Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$ : it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $μ_c \approx 13.607$ , above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$: it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $μ_c \approx 13.607$, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.

arXiv:1211.5557Ядерная физикаJan 1, 20144 citations

A Solution to the Sign Problem Using a Sum of Controlled Few-Fermions

Wei, David H.

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is proven to assert that any bounded-error quantum polynomial time (BQP) algorithm can be encoded into a sum of controlled few-fermions and simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely the same as the class of bounded-error probabilistic polynomial time (BPP), namely, BPP = BQP.A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is proven to assert that any bounded-error quantum polynomial time (BQP) algorithm can be encoded into a sum of controlled few-fermions and simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely the same as the class of bounded-error probabilistic polynomial time (BPP), namely, BPP = BQP.

arXiv:2208.13744Jun 8, 20220 citations

The Many-Fermion Problem

WORLD SCIENTIFIC eBooksMar 1, 19930 citations

m

and a distinct particle of mass

m_1

: it turns out that two

L^P = 1^-

three-body bound states emerge if mass ratio

m/m_1

increases up to the critical value

μ_c \approx 13.607

, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for

m/m_1

near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.