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For general antiferromagnetic 2-spin systems, including the hardcore model and the antiferromagnetic Ising model, there is an $\mathsf{FPTAS}$ for the partition function on graphs of maximum degree $\Delta$ when the infinite regular tree lies in the uniqueness region by Li et al. (2013). Moreover, in the tree non-uniqueness region, Sly (2010) showed that there is no $\mathsf{FPRAS}$ to estimate the partition function unless $\mathsf{NP}=\mathsf{RP}$. The algorithmic results follow from the correlation decay approach due to Weitz (2006) or the polynomial interpolation approach developed by Barvinok (2016). However the running time is only polynomial for constant $\Delta$. For the hardcore model, recent work of Anari et al. (2020) establishes rapid mixing of the simple single-site Markov chain known as the Glauber dynamics in the tree uniqueness region. Our work simplifies their analysis of the Glauber dynamics by considering the total pairwise influence of a fixed vertex $v$ on other vertices, as opposed to the total influence on $v$, thereby extending their work to all 2-spin models and improving the mixing time. More importantly our proof ties together the three disparate algorithmic approaches: we show that contraction of the tree recursions with a suitable potential function, which is the primary technique for establishing efficiency of Weitz's correlation decay approach and Barvinok's polynomial interpolation approach, also establishes rapid mixing of the Glauber dynamics. We emphasize that this connection holds for all 2-spin models (both antiferromagnetic and ferromagnetic), and existing proofs for correlation decay or polynomial interpolation immediately imply rapid mixing of Glauber dynamics. Our proof utilizes that the graph partition function divides that of Weitz's self-avoiding walk trees, leading to new tools for analyzing influence of vertices., Comment: Section 7 and Appendix E are updated to fix a small error

We derive a factorization theorem that allows for resummation of small-$x$ logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor $W^{\mu\nu}$ in deep inelastic scattering, and leads to the definition of a new gauge invariant soft function $S^{\mu\nu}$ that describes quark and gluon emission in the central region. This soft function provides a new framework for extending resummed calculations for coefficient functions to higher logarithmic orders. Our factorization also defines impact factors by universal collinear functions that are process independent, for instance being identical in small-$x$ DIS and Drell-Yan., Comment: 43 pgs

We use Glauber's correlation function as well as the Green functions formalism to investigate, in the case of a dipolar atomic transition, the causal behaviour of the spontaneously emitted electromagnetic field, in the A.p coupling. This brings us to examine the role played by the longitudinal electric field, which is not described in terms of photonic (transverse) degrees of freedom., Comment: After a long break due to the covid crisis, this new version is characterized by a new author (VD) who actually already worked on this subject in his Ph.D of 2015 entitled "The photon wave function in principle and in practice". This new version contains new results concerning the role of longitudinal e-m fields in the quantum Green function; it aims at replacing the first version of 2018 (!)

This paper aims at using the functional renormalization group formalism to study the equilibrium states of a stochastic process described by a quench--disordered multilinear Langevin equation. Such an equation characterizes the evolution of a time-dependent $N$-vector $q(t)=\{q_1(t),\cdots q_N(t)\}$ and is traditionally encountered in the dynamical description of glassy systems at and out of equilibrium through the so-called Glauber model. From the connection between Langevin dynamics and quantum mechanics in imaginary time, we are able to coarse-grain the path integral of the problem in the Fourier modes, and to construct a renormalization group flow for effective Euclidean action. In the large $N$-limit we are able to solve the flow equations for both matrix and tensor disorder. The numerical solutions of the resulting exact flow equations are then investigated using standard local potential approximation, taking into account the quench disorder. In the case where the interaction is taken to be matricial, for finite $N$ the flow equations are also solved. However, the case of finite $N$ and taking into account the non-equilibrum process will be considered in a companion investigation., 60 pages, 14 figures

We provide further evidence to support the fact that a four-dimensional effective field theory description with de Sitter isometries in IIB string theory, overcoming the no-go and the swampland criteria, can only exist if de Sitter space is realized as a Glauber-Sudarshan state. We show here that this result is independent of the choice of de Sitter slicings. The Glauber-Sudarshan state, constructed by shifting the interacting vacuum in the M-theory uplift of the scenario, differs from a standard coherent state in QFT in the sense that the shape and size of the state changes with respect to time, implying changes in the graviton and the flux quanta. Despite this, the expectation values of the graviton and flux operators in such a state reproduce the exact de Sitter background, as long as we are within the temporal bound set by the onset of the strong coupling in the dual type IIA side, and satisfy the corresponding Schwinger-Dyson's equations in the presence of hierarchically controlled perturbative and non-perturbative quantum corrections. Additionally, we provide a detailed study of the fluxes supporting the Glauber-Sudarshan state in the M-theory uplift of the IIB scenario. We show explicitly how the Bianchi identities, anomaly cancellation and flux quantization conditions, along-with the constraints from the Schwinger-Dyson's equations, conspire together to provide the necessary temporal dependences to support such a state in full M-theory. We also discuss how our analysis points towards a surprising connection to the four-dimensional null energy condition, for a Friedman-Lemaitre-Robertson-Walker state in the IIB side, as a consistency condition for the existence of an effective field theory description in M-theory., 188 pages, 33 tables, LaTex; comments welcome. v2: Typos corrected and reference updated; Matches version to appear in "Fortschritte der Physik"

In QCD, the amplitude for multiple soft gluon emissions has been shown to exhibit a form of coherence, wherein one-loop corrections are rendered IR finite by the transverse momentum of the real emissions. Using a sequence of soft-collinear effective theories (SCET) with Glauber operators, we present a compact and elegant derivation of this property. Our derivation highlights an important role played by the Lipatov vertex. The EFT approach provides increased physical intuition and, for the first time, a clear road map for how this result can be extended to higher loop orders.

The coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.

Background: In the previous paper, we predicted reaction cross sections σ R for 40 − 60 , 62 , 64 Ca+12C scattering at 280 MeV/nucleon, using the chiral g -matrix folding model with the densities calculated with the Gogny-D1S Hartree–Fock-Bogoliubov (GHFB) with and without the angular momentum projection (AMP), since Tanaka et al. measured interaction cross sections σ I ( ≈ σ R ) for 42 − 51 Ca in RIKEN and determined neutron skin r skin ( RIKEN ) using the optical limit of the Glauber model with the Woos-Saxon densities. Purpose: Our purpose is to reanalyze the r skin from the σ I using the chiral g -matrix folding model. Our analysis is superior to theirs, since the chiral g -matrix folding model (the GHFB and GHFB+AMP densities) is much better than the optical limit of the Glauber model (the Woos-Saxon densities). Methods: Our model is the chiral g -matrix folding model with the densities scaled from the GHFB and GHFB+AMP densities. Results: We scale the GHFB and GHFB+AMP densities so that the σ R of the scaled densities can agree with the central values of σ I under the condition that the proton radius of the scaled proton density equals the data determined from the isotope shift based on the electron scattering. The r skin thus determined are close to their results r skin 42 − 51 ( RIKEN ) , except for 48Ca. For 48Ca, our value r skin 48 is 0.105 ± 0.06 fm, while their value is r m 48 ( RIKEN ) = 0 . 146 ± 0 . 06 fm. We then take the weighted mean and its error of our result r skin 48 ( σ I ) = 0 . 105 ± 0 . 06 fm and the result r skin 48 ( E 1 pE ) = 0 . 17 ± 0 . 03 fm of the high-resolution E 1 polarizability experiment (E1pE). Our final result is r skin 48 = 0 . 157 ± 0 . 027 fm. Conclusion: Our conclusion is r skin 48 = 0 . 157 ± 0 . 027 fm for 48Ca. For 42 − 47 , 49 − 51 Ca, our results on r skin are similar to theirs. Our result for 48Ca is related to CREX.

The simulation of transverse momentum ( P T ) spectra of inclusive charged hadrons computed with absolute pseudorapidity below 0.8 ( | η | 0 . 8 ) in different centrality bins in P b − P b interactions at S N N = 2 . 76 TeV are reported. The results obtained from Monte Carlo models including QGSJETII-03, QGSJET-04, EPOS1.99, and EPOS-LHC are compared with the ALICE experimental data in the P T range 0 . 15 P T 50 GeV/c, for total of nine centrality classes from (0-5 % ) to (70-80 % ). The EPOS-LHC model reproduced the P T spectra in all the centrality classes except at 20-30 and 30-40 % where the model underestimated the data at high P T only. The QGSJET models overestimated the data over the entire P T range and in all the centrality classes up to about 10%. Fit with the Tsallis–Pareto-like function of the p T spectra shows that the effective temperature depends on the centrality which increases from central to peripheral collisions as in the case of central collisions the fireball is longer lived as compared to the peripheral one. The P b − P b spectra are further oriented on the scale of the nuclear modification factor R A A using a P − P collision spectrum calculated for the same center of mass energy. Although the models could not reproduce the data but showed similar behavior only, that shows that particle suppression has a significant effect on the centrality at high P T . The suppression is maximum in the most central collisions above which there is a remarkable escalation in the nuclear modification factor. In the case of most peripheral interactions, the suppression is smaller as compared to the most central one and is nearly independent of P T . The EPOS model’s calculation exhibit suppression for all class intervals, having the robust effect for the most central interval (0-5 % ) due to the relative parton energy loss and reveals a least repression effect in most peripheral cases (70-80 % ). Results of the QGSJETII models are not included for the R A A as the models failed to predict the data. The reason is that QGSJETII is not a Glauber–based model but a model based on soft pomeron dynamics. The model does not provide the number of binary sub-collisions we need to scale down the R A A .