相关论文: Free energy of disordered urn models in the canoni…

The free energy balance equation for gyrokinetic fluctuations is derived and applied to instabilities. An additional term due to electromagnetic sources is included. This can provide a simpler way to compute the free energy balance in…

In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical…

We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method…

The one-loop free energy of the four-dimensional compact QED, which is known to be equivalent to the vector Sine-Gordon model, is calculated in the strong coupling regime. In the case, when the norm of the strength tensor of the…

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals…

By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent…

Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences, and has since inspired a huge body of related methods that use it as an integral building block. Being an…

Current theories of heteropolymers are inherently macrpscopic, but are applied to folding proteins which are only mesoscopic. In these theories, one computes the averaged free energy over sequences, always assuming that it is self-averaging…

Fast and accurate evaluation of free energy has broad applications from drug design to material engineering. Computing the absolute free energy is of particular interest since it allows the assessment of the relative stability between…

Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…

We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems…

We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…

The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the…

We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact…

Energy system models based on linear programming have been growing in size with the increasing need to model renewables with high spatial and temporal detail. Larger models lead to high computational requirements. Furthermore, seemingly…

The paper is a continuation of arXiv:2012.10364, where the approach was developed to constructing the exact matrix model for any generalized Ising system, and such model was constructed for certain 2d system. In this paper, the properties…

Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of…

The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables, the mass and the "time" (ultraviolet…

In this paper, we calculate the topological free energy for a number of ${\mathcal N} \geq 2$ Yang-Mills-Chern-Simons-matter theories at large $N$ and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the…