Related papers: A canonical transformation theory from extended no…
Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
The transcorrelated (TC) method performs a similarity transformation on the electronic Schr\"odinger equation via Jastrow factorization of the wave function. This has demonstrated significant advancements in computational electronic…
Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long…
This paper presents a canonical dual approach for solving a nonlinear population growth problem governed by the well-known logistic equation. Using the finite difference and least squares methods, the nonlinear differential equation is…
The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can…
This note provides a comprehensive examination of the various approaches to formulating relativistic hydrodynamics, with a particular emphasis on the canonical approach. Relativistic hydrodynamics plays a crucial role in understanding the…
We present a detailed derivation and numerical tests of a new mixed quantum-classical scheme to deal with non-adiabatic processes. The method is presented as the zero-th order approximation to the exact coupled dynamics of electrons and…
Conformal perturbation theory is a powerful tool to describe the behavior of statistical-mechanics models and quantum field theories in the vicinity of a critical point. In the past few years, it has been extensively used to describe…
Compactified Yang-Mills theories with one universal extra dimension were found [arXiv:1008.4638] to exhibit two types of gauge invariances: the standard gauge transformations (SGTs) and the nonstandard gauge transformations (NSGTs). In the…
Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…
It is well known that mode coupling theory (MCT) leads to a two step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic…
Thermalization of systems described by the discrete non-linear Schr\"odinger equation, in the strong disorder limit, is investigated both theoretically and numerically. We show that introducing correlations in the disorder potential, while…
In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected…
A self-consistent thermodynamic framework is presented for power-law canonical distributions based on the generalized central limit theorem by extending the discussion given by Khinchin for deriving Gibbsian canonical ensemble theory. The…
We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher order…
We discuss the cone and contraction theorem in a suitable complex analytic setting. More precisely, we establish the cone and contraction theorem of normal pairs for projective morphisms between complex analytic spaces. This result is a…
We propose mixed quantum-classical equations of motion that unify electronic coherence and phase evolution simultaneously within the exact factorization framework. Our derivation shows that incorporating the second-order electron-nuclear…
Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…