Related papers: Stein's method and a cubic mean-field model
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin…
We discuss metastable states in the mean-field version of the strong coupling BCS-model and study the evolution of a superconducting equilibrium state subjected to a dynamical semi-group with Lindblad generator in detailed balance w.r.t.…
We demonstrate that a recently introduced heuristic optimization algorithm [Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic crossover genetic updates is capable of sampling nearly uniformly among ground-state…
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. We also prove results concerning…
Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical…
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…
We propose a theoretical framework based on $SU(3)$ coherent states as a convenient tool to describe the collective state of a Bose-Einstein condensate of spin 1 atoms at thermal equilibrium. We work within the single-mode approximation,…
In ordered magnets, the elementary excitations are spin waves (magnons), which obey Bose-Einstein statistics. Similarly to Cooper pairs in superconductors, magnons can be paired into bound states under attractive interactions. The Zeeman…
Magnetization measurements were performed on TlCuCl$_3$ with gapped ground state. The critical density and the magnetic phase diagram were obtained. The interacting constant was obtained as $U/k_{\rm B} = 313$ K. The experimental phase…
We study the one-dimensional SU(4) exchange model under magnetic fields, which is the simplest effective Hamiltonian in order to investigate the quantum fluctuations concerned with the orbital degrees of freedom in coupled spin-orbit…
We consider the dilute Curie-Weiss model of size $N$, which is a generalization of the classical Curie-Weiss model where the dependency structure between the spins is not encoded by the complete graph but via the (directed)…
The possibility of obtaining the initial pure state in a usual Stern-Gerlach experiment through the recombination of the two emerging beams is investigated. We have extended the previous work of Englert, Schwinger and Scully \cite{ISG1}…
We obtain the exact physical characteristics of the triple-chain Ising model on a torus with all possible multispin interactions invariant with respect to rotation by the angle $2\pi / 3$. The exact value of the partition function in a…
We will prove the Berry-Esseen theorem for the number counting function of the circular $\beta$-ensemble (C$\beta$E), which will imply the central limit theorem for the number of points in arcs of the unit circle in mesoscopic and…
We study a spin 1 Bose condensate small enough to be treated as a single magnetic `domain': a system that we term a microcondensate. Because all particles occupy a single spatial mode, this quantum many body system has a well defined…
A new slave-spin representation of fermion operators has recently been proposed for the half-filled Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. The resulting spin…
We study a multi-group version of the mean-field or Curie-Weiss spin model. For this model, we show how, analogously to the classical (single-group) model, the three temperature regimes are defined. Then we use the method of moments to…