Ref HAL: hal-03271316_v1
Ref Arxiv: 2106.12006
DOI: 10.1007/s00023-021-01129-x
WoS: 000722791700001
Ref. & Cit.: NASA ADS
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1 Citation
Résumé:

We revisit the Riemann-Hilbert problem determined by Donaldson-Thomas invariants for the resolved conifold and for other small crepant resolutions. While this problem can be recast as a system of TBA-type equations in the conformal limit, solutions are ill-defined due to divergences in the sum over infinite trajectories in the spectrum of D2-D0-brane bound states. We explore various prescriptions to make the sum well-defined, show that one of them reproduces the existing solution in the literature, and identify an alternative solution which is better behaved in a certain limit. Furthermore, we show that a suitable asymptotic expansion of the $\tau$ function reproduces the genus expansion of the topological string partition function for any small crepant resolution. As a by-product, we conjecture a new integral representation for the double sine function.

Ref HAL: hal-03259009_v5
DOI: 10.1126/sciadv.abl5855
WoS: WOS:000757399100013
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Résumé:

Both Classical and Quantum Electrodynamics predict the existence of dipole-dipole long-range electrodynamic intermolecular forces, however these have never been hitherto experimentally observed. The discovery of completely new and unanticipated forces acting between biomolecules could have considerable impact on our understanding of the dynamics and functioning of the molecular machines at work in living organisms. Here, using two independent approaches, we demonstrate experimentally for the first time the activation of resonant electrodynamic intermolecular forces. We characterize clustering transitions induced by these forces by fluorescence correlation spectroscopy when out-of-equilibrium conditions induce collective molecular oscillation observed by Terahertz (THz) spectroscopy. This is an unprecedented experimental \textit{proof of principle} of a physical phenomenon that, having been observed for bio-macromolecules and with a long-range of action (up to 1000 ${\mathring{A}}$), could be of importance for biology. Therefore, in addition to thermal fluctuations that drive molecular motion randomly, these resonant (and thus selective) electrodynamic forces may contribute to molecular encounters in the crowded cellular space. We anticipate our findings will provide a basis for future systematic deepening of physical aspects of the reported phenomena and for future systematic assessment of the relevance of electrodynamic forces in shaping the dynamics of biomolecular encounters and recognition in biology.

Ref HAL: hal-03245252_v1
Ref Arxiv: 2105.08946
Ref INSPIRE: 1864225
DOI: 10.21468/SciPostPhys.12.3.091
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Résumé:

We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(\epsilon,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $\epsilon$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.

Ref HAL: hal-02942375_v1
Ref Arxiv: 2006.09725
DOI: 10.1007/978-3-642-27737-5_248-2
Ref. & Cit.: NASA ADS
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Résumé:

We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis on spatially heterogeneous dynamics. We review the main theoretical approaches currently available to account for these glassy phenomena, including recent developments regarding mean-field theory of liquids and glasses, novel computational tools, and connections to the jamming transition. Finally, the physics of aging and off-equilibrium dynamics exhibited by glassy materials is discussed.

Commentaires: 50 pages, 24 figs. This is an updated version of a chapter initially written in 2009 for the Encyclopedia of Complexity and Systems Science (Springer)

Ref HAL: hal-02878251_v1
Ref Arxiv: 2006.10074
DOI: 10.4310/ATMP.2021.v25.n2.a1
Ref. & Cit.: NASA ADS
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Résumé:

We derive explicit expressions for the generating functions of refined Vafa-Witten invariants $\Omega(\gamma,y)$ of $\mathbb{P}^2$ of arbitrary rank $N$ and for their non-holomorphic modular completions. In the course of derivation we also provide: i) a generalization of the recently found generating functions of $\Omega(\gamma,y)$ and their completions for Hirzebruch and del Pezzo surfaces in the canonical chamber of the moduli space to a generic chamber; ii) a version of the blow-up formula expressed directly in terms of these generating functions and its reformulation in a manifestly modular form.