arXiv subjects

Jie Gu

Publications and source records attributed to Jie Gu.

At least 55 records · Page 3Linked to original sources

arXiv2025

Resurgent properties of $T\overline{T}$-deformed conformal field theories

We elaborate on the resurgence analysis on the $T\overline{T}$-deformed 2d conformal field theory (CFT). Writing the deformed partition function as an infinite series in the deformation parameter $λ$, we develop efficient analytical methods to compute high-order terms of the $λ$-series. Based on the asymptotic behavior of the large-order perturbative series, we show that the $λ$-series is asymptotic and extract non-perturabtive contributions by resurgence. This paper extends a previous Letter of the same authors to interacting rational CFTs, with Lee-Yang CFT as a concrete example. We also discuss possible implications of the resurgence results on holography.

hep-th↗

arXiv2025

Dynamical activity universally bounds precision of response in Markovian nonequilibrium systems

The exploration of far-from-equilibrium systems has been at the forefront of nonequilibrium thermodynamics, with a particular focus on understanding the fluctuations and response of thermodynamic systems to external perturbations. In this study, we introduce a universal response kinetic uncertainty relation, which provides a fundamental trade-off between the precision of response for generic observables and dynamical activity in Markovian nonequilibrium systems. We demonstrate the practical applicability and tightness of the derived bound through illustrative examples. Our results are applicable to a broad spectrum of Markov jump processes, ranging from currents to non-current variables, from steady states to time-dependent driving, from continuous time to discrete time, and including Maxwell's demon or absolute irreversibility. Our findings not only enhance the theoretical foundation of stochastic thermodynamics but also may hold potential implications for far-from-equilibrium biochemical processes.

cond-mat.stat-mech↗

arXiv2024

Resurgence of $T\bar{T}$-deformed Partition Function

We study non-perturbative effects of torus partition function of the $T\bar{T}$-deformed 2d CFTs by resurgence. The deformed partition function can be written as an infinite series of the deformation parameter $λ$. We develop highly efficient methods to compute perturbative coefficients in the $λ$ expansion. To exemplify, the first 600 coefficients for the $T\bar{T}$-deformed free boson and free fermion are computed. Equipped with the large order perturbative data, we provide convincing numerical evidence that the $λ$ expansion series is asymptotic and not Borel resummable. We extract the non-perturbative contribution by resurgence and propose that they originate from new complex saddle points after analytically continuing the modular parameters in the integral representation of the partition function. The proposal is checked by comparing the predicted asymptotic behavior of the coefficients and large order perturbative data, which match nicely. The implications of these non-perturbative contributions for the Stokes phenomenon, which relates the positive and negative signs of $λ$, is also discussed.

hep-th↗

arXiv2024

Towards full instanton trans-series in Hofstadter's butterfly

The trans-series completion of perturbative series of a wide class of quantum mechanical systems can be determined by combining the resurgence program and extra input coming from exact WKB analysis. In this paper, we reexamine the Harper-Hofstadter model and its spectrum, Hofstadter's butterfly, in light of recent developments. We demonstrate the connection between the perturbative energy series of the Harper-Hofstadter model and the vev of $1/2$-BPS Wilson loop of 5d SYM and clarify the differences between their non-perturbative corrections. Taking insights from the cosine potential model, we construct the full energy trans-series for flux $ϕ=2π/Q$ and provide numerical evidence with remarkably high precision. Finally, we revisit the problem of self-similarity of the butterfly and discuss the possibility of a completed version of the Rammal-Wilkinson formula.

hep-th↗

arXiv2024

Thermodynamic bounds on the asymmetry of cross-correlations with dynamical activity and entropy production

Entropy production and dynamical activity are two complementary aspects in nonequilibrium physics. The asymmetry of cross-correlation, serving as a distinctive feature of nonequilibrium, also finds widespread utility. In this Letter, we establish two thermodynamic bounds on the normalized asymmetry of cross-correlation in terms of dynamical activity and entropy production rate. These bounds demonstrate broad applicability, and offer experimental testability.

cond-mat.stat-mech↗

arXiv2023

Speed limit, dissipation bound and dissipation-time trade-off in thermal relaxation processes

We investigate bounds on speed, non-adiabatic entropy production and trade-off relation between them for classical stochastic processes with time-independent transition rates. Our results show that the time required to evolve from an initial to a desired target state is bounded from below by the informational-theoretic $\infty$-Rényi divergence between these states, divided by the total rate. Furthermore, we conjecture and provide extensive numerical evidence for an information-theoretical bound on the non-adiabatic entropy production and a novel dissipation-time trade-off relation that outperforms previous bounds in some cases.

cond-mat.stat-mech↗

arXiv2023

Exact multi-instantons in topological string theory

Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations in the case of local $\mathbb{P}^2$.

hep-th↗

arXiv2023

Phase-Matching Quantum Key Distribution without Intensity Modulation

Quantum key distribution provides a promising solution for sharing secure keys between two distant parties with unconditional security. Nevertheless, quantum key distribution is still severely threatened by the imperfections of devices. In particular, the classical pulse correlation threatens security when sending decoy states. To address this problem and simplify experimental requirements, we propose a phase-matching quantum key distribution protocol without intensity modulation. Instead of using decoy states, we propose a novel method to estimate the theoretical upper bound on the phase error rate contributed by even-photon-number components. Simulation results show that the transmission distance of our protocol could reach 305 km in telecommunication fiber. Furthermore, we perform a proof-of-principle experiment to demonstrate the feasibility of our protocol, and the key rate reaches 22.5 bps under a 45 dB channel loss. Addressing the security loophole of pulse intensity correlation and replacing continuous random phase with 6 or 8 slices random phase, our protocol provides a promising solution for constructing quantum networks.

quant-ph↗

arXiv2023

Non-perturbative topological string theory on compact Calabi-Yau 3-folds

We obtain analytic and numerical results for the non-perturbative amplitudes of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our approach is based on the theory of resurgence and extends previous special results to the more general case. In particular, we obtain explicit trans-series solutions of the holomorphic anomaly equations. Our results predict the all orders, large genus asymptotics of the topological string free energies, which we test in detail against high genus perturbative series obtained recently in the compact case. We also provide additional evidence that the Stokes constants appearing in the resurgent structure are closely related to integer BPS invariants.

hep-th↗

arXiv2023

Empowering General-purpose User Representation with Full-life Cycle Behavior Modeling

User Modeling plays an essential role in industry. In this field, task-agnostic approaches, which generate general-purpose representation applicable to diverse downstream user cognition tasks, is a promising direction being more valuable and economical than task-specific representation learning. With the rapid development of Internet service platforms, user behaviors have been accumulated continuously. However, existing general-purpose user representation researches have little ability for full-life cycle modeling on extremely long behavior sequences since user registration. In this study, we propose a novel framework called full- Life cycle User Representation Model (LURM) to tackle this challenge. Specifically, LURM consists of two cascaded sub-models: (I) Bag-of-Interests (BoI) encodes user behaviors in any time period into a sparse vector with super-high dimension (e.g., 10^5); (II) Self-supervised Multi-anchor Encoder Network (SMEN) maps sequences of BoI features to multiple low-dimensional user representations. Specially, SMEN achieves almost lossless dimensionality reduction, benefiting from a novel multi-anchor module which can learn different aspects of user interests. Experiments on several benchmark datasets show that our approach outperforms state-of-the-art general-purpose representation methods.

cs.LG↗

arXiv2023

Relations between Stokes constants of unrefined and Nekrasov-Shatashvili topological strings

In this paper we demonstrate that the Stokes constants of unrefined free energies and the Stokes constants of Nekrasov-Shatashvili free energies of topological string on a non-compact Calabi-Yau threefold are identical, possibly up to a sign, for any Borel singularity which is not associated to a compact two-cycle that intersects only with non-compact four-cycles. Since the Stokes constants of Nekrasov-Shatashvili free energies are conjectured to coincide with those of quantum periods and therefore have the interpretation of BPS invariants, our results give strong support that the Stokes constants of unrefined free energies may also be identified with BPS invariants.

hep-th↗

arXiv2023

Simple security proof of coherent-one-way quantum key distribution

Coherent-one-way quantum key distribution (COW-QKD), which requires a simple experimental setup and has the ability to withstand photon-number-splitting attacks, has been not only experimentally implemented but also commercially applied. However, recent studies have shown that the current COW-QKD system is insecure and can only distribute secret keys safely within 20 km of the optical fiber length. In this study, we propose a practical implementation of COW-QKD by adding a two-pulse vacuum state as a new decoy sequence. This proposal maintains the original experimental setup as well as the simplicity of its implementation. Utilizing detailed observations on the monitoring line to provide an analytical upper bound on the phase error rate, we provide a high-performance COW-QKD asymptotically secure against coherent attacks. This ensures the availability of COW-QKD within 100 km and establishes theoretical foundations for further applications.

quant-ph↗

arXiv2023

Experimental quantum secret sharing based on phase encoding of coherent states

Quantum secret sharing (QSS) is one of the basic communication primitives in future quantum networks which addresses part of the basic cryptographic tasks of multiparty communication and computation. Nevertheless, it is a challenge to provide a practical QSS protocol with security against general attacks. A QSS protocol that balances security and practicality is still lacking. Here, we propose a QSS protocol with simple phase encoding of coherent states among three parties. Removing the requirement of impractical entangled resources and the need for phase randomization, our protocol can be implemented with accessible technology. We provide the finite-key analysis against coherent attacks and implement a proof-of-principle experiment to demonstrate our scheme's feasibility. Our scheme achieves a key rate of 85.3 bps under a 35 dB channel loss. Combined with security against general attacks and accessible technology, our protocol is a promising candidate for practical multiparty quantum communication networks.

quant-ph↗

arXiv2023

On the resurgent structure of quantum periods

Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations satisfied by these quantities, and we obtain exact multi-instanton solutions for these trans-series. Building on this result, we propose a unified perspective on the resurgent structure of quantum periods. We show for example that the Delabaere-Pham formula, which was originally obtained in quantum mechanical examples, is a generic feature of quantum periods. We illustrate our general results with explicit calculations for the double-well in quantum mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$.

hep-th↗

arXiv2023

Resurgence in complex Chern-Simons theory at generic levels

In this note we study the resurgent structure of $sl(2,\mathbb{C})$ Chern-Simons state integral models on knot complements $S^3\backslash\mathbf{4}_1,S^3\backslash\mathbf{5}_2$ with generic discrete level $k\geq 1$ and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of the knot extended by the holonomy parameter. Despite increasing complication of the asymptotic series as the level $k$ increases, the resurgent structure of the asymptotic series is universal: both the distribution of Borel plane singularities and the associated Stokes constants are independent of the level $k$.

hep-th↗

arXiv2023

Work statistics in slow thermodynamic processes

We apply the adiabatic approximation to slow but finite-time thermodynamic processes and obtain the full counting statistics of work. The average work consists of change in free energy and the dissipated work, and we identify each term as a dynamical- and geometric-phase-like quantity. An expression for the friction tensor, the key quantity in thermodynamic geometry, is explicitly given. The dynamical and geometric phases are proved to be related to each other via the fluctuation-dissipation relation.

cond-mat.stat-mech↗

arXiv2022

The descendants of the 3d-index

In the study of 3d-3d correspondence occurs a natural $q$-Weyl algebra associated to an ideal triangulation of a 3-manifold with torus boundary components, and a module of it. We study the action of this module on the (rotated) 3d-index of Dimofte-Gaiotto-Gukov and we conjecture some structural properties: bilinear factorization in terms of holomorphic blocks, pair of linear $q$-difference equations, the determination of the 3d-index in terms of a finite size matrix of rational functions and the asymptotic expansion of the $q$-series as $q$ tends to 1 to all orders. We illustrate our conjectures with computations for the case of the three simplest hyperbolic knots.

math.GT↗

arXiv2022

Experimental measurement-device-independent type quantum key distribution with flawed and correlated sources

The security of quantum key distribution (QKD) is severely threatened by discrepancies between realistic devices and theoretical assumptions. Recently, a significant framework called the reference technique was proposed to provide security against arbitrary source flaws under current technology such as state preparation flaws, side channels caused by mode dependencies, the Trojan horse atttacks and pulse correlations. Here, we adopt the reference technique to prove security of an efficient four-phase measurement-device-independent QKD using laser pulses against potential source imperfections. We present a characterization of source flaws and connect them to experiments, together with a finite-key analysis against coherent attacks. In addition, we demonstrate the feasibility of our protocol through a proof-of-principle experimental implementation and achieve a secure key rate of 253 bps with a 20 dB channel loss. Compared with previous QKD protocols with imperfect devices, our study considerably improves both the secure key rate and the transmission distance, and shows application potential in the practical deployment of secure QKD with device imperfections.

quant-ph↗