Central limit theorem over non-linear functionals of empirical measures
with applications to the **mean**-**field** fluctuation of interacting particle
systems

**mean**-

**field**limiting measure (as the number of particles goes to infinity), when the dependence on measure is nonlinear. Expand abstract.

**mean**-

**field**limiting measure (as the number of particles goes to infinity), when the dependence on measure is nonlinear.

10/10 relevant

arXiv

**Mean** **Field** Theory for the Quantum Rabi Model, Inconsistency to the
Rotating Wave Approximation

**mean**

**field**theory (MFT) was applied to replace the operators by equivalent expectation values. Expand abstract.

**mean**

**field**theory (MFT) was applied to replace the operators by equivalent expectation values. The Rabi model was reduced to a fourth orders NDE describing atoms position. Solution by the harmonic balance method (HBM) showed good accuracy and consistency to the numerical results, which introduces it as a useful tool in the quantum dynamics studies.

10/10 relevant

arXiv

Consensus-Based Optimization on the Sphere I: Well-Posedness and
**Mean**-**Field** Limit

**mean**-

**field**approximation for large particle limit. Expand abstract.

**field**to favor exploration, whose variance is a function of the distance of the particles to the consensus point. In particular, as soon as the consensus is reached, then the stochastic component vanishes. In this paper, we study the well-posedness of the model and we derive rigorously its

**mean**-

**field**approximation for large particle limit.

10/10 relevant

arXiv

Schwinger Boson **mean** **field** theory of kagome Heisenberg antiferromagnet
with Dzyaloshinskii-Moriya interaction

**mean**

**field**theory (SBMFT). Expand abstract.

**mean**

**field**theory (SBMFT). Within SBMFT framework, Messio et al had argued that the ground state of kagome antiferromagnet is possibly a chiral topological spin liquid (Phys. Rev. Lett. 108, 207204 (2012)). Thus, we have computed zero-temperature ground state phase diagram considering the time-reversal breaking states as well as fully symmetric Ans\"atze. We discuss the relevance of these results in experiments and other studies. Finally, we have computed the static and dynamic spin structure factors in relevant phases.

10/10 relevant

arXiv

Splitting methods and short time existence for the master equations in
**mean** **field** games

**mean**

**field**game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Expand abstract.

**mean**

**field**game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite dimensional equations stated in the space of probability measures. Our new approach simplifies, shortens and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.

10/10 relevant

arXiv

Single $\Lambda_c^+$ hypernuclei within quark **mean**-**field** model

**mean**-

**field**(QMF) model is applied to study the single $\Lambda^+_c$ hypernuclei. The charm baryon, $\Lambda^+_c$, is constructed by three constituent quarks, $u, ~d$, and $c$, confined by central harmonic oscillator potentials. The confinement potential strength of charm quark is determined by fitting the experimental masses of charm baryons, $\Lambda^+_c,~\Sigma^+_c$, and $\Xi^{++}_{cc}$. The effects of pions and gluons are also considered to describe the baryons at the quark level. The baryons in $\Lambda^+_c$ hypernuclei interact with each other through exchanging the $\sigma,~\omega$, and $\rho$ mesons between the quarks confined in different baryons. The $\Lambda^+_c N$ potential in the QMF model is strongly dependent on the coupling constant between $\omega$ meson and $\Lambda^+_c$, $g_{\omega\Lambda^+_c}$. When the conventional quark counting rule is used, i. e., $g_{\omega\Lambda^+_c}=2/3g_{\omega N}$, the massive $\Lambda^+_c$ hypernucleus can exist, whose single $\Lambda^+_c$ binding energy is smaller with the mass number increasing due to the strong Coulomb repulsion between $\Lambda^+_c$ and protons. When $g_{\omega\Lambda^+_c}$ is fixed by the latest lattice $\Lambda^+_c N$ potential, the $\Lambda^+_c$ hypernuclei only can exist up to $A\sim 50$.

10/10 relevant

arXiv

Modeling the spin-Peierls transition of spin-$1/2$ chains with correlated states: $J_1-J_2$ model, CuGeO$_3$ and TTF-CuS$_4$C$_4$(CF$_3$)$_4$

**mean**

**field**for $T < T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2 = \alpha J_1$ between first and second neighbors, respectively, and variable frustration $0 \leq \alpha \leq 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to

**mean**

**field**results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $\delta(T)$. The relation between $T_{SP}$ and $\Delta(\delta,\alpha)$, the $T = 0$ gap induced by dimerization, depends strongly on $\alpha$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS$_4$C$_4$(CF$_3$)$_4$ crystals ($J_1 = 79$ K, $\alpha = 0$, $T_{SP} = 12$ K) and CuGeO$_3$ crystals ($J_1 = 160$ K, $\alpha = 0.35$, $T_{SP} = 14$ K). The same parameters describe the specific heat anomaly of CuGeO$_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $\delta(0)$ limits the range of spin correlations at $T = 0$ while $T > 0$ limits the range at $\delta= 0$.

4/10 relevant

arXiv

Correlation-induced steady states and limit cycles in driven dissipative quantum systems

**mean**magnetization values that lie between the two bistable mean-

**field**values, and whose correlation functions have properties reminiscent of both. Expand abstract.

**mean**

**field**dressed by the feedback of quantum fluctuations at leading order. This approach allows us to study the effect of correlations in large lattices with over one hundred thousand spins, as the spatial dimension is increased up to five. In dimension two and higher we find two new states that are stabilized by quantum correlations and do not exist in the

**mean**-

**field**limit of the model. One of these is a steady state with

**mean**magnetization values that lie between the two bistable

**mean**-

**field**values, and whose correlation functions have properties reminiscent of both. The correlation length of the new phase diverges at a critical point, beyond which we find emerging a new limit cycle state with the magnetization and correlators oscillating periodically in time.

7/10 relevant

arXiv

Decay of Correlation Rate in the **Mean** **Field** Limit of Point Vortices
Ensembles

**means**of Gaussian integration techniques, inspired by the correspondence between the 2-dimensional Coulomb gas and the Sine-Gordon Euclidean

**field**... Expand abstract.

**Mean**

**Field**limit of Gibbsian ensembles of 2-dimensional point vortices on the torus. It is a classical result that in such limit correlations functions converge to 1, that is, point vortices decorrelate: we compute the rate at which this convergence takes place by

**means**of Gaussian integration techniques, inspired by the correspondence between the 2-dimensional Coulomb gas and the Sine-Gordon Euclidean

**field**theory.

10/10 relevant

arXiv

On the diffusive-**mean** **field** limit for weakly interacting diffusions
exhibiting phase transitions

**mean**

**field**limit and derive optimal rates of convergence in relative entropy of the Gibbs measure to the (unique) limit of the mean field energy below the critical temperature. Expand abstract.

**mean**

**field**and diffusive(homogenisation)limits. In particular, we show that these two limits do not commute if the

**mean**

**field**system constrained to the torus undergoes a phase transition, that is to say if it admits more than one steady state. A typical example of such a system on the torus is given by the noisy Kuramoto model of

**mean**

**field**plane rotators. As a by-product of our main results, we also analyse the energetic consequences of the central limit theorem for fluctuations around the

**mean**

**field**limit and derive optimal rates of convergence in relative entropy of the Gibbs measure to the (unique) limit of the

**mean**

**field**energy below the critical temperature.

10/10 relevant

arXiv