Fluctuations and Linear Response in Supercooled Liquids

Johannes K. Nielsen

    Publikation: Bog/antologi/afhandling/rapportPh.d.-afhandlingForskning

    Resumé

    Fluctuation dissipation theorems are derived for thermodynamic properties like frequency dependent specific heat and compressibility. First the case where a systems dynamics are restricted by constant volume and energy is considered. The dynamic linear response to a heat pulse and a volume change at time zero is calculated, under assumption of energy conservation. Then the case of isothermal isobaric conditions are treated by a slight modification of ordinary linear response theory. In both cases the perturbation cannot be stated through the Hamiltonian, but has to be imposed by variation of the external thermodynamic system parameters. In thermodynamic response theory equivalence between ensembles is broken, but time correlation functions sampled in different ensembles are connected through the Maxwell relations of thermodynamics generalized to the frequency domain. Different applications of the theory in the field of supercooled liquids are showed. First the full frequency dependent thermodynamic response matrix is extracted from simulations of a binary Lennard Jones liquid. Secondly some simple stochastic models of supercooled liquids are analysed in the framework of linear thermodynamic response theory. In addition low temperature universality of the specific heat is discussed. Analysis of hydrogen bond dynamics in supercooled SPC/E model water shows that there is a separation between a fast (local) time scale, and a slow (collective) time scale in the supercooled regime. Time temperature scaling of the hydrogen bond correlation function is discussed in terms of a diffusion model.
    OriginalsprogEngelsk
    Udgivelses stedRoskilde
    ForlagRoskilde Universitet
    Antal sider104
    StatusUdgivet - 1998

    Citer dette

    Nielsen, J. K. (1998). Fluctuations and Linear Response in Supercooled Liquids. Roskilde: Roskilde Universitet.
    Nielsen, Johannes K. / Fluctuations and Linear Response in Supercooled Liquids. Roskilde : Roskilde Universitet, 1998. 104 s.
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    title = "Fluctuations and Linear Response in Supercooled Liquids",
    abstract = "Fluctuation dissipation theorems are derived for thermodynamic properties like frequency dependent specific heat and compressibility. First the case where a systems dynamics are restricted by constant volume and energy is considered. The dynamic linear response to a heat pulse and a volume change at time zero is calculated, under assumption of energy conservation. Then the case of isothermal isobaric conditions are treated by a slight modification of ordinary linear response theory. In both cases the perturbation cannot be stated through the Hamiltonian, but has to be imposed by variation of the external thermodynamic system parameters. In thermodynamic response theory equivalence between ensembles is broken, but time correlation functions sampled in different ensembles are connected through the Maxwell relations of thermodynamics generalized to the frequency domain. Different applications of the theory in the field of supercooled liquids are showed. First the full frequency dependent thermodynamic response matrix is extracted from simulations of a binary Lennard Jones liquid. Secondly some simple stochastic models of supercooled liquids are analysed in the framework of linear thermodynamic response theory. In addition low temperature universality of the specific heat is discussed. Analysis of hydrogen bond dynamics in supercooled SPC/E model water shows that there is a separation between a fast (local) time scale, and a slow (collective) time scale in the supercooled regime. Time temperature scaling of the hydrogen bond correlation function is discussed in terms of a diffusion model.",
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    Nielsen, JK 1998, Fluctuations and Linear Response in Supercooled Liquids. Roskilde Universitet, Roskilde.

    Fluctuations and Linear Response in Supercooled Liquids. / Nielsen, Johannes K.

    Roskilde : Roskilde Universitet, 1998. 104 s.

    Publikation: Bog/antologi/afhandling/rapportPh.d.-afhandlingForskning

    TY - BOOK

    T1 - Fluctuations and Linear Response in Supercooled Liquids

    AU - Nielsen, Johannes K.

    PY - 1998

    Y1 - 1998

    N2 - Fluctuation dissipation theorems are derived for thermodynamic properties like frequency dependent specific heat and compressibility. First the case where a systems dynamics are restricted by constant volume and energy is considered. The dynamic linear response to a heat pulse and a volume change at time zero is calculated, under assumption of energy conservation. Then the case of isothermal isobaric conditions are treated by a slight modification of ordinary linear response theory. In both cases the perturbation cannot be stated through the Hamiltonian, but has to be imposed by variation of the external thermodynamic system parameters. In thermodynamic response theory equivalence between ensembles is broken, but time correlation functions sampled in different ensembles are connected through the Maxwell relations of thermodynamics generalized to the frequency domain. Different applications of the theory in the field of supercooled liquids are showed. First the full frequency dependent thermodynamic response matrix is extracted from simulations of a binary Lennard Jones liquid. Secondly some simple stochastic models of supercooled liquids are analysed in the framework of linear thermodynamic response theory. In addition low temperature universality of the specific heat is discussed. Analysis of hydrogen bond dynamics in supercooled SPC/E model water shows that there is a separation between a fast (local) time scale, and a slow (collective) time scale in the supercooled regime. Time temperature scaling of the hydrogen bond correlation function is discussed in terms of a diffusion model.

    AB - Fluctuation dissipation theorems are derived for thermodynamic properties like frequency dependent specific heat and compressibility. First the case where a systems dynamics are restricted by constant volume and energy is considered. The dynamic linear response to a heat pulse and a volume change at time zero is calculated, under assumption of energy conservation. Then the case of isothermal isobaric conditions are treated by a slight modification of ordinary linear response theory. In both cases the perturbation cannot be stated through the Hamiltonian, but has to be imposed by variation of the external thermodynamic system parameters. In thermodynamic response theory equivalence between ensembles is broken, but time correlation functions sampled in different ensembles are connected through the Maxwell relations of thermodynamics generalized to the frequency domain. Different applications of the theory in the field of supercooled liquids are showed. First the full frequency dependent thermodynamic response matrix is extracted from simulations of a binary Lennard Jones liquid. Secondly some simple stochastic models of supercooled liquids are analysed in the framework of linear thermodynamic response theory. In addition low temperature universality of the specific heat is discussed. Analysis of hydrogen bond dynamics in supercooled SPC/E model water shows that there is a separation between a fast (local) time scale, and a slow (collective) time scale in the supercooled regime. Time temperature scaling of the hydrogen bond correlation function is discussed in terms of a diffusion model.

    M3 - Ph.D. thesis

    BT - Fluctuations and Linear Response in Supercooled Liquids

    PB - Roskilde Universitet

    CY - Roskilde

    ER -

    Nielsen JK. Fluctuations and Linear Response in Supercooled Liquids. Roskilde: Roskilde Universitet, 1998. 104 s.