Time-Dependent Variational Principle for Predicting the Expectation Value of an Observable

Balian, Roger; Vénéroni, M.

doi:10.1103/physrevlett.47.1353

Cited by 113 publications

(85 citation statements)

References 7 publications

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“…It is shown in ref. [13], in small amplitude limit, that this approach gives rise to the same expression for dispersions of one-body observables as the one obtained in the variational description of Balian and Vénéroni (BV) [14,15]. In other applications, the average version of SMF theory was recently employed [16][17][18] to successfully reconcile onset of dissipation in TDHF and to calculate transport coefficients for relative momentum and nucleon-exchange in deep-inelastic heavy-ion collisions [19].…”

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confidence: 96%

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

2012

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Dynamics of spontaneous symmetry breaking and fluctuations in the Lipkin-Meshkov-Glick model are investigated in a stochastic mean-field approach. Different from the standard mean-field, in the stochastic approach, initial state fluctuations, are incorporated. In weak coupling, the approach perfectly reproduces the exact quantal dynamics. On the other hand, for increasing coupling strength, above the symmetry breaking threshold, the approach provides description of gross properties (i.e. time averaged behavior) of the exact quantal evolution.

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confidence: 96%

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

2012

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“…However, it can be solved exactly for simple cases only. The Balian-Vénéroni (BV) variational principle [2] offers an elegant starting point to build approximations of the many-body dynamics and has been applied to different problems in nuclear physics [3][4][5][6][7][8], hot Fermi gas [9], φ 4 theory [10], and Boson systems [11,12]. In particular, applications to deep-inelastic collisions (DIC) of atomic nuclei should be of interests to the upcoming exotic beam facilities.…”

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confidence: 99%

Particle-Number Fluctuations and Correlations in Transfer Reactions Obtained Using the Balian-Vénéroni Variational Principle

2011

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The Balian-Vénéroni (BV) variational principle, which optimizes the evolution of the state according to the relevant observable in a given variational space, is used at the mean-field level to determine the particle number fluctuations in fragments of many-body systems. For fermions, the numerical evaluation of such fluctuations requires the use of a time-dependent Hartree-Fock (TDHF) code. Proton, neutron and total nucleon number fluctuations in fragments produced in collisions of two 40 Ca are computed for a large range of angular momenta at a center of mass energy Ec.m. = 128 MeV, well above the fusion barrier. For deep-inelastic collisions, the fluctuations calculated from the BV variational principle are much larger than standard TDHF results, and closer to mass and charge experimental fluctuations. For the first time, correlations between proton and neutron numbers are determined within a quantum microscopic approach. These correlations are shown to be larger with exotic systems where charge equilibration occurs.The quantum many-body problem is the root of many theoretical fields aiming at describing interacting particles such as electrons in metals, molecules, atomic clusters, Bose-Einstein condensates, or atomic nuclei [1]. However, it can be solved exactly for simple cases only. The Balian-Vénéroni (BV) variational principle [2] offers an elegant starting point to build approximations of the many-body dynamics and has been applied to different problems in nuclear physics [3][4][5][6][7][8], hot Fermi gas [9], φ 4 theory [10], and Boson systems [11,12]. In particular, applications to deep-inelastic collisions (DIC) of atomic nuclei should be of interests to the upcoming exotic beam facilities. DIC will be used to investigate the role of the isospin degree of freedom in reactions and to extract the density dependence of the symmetry energy. Such reactions will produce nuclei in extreme, sometimes unknown, states (e.g., rotating nuclei with a neutron skin, or nuclei at or beyond the drip-lines).Assuming an initial density matrixD 0 at t 0 , The BV variational principle optimizes the expectation value of an observable Q = Tr(DQ) at a later time t 1 . In this approach, both the stateD(t) and the observableQ(t) vary between t 0 and t 1 within their respective variational spaces. In most practical applications, mean-field models are considered in a first approximation, and, eventually, serve as a basis for beyond-mean-field approaches [13,14]. For instance, restricting the variational space ofD(t) to pure independent particle states, and the one ofQ(t) to one-body operators, leads to the TDHF equation [15] ih ∂ρwhere ρ is the one-body density-matrix and h[ρ] is the Hartree-Fock (HF) single-particle Hamiltonian. According to this variational approach, TDHF is, then, the best mean-field theory to describe expectation values of onebody observables. However, it should not be used, in principle, to determine their fluctuations and correlations σ XY = XŶ − X Ŷ , (X andŶ are one-body operators, and fluctuations corre...

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“…This is a nice theoretical tool, but a rather difficult definition as far as experiments are concerned. Another possibility is to introduce entropy as a metric [61] …”

Section: Distance To Equilibriummentioning

confidence: 99%

“…This ensemble of correlations may lead to a statistical ensemble of realizations after a finite time. This phenomenon is often described introducing stochastic dynamics, i.e.assuming that the unobserved part of the dynamics which is averaged over is a random process [61,62].…”

Section: Maximum Entropy Statesmentioning

confidence: 99%

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Phase Transitions in Finite Systems using Information Theory

Chomaz

Gulminelli²

2008

AIP Conference Proceedings

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Abstract. In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of information theory. Information theory provides a thermodynamically-consistent treatment of finite, open, transient and expanding systems which are difficult problems in approaches using standard statistical ensembles.As an example, we analyze is the problem of boundary conditions, which in the framework of information theory must also be treated statistically. We recall that out of the thermodynamical limit the different ensembles are not equivalent and in particular they may lead to dramatically different equation of states, in the region of a first order phase transition. We recall the recent progresses achieved in the understanding of first-order phase transition in finite systems: the equivalence between the Yang-Lee theorem and the occurrence of bimodalities in the intensive ensemble and the presence of inverted curvatures of the thermodynamic potential of the associated extensive ensemble. We come back to the concept of order parameters and to the role of constraints on order parameters in order to predict the expected signature of first-order phase transition: in absence of any constraint (intensive ensemble) bimobality of the event distribution is expected while an inverted curvature of the thermodynamic potential is expected at a fixe value of the order parameter (extensive ensemble) in between the phases (coexistence zone). We stress that this discussion is not restricted to the possible occurrence of negative specific heat, but can also include negative compressibility's and negative susceptibilities, and in fact any curvature anomaly of the thermodynamic potential.

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Time-Dependent Variational Principle for Predicting the Expectation Value of an Observable

Cited by 113 publications

References 7 publications

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations

Particle-Number Fluctuations and Correlations in Transfer Reactions Obtained Using the Balian-Vénéroni Variational Principle

Phase Transitions in Finite Systems using Information Theory

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