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The critical dynamics of Model H with a conserved order parameter coupled to a transverse momentum density which describes the gas-liquid or binary-fluid transitions is investigated within the functional renormalization group approach formulated on the closed time path. According to the dynamic scaling analysis, Model H and QCD critical end point belong to the same dynamic universality class in the critical region. The higher-order correction of the transport coefficient $\bar\lambda$ and shear viscosity $\bar\eta$ arising from mode-couplings are obtained by calculating the two-point correlation functions. The flow equation of a dimensionless coupling constant for nondissipative interactions is derived to look for the fixed-point solution of the system. The scaling relation between the critical exponent of the transport coefficient and that of the shear viscosity is estimated. Finally, the dynamic critical exponent $z$ is obtained as a function of the spatial dimension $d$., Comment: 10 pages, 6 figures

High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition metal complexes via optically-detected magnetic resonance (ODMR) mechanisms analogous to the diamond-NV colour centre. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are $\pi$-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realise a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimise radical-radical interactions in the ground state, generating $\pi$-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarisation. The molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular colour centres., Comment: 12 pages, 5 figures, 1 table. Minor edits made to the manuscript text

Recently, in studies of holographic models and hydrodynamics with spontaneous breaking of approximate symmetries, it has been proposed that the damping of pseudo-Goldstone modes at finite temperatures is universally constrained in the way that $\Omega_{\varphi}/m_{\varphi}^2\simeq D_{\varphi}$ in the broken phase, where $\Omega_{\varphi}$ and $m_{\varphi} $ are the relaxation rate at zero wavenumber and the mass of pseudo-Goldstones, $D_{\varphi}$ is the Goldstone diffusivity in the limit of purely spontaneous breaking. In this paper, we investigate the pseudo-Goldstone damping in a purely relaxational O($N$) model by performing the functional renormalization group calculations at the full quantum and stochastic level within the Schwinger-Keldysh formalism. We find that, away from the critical temperature, the proposed relation is always valid. When the temperature is very close to the critical value such that the mass of the Higgs mode is comparable to the mass of the pseudo-Goldstone modes, the pseudo-Goldstone damping displays a novel scaling behavior that follows $\Omega_\varphi/m_\varphi^2\propto m_{\varphi}^{\Delta_\eta}$ with a correction $\Delta_\eta$ controlled by the critical universalities. Moreover, we study how the correction depends on the value of $N$ and show that $\Delta_\eta \rightarrow 0$ when fluctuations are infinitely suppressed in the large $N$ limit. In this case, the proposed relation works even in the critical region. Finally, we match our results to the dissipative sector of the pion dynamics near the chiral phase transition., Comment: V2:minor revision, references added, discussion on the pure SSB case has been moved to the supplement

The Schwinger-Keldysh functional renormalization group (fRG) developed in [1] is employed to investigate critical dynamics related to a second-order phase transition. The effective action of model A is expanded to the order of $O(\partial^2)$ in the derivative expansion for the $O(N)$ symmetry. By solving the fixed-point equations of effective potential and wave function, we obtain static and dynamic critical exponents for different values of the spatial dimension $d$ and the field component number $N$. It is found that one has $z \geq 2$ in the whole range of $2\leq d\leq 4$ for the case of $N=1$, while in the case of $N=4$ the dynamic critical exponent turns to $z < 2$ when the dimension approach towards $d=2$., Comment: 11 pages, 11 figures

We investigate theoretically the enhancement of mechanical squeezing in a multimode optomechanical system by introducing a coherent phonon-photon interaction via the backward stimulated Brillouin scattering (BSBS) process. The coherent photon-phonon interaction where two optical modes couple to a Brillouin acoustic mode with a large decay rate provides an extra channel for the cooling of a Duffing mechanical oscillator. The squeezing degree and the robustness to the thermal noises of the Duffing mechanical mode can be enhanced greatly. When the Duffing nonlinearity is weak, the squeezing degree of the mechanical mode in the presence of BSBS can be improved more than one order of magnitude compared with the absence of BSBS. Our scheme may be extended to other quantum systems to study novel quantum effects.

The chiral crossover of QCD at finite temperature and vanishing baryon density turns into a second order phase transition if lighter than physical quark masses are considered. If this transition occurs sufficiently close to the physical point, its universal critical behaviour would largely control the physics of the QCD phase transition. We quantify the size of this region in QCD using functional approaches, both Dyson-Schwinger equations and the functional renormalisation group. The latter allows us to study both critical and non-critical effects on an equal footing, facilitating a precise determination of the scaling regime. We find that the physical point is far away from the critical region. Importantly, we show that the physics of the chiral crossover is dominated by soft modes even far beyond the critical region. While scaling functions determine all thermodynamic properties of the system in the critical region, the order parameter potential is the relevant quantity away from it. We compute this potential in QCD using the functional renormalisation group and Dyson-Schwinger equations and provide a simple parametrisation for phenomenological applications., Comment: 7+8 pages, 5+4 figures

Topological insulators are insulators in the bulk but feature chiral energy propagation along the boundary. This property is topological in nature and therefore robust to disorder. Originally discovered in electronic materials, topologically protected boundary transport has since been observed in many other physical systems. Thus, it is natural to ask whether this phenomenon finds relevance in a broader context. We choreograph a dance in which a group of humans, arranged on a square grid, behave as a topological insulator. The dance features unidirectional flow of movement through dancers on the lattice edge. This effect persists when people are removed from the dance floor. Our work extends the applicability of wave physics to the performance arts.

Polariton chemistry has emerged as an appealing branch of synthetic chemistry that promises mode selectivity and a cleaner approach to kinetic control. Of particular interest are the numerous experiments in which reactivity has been modified by virtue of performing the reaction inside infrared optical microcavities in the absence of optical pumping; this effort is known as "vibropolaritonic chemistry." The optimal conditions for these observations are (1) resonance between cavity and reactive modes at normal incidence ($k=0$), and (2) monotonic increase of the effect with the concentration of emitters in the sample. Importantly, vibropolaritonic chemistry has only been experimentally demonstrated in the so-called "collective" strong coupling regime, where there is a macroscopic number of molecules (rather than a single molecule) coupled to each photon mode of the microcavity. Strikingly, efforts to understand this phenomenon from a conceptual standpoint have encountered several roadblocks and no single, unifying theory has surfaced thus far. This perspective documents the most relevant approaches taken by theorists, laying out the contributions and unresolved challenges from each work. We expect this manuscript to not only serve as a primer for experimentalists and theorists alike, but also inform future endeavors in the quest for the ultimate formalism of vibropolaritonic chemical kinetics., Comment: 18 pages, 5 figures

Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to obtain a global fixed-point potential with high numerical accuracy, that incorporates the correct asymptotic behavior in the limit of large field. Our calculated global potential is in good agreement with the Taylor expansion in the region of small field, and it also coincides with the Laurent expansion in the regime of large field. Laurent expansion of the potential in the limit of large field for general case, that the spatial dimension $d$ is a continuous variable in the range $2\leq d \leq 4$, is obtained. Eigenfunctions and eigenvalues of perturbations near the Wilson-Fisher fixed point are computed with the method of eigenperturbations. Critical exponents for different values of $d$ and $N$ of the $O(N)$ universality class are calculated., Comment: 10 pages, 4 figures, 1 table; v2: minor changes, discussions and references added

Following experimental evidence that vibrational polaritons, formed from collective vibrational strong coupling (VSC) in optical microcavities, can modify ground-state reaction rates, a spate of theoretical explanations relying on cavity-induced frictions has been proposed through the Pollak-Grabert-H\"anggi (PGH) theory, which goes beyond transition state theory (TST). However, by considering only a single reacting molecule coupled to light, these works do not capture the ensemble effects present in experiments. Moreover, the relevant light-matter coupling should have been $\sqrt{N}$ times smaller than those used by preceding works, where $N\approx10^{6}-10^{12}$ is the ensemble size. In this work, we explain why this distinction is significant and can nullify effects from these cavity-induced frictions. By analytically extending the cavity PGH model to realistic values of $N$, we show how this model succumbs to the polariton "large $N$ problem", that is, the situation whereby the single reacting molecule feels only a tiny $1/N$ part of the collective light-matter interaction intensity, where $N$ is large., Comment: 9 pages, 4 figures

The rate of non-radiative decay between two molecular electronic states is succinctly described by the energy gap law, which suggests an approximately-exponential dependence of the rate on the electronic energy gap. Here, we inquire whether this rate is modified under vibrational strong coupling, a regime whereby the molecular vibrations are strongly coupled to an infrared cavity. We show that, under most conditions, the collective light-matter coupling strength is not large enough to counter the entropic penalty involved with using the polariton modes, so the energy gap law remains unchanged. This effect (or the lack thereof) may be reversed with deep strong light-matter couplings or large detunings, both of which increase the upper polariton frequency. Finally, we demonstrate how vibrational polariton condensates mitigate the entropy problem by providing large occupation numbers in the polariton modes., Comment: 12 pages, 5 figures

We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows are manifestly finite in general non-perturbative truncation schemes also for regularisation schemes that do not implement an infrared suppression of the loops in the flow. Specifically, this formulation includes finite functional flows for the effective action with a spectral Callan-Symanzik cutoff, and therefore gives access to Lorentz invariant spectral flows. The functional setup is fully non-perturbative and allows for the spectral treatment of general theories. In particular, this includes theories that do not admit a perturbative renormalisation such as asymptotically safe theories. Finally, the application of the Lorentz invariant spectral functional renormalisation group is briefly discussed for theories ranging from real scalar and Yukawa theories to gauge theories and quantum gravity., Comment: 31 pages, 1 figure

In this work, we aim to learn multi-level user intents from the co-interacted patterns of items, so as to obtain high-quality representations of users and items and further enhance the recommendation performance. Towards this end, we develop a novel framework, Hierarchical User Intent Graph Network, which exhibits user intents in a hierarchical graph structure, from the fine-grained to coarse-grained intents. In particular, we get the multi-level user intents by recursively performing two operations: 1) intra-level aggregation, which distills the signal pertinent to user intents from co-interacted item graphs; and 2) inter-level aggregation, which constitutes the supernode in higher levels to model coarser-grained user intents via gathering the nodes' representations in the lower ones. Then, we refine the user and item representations as a distribution over the discovered intents, instead of simple pre-existing features. To demonstrate the effectiveness of our model, we conducted extensive experiments on three public datasets. Our model achieves significant improvements over the state-of-the-art methods, including MMGCN and DisenGCN. Furthermore, by visualizing the item representations, we provide the semantics of user intents.

In this paper, the real-time dynamics of the $O(4)$ scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its $n$-point correlation functions are derived in terms of the "classical" and "quantum" fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the phase transition near the critical temperature in the $O(4)$ scalar theory in $3+1$ dimensions, and the value is found to be $z\simeq 2.023$., Comment: 25 pages, 14 figures; v3: minor revision, discussions updated and reference added