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A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
A nonequilibrium Green's functions (NEGF) approach for spatially inhomogeneous, strongly correlated artificial atoms is presented and applied to compute the time-dependent properties while starting from a (correlated) initial few-electron…
The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGF) or reduced density matrix methods. Approximations are introduced…
We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a new regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations…
Quantum correlations are key information about the structures and dynamics of quantum many-body systems. There are many types of high-order quantum correlations with different time orderings, but only a few of them are accessible to the…
We formulate a new Hartree-Fock-Bogoliubov method applicable to weakly bound deformed nuclei using the coordinate-space Green's function technique. An emphasis is put on treatment of quasiparticle states in the continuum, on which we impose…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
Employing a recently developed method that is numerically accurate within a model space simulating the real-time dynamics of few-body systems interacting with macroscopic environmental quantum fields, we analyze the full dynamics of an…
The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
This chapter seeks to outline a few basic problems in quantum statistical physics where recent experimental advances from the atomic physics community offer the hope of dramatic progress. The focus is on nonequilibrium situations where the…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
It is shown that statistical mechanics is applicable to quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, etc., where the residual two-body interaction is sufficiently strong. This interaction mixes…