اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGlobal space-time update
39
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The Stochastic Green Function (SGF) algorithm is able to simulate any Hamiltonian that does not suffer from the so-called sign problem. We propose a new global space-time update scheme for the SGF algorithm which, in addition to being simpler than the previous formulation, reduces auto-correlation times. Using as a concrete example the extended Bose-Hubbard model and the complex Hamiltonian with six-site ring-exchange interactions which was recently studied in ArXiv:1206.2566v1, we present a comprehensive review of the SGF algorithm and the new updating scheme. Measurements of non-trivial physical quantities are presented in detail. While the SGF algorithm works in the canonical ensemble by nature, we give a simple extension that allows us to perform simulations in the grand-canonical ensemble too. We also discuss an optimized implementation which allows for access to large system sizes.
قيم البحث
اقرأ أيضاً
We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an effi
cient integrable Trotterization of non-relativistic $sigma$-models with complex Grassmannian manifolds as target spaces, including, as special cases, the higher-rank analogues of the Landau-Lifshitz field theory on complex projective spaces. As an application, we study transport of Noether charges in canonical local equilibrium states. We find a clear signature of superdiffusive behavior in the Kardar-Parisi-Zhang universality class, irrespectively of the chosen underlying global unitary symmetry group and the quotient structure of the compact phase space, providing a strong indication of superuniversal physics.
Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them covariant wit
h respect to nonlinear transform of variables. In this work, we construct rigorous and covariant formulations of time-slicing path integrals for quantum and classical stochastic dynamics in curved space. We first establish a rigorous criterion for correct time-slice actions of path integrals (Lemma 1). This implies the existence of infinitely many equivalent representations for time-slicing path integral. We then show that, for any dynamics with second order generator, all time-slice actions are asymptotically equivalent to a Gaussian (Lemma 2). Using these results, we further construct a continuous family of equivalent actions parameterized by an interpolation parameter $alpha in [0,1]$ (Lemma 3). The action generically contains a spurious drift term linear in $Delta boldsymbol x$, whose concrete form depends on $alpha$. Finally we also establish the covariance of our path-integral formalism, by demonstrating how the action transforms under nonlinear transform of variables. The $alpha = 0$ representation of time-slice action is particularly convenient because it is Gaussian and invariant, as long as $Delta boldsymbol x$ transforms according to Itos formula.
How much time does it take two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the random time it takes the two molecules to meet. However, this is not alwa
ys the case as molecules switch stochastically between reactive and non-reactive states. In such cases, the reaction is said to be ``gated by the internal states of the molecules involved which could have a dramatic influence on kinetics. A unified, continuous-time, approach to gated reactions on networks was presented in [Phys. Rev. Lett. 127, 018301, 2021]. Here, we build on this recent advancement and develop an analogous discrete-time version of the theory. Similar to continuous-time, we employ a renewal approach to show that the gated reaction time can always be expressed in terms of the corresponding ungated first-passage and return times; which yields formulas for the generating function of the gated reaction-time distribution and its corresponding mean and variance. In cases where the mean reaction time diverges, we show that the long-time asymptotics of the gated problem is inherited from its ungated counterpart, where only the pre-factor of the power law tail changes. The discretization of time also gives rise to new phenomena that do not exist in the continuous-time analogue. Crucially, when the internal gating dynamics is in, or out of, phase with the spatial process governing molecular encounters resonance and anti-resonance phenomena emerge. These phenomena are illustrated using two case studies which also serve to show how the general approach presented herein greatly simplifies the analysis of gated reactions.
We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called glass transition is a manifestation of low action tails in these distributions where th
e entropy of trajectory space is sub-extensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature T_g which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models, and note how these ideas apply more generally.
Super-diffusion, characterized by a spreading rate $t^{1/alpha}$ of the probability density function $p(x,t) = t^{-1/alpha} p left( t^{-1/alpha} x , 1 right)$, where $t$ is time, may be modeled by space-fractional diffusion equations with order $1 <
alpha < 2$. Some applications in biophysics (calcium spark diffusion), image processing, and computational fluid dynamics utilize integer-order and fractional-order exponents beyond than this range ($alpha > 2$), known as high-order diffusion, or hyperdiffusion. Recently, space-time duality, motivated by Zolotarevs duality law for stable densities, established a link between time-fractional and space-fractional diffusion for $1 < alpha leq 2$. This paper extends space-time duality to fractional exponents $1<alpha leq 3$, and several applications are presented. In particular, it will be shown that space-fractional diffusion equations with order $2<alpha leq 3$ model sub-diffusion and have a stochastic interpretation. A space-time duality for tempered fractional equations, which models transient anomalous diffusion, is also developed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
