Update bosonic_exchange.cpp
updated documentation of reduced/physical beta convention
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@ -381,16 +381,15 @@ void BosonicExchange::spring_force_interior_bead(double **f) const
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double BosonicExchange::prim_estimator()
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double BosonicExchange::prim_estimator()
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{
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{
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// In the "reduced-beta convention" [e.g. in J. Chem. Phys. 133, 124104 (2010); also J. Chem. Phys. 74, 4078-4095 (1981)],
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// In the "reduced-beta convention" [e.g., in J. Chem. Phys. 133, 124104 (2010); also J. Chem. Phys. 74, 4078-4095 (1981)],
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// the Boltzmann exponents have the form exp[-(beta/P)H], where H is the classical Hamiltonian of the
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// the Boltzmann exponents have the form exp[-(beta/P)H], where H is the classical Hamiltonian of the
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// ring polymers. This results in a canonical distribution at P times the physical temperature.
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// ring polymers. This results in a canonical distribution at P times the physical temperature.
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// In contrast, the "physical-beta convention" [e.g. in J. Chem. Phys. 99, 2796-2808 (1993)] uses weights of the form exp(-beta*H),
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// In contrast, the "physical-beta convention" [e.g., in J. Chem. Phys. 99, 2796-2808 (1993)] uses weights of the form exp(-beta*H),
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// such that the temperature of the canonical ensemble coincides with the physical temperature.
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// such that the temperature of the canonical ensemble coincides with the physical temperature.
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// Notably, the classical Hamiltonians of the two conventions differ, with the spring constant
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// Notably, the classical Hamiltonians of the two conventions differ, with the spring constant
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// in the reduced-beta convention being P times larger than that in the physical-beta convention. Additionally, the reduced-beta convention
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// in the reduced-beta convention being P times larger than that in the physical-beta convention. Additionally, the reduced-beta convention
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// lacks a 1/P prefactor in front of the external potential. The Hamiltonians of the two conventions are related through
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// lacks a 1/P prefactor in front of the external potential. The Hamiltonians of the two conventions are related through
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// H_physical = H_reduced / P. Note however that the expressions for the various estimators are unaffected by this choice,
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// H_physical = H_reduced / P. The code below was designed to be compatible with both conventions,
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// so as the algorithm for bosonic exchange. The code below was designed to be compatible with both conventions,
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// and the choice of convention only affects a single calculation within it.
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// and the choice of convention only affects a single calculation within it.
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// Setting the following boolean variable to false amounts to adopting the reduced-beta convention.
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// Setting the following boolean variable to false amounts to adopting the reduced-beta convention.
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double convention_correction = (physical_beta_convention ? 1 : 1.0 / np);
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double convention_correction = (physical_beta_convention ? 1 : 1.0 / np);
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