Quantal corrections to mean-field dynamics including pairing

Abstract

Extending the stochastic mean-field model by including pairing, an approach is proposed for describing evolutions of complex many-body systems in terms of an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is determined by incorporating fluctuations in the initial state. Non-linear evolution of the initial fluctuations provides an approximate description of quantal correlations and fluctuations of collective observables. Since the initial-state fluctuations break the particle-number symmetry, the dynamical description in which pairing correlations play a crucial role is greatly improved as compare to the mean-field evolution. The approach is illustrated for a system of particles governed by a pairing Hamiltonian. Under certain conditions, it is possible to provide an approximate description for quantal evolution of a system in terms of an ensemble of classical trajectories with proper choice of initial conditions. This aspect appears naturally in the path integral formulation of quantum dynamics and has been recognized in refs. [1,2]. In recent years, this idea has been pushed forward to improved the mean-field description of many-body interacting systems [3,4]. Mean-field description cannot describe essential quantal effects associated to collective motion and severely underestimates fluctuations of collective observables. By considering an ensemble of mean-field trajectories with a specific choice of the fluctuations (quantal zero-point and thermal) in the initial state, it is possible to overcome some of these shortcomings. Several applications, especially in the nuclear physics context [5][6][7][8], have shown that this approach can improve the mean-field description by including important dissipative aspects in transport properties of heavy-ion collisions. More recently, we illustrated that such an approach, in addition to fluctuations, can accurately tackle the problem of symmetry breaking close to bifurcation point in collective energy landscape [9]. Up to now, the stochastic mean-field (SMF) approach with initial fluctuations has been developed starting from a Time-Dependent HartreeFock (TDHF) version of the mean-field. Nowadays, there are increasing interests in the treatment of pairing to describe evolution of strongly interacting Fermi liquids [10][11][12][13][14] employing the Time-Dependent Hartree-Fock Bogoliubov (TDHFB) approach or its simplified BCS limit. While the TDHFB theory provides an important improvement beyond TDHF, it still suffers from the above quoted limitations: i.e. underestimation of quantum collective fluctuations and impossibility to spontaneously break symmetries. Due to the successful description of * Electronic address: lacroix@ganil.fr the SMF approach in geometric symmetry breaking, it is rather tempting to introduce quantum fluctuations through initial sampling to treat pairing where the U (1) symmetry breaking plays an important role.In this work, we present an extension of the SMF approach by incorporating pairing into the description. In the standa...

Microscopic Phase-Space Exploration Modeling ofFm258Spontaneous Fission

“…In nuclear physics this approach, called stochastic mean field [36], has been originally introduced such that initial fluctuations in collective space are reproduced through arXiv:1609.01424v2 [nucl-th] 21 Mar 2017 fluctuations of the initial one-body density. In a series of works, it was shown that it surprisingly well accounts for correlations beyond mean-field [37][38][39] while treating properly the dynamic close to a spontaneous symmetry breaking [38]. It is also able to include approximately many-body correlation to all orders by connecting the evolution to the BBGKY hierarchy [40].…”

“…[41]. Although the stochastic mean-field technique was applied to simple models [37][38][39]42] or to obtain expressions of transport coefficients [40,[43][44][45][46], we present here the first application to a realistic physical phenomena where the phasespace sampling is explicitly made.…”

Nucleon exchange in heavy-ion collisions within a stochastic mean-field approach

“…In a recent application, the SMF approach is tested with Lipkin-Meshkov-Glick model, and it is found that the gross properties of the model are well produced in the SMF approach [17]. The SMF approach was also extended by including pairing interaction [18].…”

Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

“…[13], extended in Ref. [14] to describe small superfluid systems and shown to be competitive with most recent NEGF theories applied to lattice systems in Ref. [15].…”

“…[12], some formal arguments were given to support these ideas. Afterwards, it was shown in different test cases that the SMF concept [11,13,14] can be more predictive and versatile than anticipated. In the present article, we analyze in more details the hypothesis made for the initial sampling, i.e.…”