相关论文: A Variational Perturbation Approximation Method in…
In a paper [8] the authors classify entropy into three categories, as a thermodynamics quantity, as a measure of information production, and as a means of statistical inference. An entropy measure introduced by Mathai falls into the second…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
We develop an extension of the Gutzwiller approximation to finite temperatures based on the Dirac-Frenkel variational principle. Our method does not rely on any entropy inequality, and is substantially more accurate than the approaches…
We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality…
This paper is committed to investigate an extension of the classical adaptive biasing force method, which is used to compute the free energy related to the Boltzmann-Gibbs measure and a reaction coordinate function. The issue of this…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex…
A variational principle for the rate distortion (RD) theory with Bregman divergences is formulated within the ambit of the generalized (nonextensive) statistics of Tsallis. The Tsallis-Bregman RD lower bound is established. Alternate…
We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of `pressure' effect of fluid, which is kinematically caused by velocity dispersion, to aim…
The ``close limit,'' a method based on perturbations of Schwarzschild spacetime, has proved to be a very useful tool for finding approximate solutions to models of black hole collisions. Calculations carried out with second order…
The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed…
We present a systematic study of the Rayleigh--Ritz variational method for quantum oscillators in the Segal--Bargmann space. We rigorously derive the normalizability condition $|\alpha| < \tfrac{1}{2}$ for generalized Gaussian trial…
We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying…
It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the limit distribution is also deduced. This demonstration…
We develop and test methods that include second and third-order perturbation theory (MP3) using orbitals obtained from regularized orbital-optimized second-order perturbation theory, $\kappa$-OOMP2, denoted as MP3:$\kappa$-OOMP2. Testing…
Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbative series (TPS) of any order in gauge theories. The approximants reproduce the TPS when expanded in power…
A function $f=f_T$ is called least energy approximation to a function $B$ on the interval $[0,T]$ with penalty $Q$ if it solves the variational problem $$ \int_0^T \left[ f'(t)^2 + Q(f(t)-B(t)) \right] dt \searrow \min. $$ For quadratic…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
In this paper, we develop a variational perturbation (VP) scheme for calculating vacuum expectation values (VEVs) of local fields in quantum field theories. For a comparatively general scalar field model, the VEV of a comparatively general…