Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Landau-Zener Effect In The Time-Dependent Hartree-Fock-Bogoliubov Equations

M. Mirea, L. Trache, Sabin Stoica

Published Jan 1, 2008• 0 citations
Publisher

Abstract

If the Hartree‐Fock‐Bogoliubov equations of motion are solved in the case of seniority one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility that the unpaired nucleon skips from one orbital to another. A new set of coupled channel equations based on the time dependent Hartree‐Fock‐Bogoliubov formalism is deduced. This system includes a mechanism similar to the Landau‐Zener effect, allowing that the unpaired nucleon jumps from one level to another.

DOI
10.1063/1.2870415

Related papers

LANDAU-ZENER EFFECT GENERALIZED FOR SUPERFLUID SYSTEMS

M. Mirea

The Landau-Zener effect explains the promotion mechanism from one adiabatic intrinsic energy level to another one when the generalized coordinates vary. The two levels have the same spin. In the case of single-particle models without including residual interactions, it is possible to quantify the Landau-Zener effect by mean of a time dependent system of coupled channel equations. At this conference, a generalization of the Landau-Zener equations for seniority one superfluid nuclear systems is presented. A new set of time dependent coupled channel equations are derived in detail. The particular cases of these equations are the classical time dependent Landau-Zener equations and the time dependent Hartree-Fock-Bogoliubov equations for even systems.

•Jan 1, 2009•0 citations

Extension of time-dependent Hartree-Fock-Bogoliubov equations

M. Tohyama, Peter Schuck

An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a pairing model and a fermion system trapped in a harmonic potential to test its feasibility by comparison with exact solutions. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.

arXiv:1411.5730•Physical Review C•Mar 13, 2015•5 citations

Pairing dynamics in particle transport

Guillaume Scamps, Denis Lacroix A, G. F. Bertsch +1 more

We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of time-dependent Hartree-Fock $(\mathrm{TDHF})+\mathrm{BCS}$, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in $\mathrm{TDHF}+\mathrm{BCS}$, but there are other problems with the BCS approximation that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the $U$ and $V$ Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schr\"odinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schr\"odinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.

arXiv:1202.2681•Physical Review C•Mar 23, 2012•55 citations

Landau-Zener problem with decay and dephasing

Y. Avishai, Y. B. Band

Two aspects of the classic two-level Landau-Zener (LZ) problem are considered. First, we address the LZ problem when one or both levels decay, i.e., ${\ensuremath{\varepsilon}}_{j}(t)\ensuremath{\rightarrow}{\ensuremath{\varepsilon}}_{j}(t)\ensuremath{-}i{\ensuremath{\Gamma}}_{j}/2$. We find that if the system evolves from an initial time $\ensuremath{-}T$ to a final time $+T$ such that $|{\ensuremath{\varepsilon}}_{1}(\ifmmode\pm\else\textpm\fi{}T)\ensuremath{-}{\ensuremath{\varepsilon}}_{2}(\ifmmode\pm\else\textpm\fi{}T)|$ is not too large, the LZ survival probability of a state $|j\ensuremath{\rangle}$ can increase with increasing decay rate of the other state $|i\ensuremath{\ne}j\ensuremath{\rangle}$. This surprising result occurs because the decay results in crossing of the two eigenvalues of the instantaneous non-Hermitian Hamiltonian. On the other hand, if $|{\ensuremath{\varepsilon}}_{1}(\ifmmode\pm\else\textpm\fi{}T)\ensuremath{-}{\ensuremath{\varepsilon}}_{2}(\ifmmode\pm\else\textpm\fi{}T)|\ensuremath{\rightarrow}\ensuremath{\infty}$ as $T\ensuremath{\rightarrow}\ensuremath{\infty}$, the probability is independent of the decay rate. These results are based on analytic solutions of the time-dependent Schr\"odinger equations for two cases: (a) the energy levels depend linearly on time, and (b) the energy levels are bounded and of the form ${\ensuremath{\varepsilon}}_{1,2}(t)=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varepsilon}tanh(t/\mathcal{T})$. Second, we study LZ transitions affected by dephasing by formulating the Landau-Zener problem with noise in terms of a Schr\"odinger-Langevin stochastic coupled set of differential equations. The LZ survival probability then becomes a random variable whose probability distribution is shown to behave very differently for long and short dephasing times. We also discuss the combined effects of decay and dephasing on the LZ probability.

arXiv:1311.3919•Physical Review A•Sep 30, 2014•22 citations

Time-dependent Hartree-Fock-Bogoliubov approximation and nonintegrable quantum phase

Aurel Bulgac

We shall show how the so-called Berry's or quantum nonintegrable phase appears in the context of the time-dependent Hartree-Fock-Bogoliubov equations. It is shown that the right requantization of the time-dependent Hartree-Fock-Bogoliubov equations is achieved only when Berry's phase is properly taken into account.

Physical Review C•May 1, 1990•18 citations

Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction

Aurel Bulgac, Y. C. Yu

We introduce a natural and simple way to implement the regularization scheme of the Hartree-Fock-Bogoliubov equations with zero range pairing interaction. The renormalization scheme proves to be equivalent to a simple energy cutoff with a position dependent running coupling constant.

arXiv:nucl-th/0106062•Physical Review Letters•Jan 14, 2002•182 citations
If the Hartree‐Fock‐Bogoliubov equations of motion are solved in the case of seniority one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility that the unpaired nucleon skips from one orbital to another. A new set of coupled channel equations based on the time dependent Hartree‐Fock‐Bogoliubov formalism is deduced. This system includes a mechanism similar to the Landau‐Zener effect, allowing that the unpaired nucleon jumps from one level to another.
The Landau-Zener effect explains the promotion mechanism from one adiabatic intrinsic energy level to another one when the generalized coordinates vary. The two levels have the same spin. In the case of single-particle models without including residual interactions, it is possible to quantify the Landau-Zener effect by mean of a time dependent system of coupled channel equations. At this conference, a generalization of the Landau-Zener equations for seniority one superfluid nuclear systems is presented. A new set of time dependent coupled channel equations are derived in detail. The particular cases of these equations are the classical time dependent Landau-Zener equations and the time dependent Hartree-Fock-Bogoliubov equations for even systems.
An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB) which includes higher-order effects such as screening of the pairing correlation is proposed. ETDHFB is applied to a pairing model and a fermion system trapped in a harmonic potential to test its feasibility by comparison with exact solutions. With the use of perturbative expressions for the pairing tensor and the two-body density matrix derived from ETDHFB, the screening effect is investigated for atomic fermion systems and isotopes of tin nuclei. It is found that the screening effect on the pairing correlation is not significant.
We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of time-dependent Hartree-Fock (TDHF)+BCS(\mathrm{TDHF})+\mathrm{BCS}(TDHF)+BCS, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in TDHF+BCS\mathrm{TDHF}+\mathrm{BCS}TDHF+BCS, but there are other problems with the BCS approximation that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the UUU and VVV Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schr\"odinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schr\"odinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.
Two aspects of the classic two-level Landau-Zener (LZ) problem are considered. First, we address the LZ problem when one or both levels decay, i.e., ${\ensuremath{\varepsilon}}_{j}(t)\ensuremath{\rightarrow}{\ensuremath{\varepsilon}}_{j}(t)\ensuremath{-}i{\ensuremath{\Gamma}}_{j}/2$. We find that if the system evolves from an initial time $\ensuremath{-}T$ to a final time +T+T+T such that $|{\ensuremath{\varepsilon}}_{1}(\ifmmode\pm\else\textpm\fi{}T)\ensuremath{-}{\ensuremath{\varepsilon}}_{2}(\ifmmode\pm\else\textpm\fi{}T)|$ is not too large, the LZ survival probability of a state $|j\ensuremath{\rangle}$ can increase with increasing decay rate of the other state $|i\ensuremath{\ne}j\ensuremath{\rangle}$. This surprising result occurs because the decay results in crossing of the two eigenvalues of the instantaneous non-Hermitian Hamiltonian. On the other hand, if $|{\ensuremath{\varepsilon}}_{1}(\ifmmode\pm\else\textpm\fi{}T)\ensuremath{-}{\ensuremath{\varepsilon}}_{2}(\ifmmode\pm\else\textpm\fi{}T)|\ensuremath{\rightarrow}\ensuremath{\infty}$ as $T\ensuremath{\rightarrow}\ensuremath{\infty}$, the probability is independent of the decay rate. These results are based on analytic solutions of the time-dependent Schr\"odinger equations for two cases: (a) the energy levels depend linearly on time, and (b) the energy levels are bounded and of the form ${\ensuremath{\varepsilon}}_{1,2}(t)=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varepsilon}tanh(t/\mathcal{T})$. Second, we study LZ transitions affected by dephasing by formulating the Landau-Zener problem with noise in terms of a Schr\"odinger-Langevin stochastic coupled set of differential equations. The LZ survival probability then becomes a random variable whose probability distribution is shown to behave very differently for long and short dephasing times. We also discuss the combined effects of decay and dephasing on the LZ probability.