Related papers: The Stochastic State Selection Method for Energy E…
The study of interacting spin systems is of fundamental importance for modern condensed matter physics. On frustrated lattices, magnetic exchange interactions cannot be simultaneously satisfied, and often give rise to competing exotic…
Two quantum spin models with bilinear-biquadratic exchange interactions are constructed on the checkerboard lattice. It is proved that, under certain sufficient conditions on the exchange parameters, their ground states consist of two…
We introduce potential-energy gating, a method for robust state estimation in systems governed by double-well stochastic dynamics. The observation noise covariance of a Bayesian filter is modulated by the local value of a known or assumed…
A hybrid dynamical system switches between dynamic regimes at time- or state-triggered events. We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system's state. We formulate state…
We show that, in certain circumstances, exact excitation energies appear as locally site-independent (or flat) modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in the variational…
We compare the ground state of the random-field Ising model with Gaussian distributed random fields, with its non-equilibrium hysteretic counterpart, the demagnetized state. This is a low energy state obtained by a sequence of slow magnetic…
We study the $S=1/2$ square-kagome lattice Heisenberg antiferromagnet with the trimarized modulation. In the trimerized limit, each trimer hosts the four-fold degenearte ground states characterized by the spin and chirality degrees of…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach…
We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show the dominance of the pairwise terms in the autoregressive…
Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…
We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…
Extensions of the Shastry-Sutherland model are possible in various ways. In particular, it is possible to construct a natural model in three dimensions which has the exact dimer ground state. Recently found spin gap system SrCu_2(BO_3)_2…
The recent development in the field of 2D magnetic materials urges reliable theoretical methodology for determination of magnetic properties. Among the available methods, ab initio four-state energy mapping based on Density Functional…
In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms.…
A stochastic Lie system on a manifold $M$ is a stochastic differential equation whose dynamics is described by a linear combination with functions depending on $\mathbb{R}^\ell$-valued semi-martigales of vector fields on $M$ spanning a…
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…
In this short article, we showcase the derivation of the optimal (minimum error variance) estimator, when one part of the stochastic LTI system output is not measured but is able to be predicted from the measured system outputs. Similar…
The paper presents a Gaussian/kernel process regression method for real-time state estimation and forecasting of phase angle and angular speed in systems with a high penetration of solar generation units, operating under a sparse…
Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin…