKP applications. Although ZK-friendly hashes have improved the performance of ZKP generation in software, the underlying computation of ZKPs, including CRH functions, must be optimized on hardware to enable practical applications. The challenge we address in this work is determining how to efficiently incorporate ZK-friendly hash functions, such as MiMC, into hardware accelerators, thus enabling more practical applications. In this work, we introduce AMAZE, a highly hardware-optimized open-source framework for computing the MiMC block cipher and hash function. Our solution has been primarily directed at resource-constrained edge devices; consequently, we provide several implementations of MiMC with varying power, resource, and latency profiles. Our extensive evaluations show that the AMAZE-powered implementation of MiMC outperforms standard CPU implementations by more than 13$\times$. In all settings, AMAZE enables efficient ZK-friendly hashing on resource-constrained devices. Finally, we highlight AMAZE's underlying open-source arithmetic backend as part of our end-to-end design, thus allowing developers to utilize the AMAZE framework for custom ZKP applications.

cs.CR↗

arXiv2024

Ginzburg-Landau approach to the Gross-Neveu model: success and failure

The phase diagram of the Gross-Neveu model in 1+1 dimensions is studied using Ginzburg-Landau expansion. It predicts several features of the exact phase diagram correctly even at low orders. It is shown that increasing the order of the expansion improves the accuracy of the crystal phase except for very small temperatures, where the expansion completely fails regardless of the order of the expansion. The source of this behaviour seems to be related to the Silver-Blaze phenomenon.

hep-th↗

arXiv2018

Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function

We describe the non-perturbative trans-series, at both weak- and strong-coupling, of the large N approximation to the beta function of the Gross-Witten-Wadia unitary matrix model. This system models a running coupling, and the structure of the trans-series changes as one crosses the large N phase transition. The perturbative beta function acquires a non-perturbative trans-series completion at large but finite $N$ in the 't Hooft limit, as does the running coupling.

hep-th↗

arXiv2018

Tri-Compress: A Cascaded Data Compression Framework for Smart Electricity Distribution Systems

Modern smart distribution system requires storage, transmission and processing of big data generated by sensors installed in electric meters. On one hand, this data is essentially required for intelligent decision making by smart grid but on the other hand storage, transmission and processing of that huge amount of data is also a challenge. Present approaches to compress this information have only relied on the traditional matrix decomposition techniques benefitting from low number of principal components to represent the entire data. This paper proposes a cascaded data compression technique that blends three different methods in order to achieve high compression rate for efficient storage and transmission. In the first and second stages, two lossy data compression techniques are used, namely Singular Value Decomposition (SVD) and Normalization; Third stage achieves further compression by using the technique of Sparsity Encoding (SE) which is a lossless compression technique but only having appreciable benefits for sparse data sets. Our simulation results show that the combined use of the 3 techniques achieves data compression ratio to be 15% higher than state of the art SVD for small, sparse datasets and up to 28% higher in large, non-sparse datasets with acceptable Mean Absolute Error (MAE).

eess.SP↗

arXiv2018

Ginzburg-Landau Type Approach to the 1+1 Gross Neveu Model - Beyond Lowest Non-Trivial Order

This paper presents a case study of the effects of increasing the order of a Ginzburg-Landau type expansion, by using the well known Gross-Neveu model in 1+1 dimensions as a test case. It is found that as the order of expansion increases, the predicted phase diagram increasingly resembles the known exact phase diagram. Finally, some properties of arbitrary large order phase diagrams are examined.

hep-th↗

arXiv2017

Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling $g^2$ and a gauge index $N$, as a system passes through a large $N$ phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms `condense' at the transition point to match with the double-scaling limit trans-series. We also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.

hep-th↗