Related papers: Contour integral method for thermal and quantal fl…
Self-consistent factorization of two-body residual interaction is proposed for arbitrary density- and current-dependent energy functionals. Following this procedure, a separable RPA (SRPA) method is constructed. SRPA dramatically simplifies…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
The book deals with a stochastic formulation of path integration in real time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters deal with quantum and classical mechanics, probability theory and stochastic calculus,…
We compute the single particle spectral function of a Bose liquid on a lattice, at integer filling, close to the superfluid-Mott transition. We use a `static path approximation' that retains all the classical thermal fluctuations in the…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
The random phase approximation (RPA) as formulated as an orbital-dependent, fifth-rung functional within the density functional theory (DFT) framework offers a promising approach for calculating the ground-state energies and the derived…
We develop the contour integral method for numerically solving the Feynman-Kac equation with two internal states [P. B. Xu and W. H. Deng, Math. Model. Nat. Phenom., 13 (2018), 10], describing the functional distribution of particle's…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…
We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes. The threshold we obtain is almost tight up to an integrality gap. Our technique is based on…
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…
In the present work we introduce a computational approach to the absolute rovibrational quantum partition function using the path-integral formalism of quantum mechanics in combination with the nested sampling technique. The numerical…
The optimized random phase approximation (ORPA) for classical liquids is re-examined in the framework of the generating functional approach to the integral equations. We show that the two main variants of the approximation correspond to the…
The random phase approximation (RPA) to the correlation energy is extended to fractional occupations and its performance examined for exact conditions on fractional charges and fractional spins. RPA satisfies the constancy condition for…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
Imaginary-time path integral (PI) is a rigorous tool to treat nuclear quantum effects in static properties. However, with its high computational demand, it is crucial to devise precise estimators. We introduce generalized PI estimators for…
We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses…
Using the technique of Pade Approximants for the correlation contributions of charged particles we are able to reproduce complex mathematical expressions by simple algebraic formulas. The Pade formulas are analytical expressions, which…
A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward…
We construct the path integral formulation of the partition function for a free scalar thermal field theory using coherent states, first in the ladder operator basis and then in the field operator basis. In so doing, we provide for the…