Probabilities of many-body decays of fermions

K. Kilimann, D. Kremp, G. Röpke

Manan Vyas, V K B Kota

Abstract In an m particle quantum system, the rank of interactions and the nature of particles (fermions or bosons) can strongly affect the dynamics of the system. To explore this, we study the nonequilibrium dynamics with particles in a one-body mean-field and quenched by an interaction of body-rank k = 2, 3, …, m . Using fermionic embedded Gaussian orthogonal ensembles (EGOEs) and bosonic embedded Gaussian orthogonal ensembles (BEGOEs) of one plus k -body interactions (also the unitary variants EGUE and BEGUE), it is seen that the short time decay of the survival probability of many-particle systems is given by the Fourier transform of the generating function of the q -Hermite polynomials. Deriving the formulas for q for both fermion and boson systems as a function of m , k and the number of single particle states N , we have verified that the Fourier transform of agrees very well with the numerical ensemble calculations for both fermion and boson systems. These results bridge the gap between the known results for k = 2 and k = m .

José M. Arias, María Isabel Gallardo, Manuel Lozano

Adolfo del Campo

While exponential decay is ubiquitous in nature, deviations at both short and long times are dictated by quantum mechanics. Nonexponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time nonexponential behavior of the nonescape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that, whereas for noninteracting bosons the long-time decay follows a power law with an exponent linear in the number of particles $N$, the exponent becomes quadratic in $N$ in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial antibunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.

節夫 三沢

Yicheng Zhang, Lev Vidmar, Marcos Rigol

We study $\mathrm{SU}(N)$ fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.