eonc::pathintegral Namespace Reference

Classes
struct	Options
class	RingPolymer
	Ring-polymer NVT step. More...
struct	Sample

Enumerations
enum class	Springs { Trotter , Eco }
	Trotter springs, or economised springs fitted to harmonic radii of gyration up to a maximum frequency (Zeng and Manolopoulos, arXiv:2607.06414). More...
enum class	Thermostat { Pile , Piglet }
	PILE-L, or a normal-mode GLE on the internal modes with a separate Langevin thermostat on the centroid. More...

Functions
void	requireTrotterSprings (const std::string &springs, const char *use)
	Economised springs and a normal-mode GLE are refused.
VectorXd	trotterEigenvalues (long nBeads)
	Dimensionless free-ring eigenvalues, mode 0 equal to 0.
VectorXd	ecoEigenvalues (long nBeads, double xmax)
MatrixXd	normalModeMatrix (long nBeads)
	Orthogonal bead-to-normal-mode matrix. Row k is mode k.

Enumeration Type Documentation

Springs

enum class eonc::pathintegral::Springs

strong

Trotter springs, or economised springs fitted to harmonic radii of gyration up to a maximum frequency (Zeng and Manolopoulos, arXiv:2607.06414).

Enumerator
Trotter
Eco

Definition at line 42 of file PathIntegral.h.

{ Trotter, Eco };

Thermostat

enum class eonc::pathintegral::Thermostat

strong

PILE-L, or a normal-mode GLE on the internal modes with a separate Langevin thermostat on the centroid.

Enumerator
Pile
Piglet

Definition at line 46 of file PathIntegral.h.

{ Pile, Piglet };

Function Documentation

ecoEigenvalues()

VectorXd eonc::pathintegral::ecoEigenvalues	(	long	nBeads,
		double	xmax )

Definition at line 273 of file PathIntegral.cpp.

                                                  {
  if (nBeads < 1) {
    throw std::invalid_argument("bead count must be positive");
  }
  VectorXd eva = VectorXd::Zero(nBeads);
  if (nBeads == 1) {
    return eva;
  }
  if (!(xmax > 0.0)) {
    throw std::invalid_argument(
        "economised springs need a positive maximum frequency");
  }
  const VectorXd y = ecoFit(nBeads, xmax);
  for (long k = 1; k < nBeads; ++k) {
    const long pair = std::min(k, nBeads - k) - 1;
    eva[k] = y[pair] / static_cast<double>(nBeads);
  }
  return eva;
}

normalModeMatrix()

MatrixXd eonc::pathintegral::normalModeMatrix

(

long

nBeads

)

Orthogonal bead-to-normal-mode matrix. Row k is mode k.

Definition at line 293 of file PathIntegral.cpp.

                                       {
  if (nBeads < 1) {
    throw std::invalid_argument("bead count must be positive");
  }
  MatrixXd b = MatrixXd::Zero(nBeads, nBeads);
  const double n = static_cast<double>(nBeads);
  for (long j = 0; j < nBeads; ++j) {
    b(0, j) = 1.0;
    for (long i = 1; i <= nBeads / 2; ++i) {
      b(i, j) = std::sqrt(2.0) * std::cos(2.0 * kPi * static_cast<double>(j) *
                                          static_cast<double>(i) / n);
    }
    for (long i = nBeads / 2 + 1; i < nBeads; ++i) {
      b(i, j) = std::sqrt(2.0) * std::sin(2.0 * kPi * static_cast<double>(j) *
                                          static_cast<double>(i) / n);
    }
  }
  if (nBeads % 2 == 0) {
    const long mid = nBeads / 2;
    for (long j = 0; j < nBeads; ++j) {
      b(mid, j) = (j % 2 == 0) ? 1.0 : -1.0;
    }
  }
  b /= std::sqrt(n);
  return b;
}

requireTrotterSprings()

void eonc::pathintegral::requireTrotterSprings	(	const std::string &	springs,
		const char *	use )

Economised springs and a normal-mode GLE are refused.

The instanton assumes Trotter springs and is refused the same way.

Definition at line 252 of file PathIntegral.cpp.

                                                                      {
  const std::string s = lower(springs);
  if (s == "eco" || s == "economised") {
    throw std::invalid_argument(
        std::string(use) +
        " requires Trotter springs; economised springs are refused");
  }
}

trotterEigenvalues()

VectorXd eonc::pathintegral::trotterEigenvalues

(

long

nBeads

)

Dimensionless free-ring eigenvalues, mode 0 equal to 0.

Physical frequencies are omegan times these values, with omegan = beads * kB * T / hbar.

Definition at line 261 of file PathIntegral.cpp.

                                         {
  if (nBeads < 1) {
    throw std::invalid_argument("bead count must be positive");
  }
  VectorXd eva(nBeads);
  for (long k = 0; k < nBeads; ++k) {
    eva[k] = 2.0 * std::sin(kPi * static_cast<double>(k) /
                            static_cast<double>(nBeads));
  }
  return eva;
}