Related papers: Particle Diagrams and Statistics of Many-Body Rand…
We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important…
Eigenvalue density generated by embedded Gaussian unitary ensemble with $k$-body interactions for two species (say $\mathbf{\pi}$ and $\mathbf{\nu}$) fermion systems is investigated by deriving formulas for the lowest six moments. Assumed…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
We consider $m$ spinless Fermions in $l > m$ degenerate single-particle levels interacting via a $k$-body random interaction with Gaussian probability distribution and $k <= m$ in the limit $l$ to infinity (the embedded $k$-body random…
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…
We study the collective association dynamics of a cold Fermi gas of $2N$ atoms in $M$ atomic modes into a single molecular bosonic mode. The many-body fermionic problem for $2^M$ amplitudes is effectively reduced to a dynamical system of…
We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the…
The embedded ensembles were introduced by Mon and French as physically more plausible stochastic models of many--body systems governed by one--and two--body interactions than provided by standard random--matrix theory. We review several…
We present a novel analytical approach for the calculation of the mean density of states in many-body systems made of confined indistinguishable and non-interacting particles. Our method makes explicit the intrinsic geometry inherent in the…
The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for…
We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction.…
In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially…
Separation between average and fluctuation parts in the state density in many-particle quantum systems with $k$-body interactions, modeled by the $k$-body embedded Gaussian orthogonal random matrices (EGOE($k$)), is demonstrated using the…
Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant…
We present a method for approximating the many-body density of states of a system of quantum identical particles, with a reduction of the computational cost by a combinatorial factor compared to the full calculation. This is carried out by…
The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed on two single-particle levels. When k = N, the ensemble is equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it corresponds…
Embedded random matrix ensembles with $k$-body interactions are well established to be appropriate for many quantum systems. For these ensemble the two point correlation function is not yet derived though these ensembles are introduced 50…
We present a general method for incorporating an external electromagnetic field into descriptions of few-body systems whose strong interactions are described by integral equations. In particular, we address the case where the integral…
Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by…