ترغب بنشر مسار تعليمي؟ اضغط هنا

KPZ-type fluctuation bounds for interacting diffusions in equilibrium

140   0   0.0 ( 0 )
 نشر من قبل Philippe Sosoe
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We study the fluctuations in equilibrium of a class of Brownian motions interacting through a potential. For a certain choice of exponential potential, the distribution of the system coincides with differences of free energies of the stationary semi-discrete or OConnell-Yor polymer. We show that for Gaussian potentials, the fluctuations are of order $N^{frac{1}{4}}$ when the time and system size coincide, whereas for a class of more general convex potentials $V$ the fluctuations are of order at most $N^{frac{1}{3}}$. In the OConnell-Yor case, we recover the known upper bounds for the fluctuation exponents using a dynamical approach, without reference to the polymer partition function interpretation.



قيم البحث

اقرأ أيضاً

We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magn itude $t^{1/3}$. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type processes. Besides this class of zero range processes, hypotheses of this argument have also been verified in the authors earlier papers for the asymmetric simple exclusion and the constant rate zero range processes, and are currently under development for a bricklayers process with exponentially increasing jump rates.
We compute the fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate regime. This regime corresponds to taking the inverse temperature to zero with the size of the system. The expone nts satisfy the KPZ scaling relation and coincide with physical predictions. In the critical case, we recover the fluctuation exponents of the Cole-Hopf solution of the KPZ equation in equilibrium and close to equilibrium.
105 - Matthew F. Lapa 2021
We derive rigorous bounds on the average momentum occupation numbers $langle n_{mathbf{k}sigma}rangle$ in the Hubbard and Kondo models in the ground state and at non-zero temperature ($T>0$) in the grand canonical ensemble. For the Hubbard model with $T>0$ our bound proves that, when interaction strength $ll k_B Tll$ Fermi energy, $langle n_{mathbf{k}sigma}rangle$ is guaranteed to be close to its value in a low temperature free fermion system. For the Kondo model with any $T>0$ our bound proves that $langle n_{mathbf{k}sigma}rangle$ tends to its non-interacting value in the infinite volume limit. In the ground state case our bounds instead show that $langle n_{mathbf{k}sigma}rangle$ approaches its non-interacting value as $mathbf{k}$ moves away from a certain surface in momentum space. For the Hubbard model at half-filling on a bipartite lattice, this surface coincides with the non-interacting Fermi surface. In the Supplemental Material we extend our results to some generaliz
175 - Akira Sakai 2007
We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical behavior for long-range oriented percolation above 2min{alpha,2} spatial dimensions.
We consider symmetric activated random walks on $mathbb{Z}$, and show that the critical density $zeta_c$ satisfies $csqrt{lambda} leq zeta_c(lambda) leq C sqrt{lambda}$ where $lambda$ denotes the sleep rate.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا