eonc::tunneling::Profile Class Reference

Energy along the path, interpolated as a monotone cubic (Fritsch and Carlson), flat at both ends because the ends of a band are minima. More...

#include <Tunneling.h>

Public Member Functions
	Profile (std::vector< double > s, std::vector< double > v)
double	operator() (double x) const
const std::vector< double > &	s () const
const std::vector< double > &	v () const

Private Attributes
std::vector< double >	s_
std::vector< double >	v_
std::vector< double >	m_

Detailed Description

Energy along the path, interpolated as a monotone cubic (Fritsch and Carlson), flat at both ends because the ends of a band are minima.

A monotone interpolant cannot invent a dip below the data, which would change the forbidden region the WKB integral runs over.

Definition at line 54 of file Tunneling.h.

Constructor & Destructor Documentation

Profile()

eonc::tunneling::Profile::Profile	(	std::vector< double >	s,
		std::vector< double >	v )

Definition at line 61 of file Tunneling.cpp.

    : s_(std::move(s)),
      v_(std::move(v)),
      m_(s_.size(), 0.0) {
  const size_t n = s_.size();
  if (n < 2 || v_.size() != n) {
    throw std::invalid_argument(
        "a profile needs matching s and V with two points or more");
  }
  for (size_t k = 1; k < n; ++k) {
    if (!(s_[k] > s_[k - 1])) {
      throw std::invalid_argument(
          "the path coordinate must increase along the band");
    }
  }
  for (size_t k = 1; k + 1 < n; ++k) {
    const double h0 = s_[k] - s_[k - 1];
    const double h1 = s_[k + 1] - s_[k];
    const double d0 = (v_[k] - v_[k - 1]) / h0;
    const double d1 = (v_[k + 1] - v_[k]) / h1;
    if (d0 * d1 <= 0.0) {
      m_[k] = 0.0;
    } else {
      const double w1 = 2.0 * h1 + h0;
      const double w2 = h1 + 2.0 * h0;
      m_[k] = (w1 + w2) / (w1 / d0 + w2 / d1);
    }
  }
}

Member Function Documentation

operator()()

double eonc::tunneling::Profile::operator()

(

double

x

)

const

Definition at line 91 of file Tunneling.cpp.

                                         {
  x = std::clamp(x, s_.front(), s_.back());
  auto it = std::upper_bound(s_.begin(), s_.end(), x);
  size_t k = static_cast<size_t>(std::distance(s_.begin(), it));
  k = std::clamp<size_t>(k == 0 ? 0 : k - 1, 0, s_.size() - 2);
  const double h = s_[k + 1] - s_[k];
  const double t = (x - s_[k]) / h;
  const double t2 = t * t;
  const double t3 = t2 * t;
  return (2 * t3 - 3 * t2 + 1) * v_[k] + (t3 - 2 * t2 + t) * h * m_[k] +
         (-2 * t3 + 3 * t2) * v_[k + 1] + (t3 - t2) * h * m_[k + 1];
}

s()

const std::vector< double > & eonc::tunneling::Profile::s ( ) const

inline

Definition at line 58 of file Tunneling.h.

{ return s_; }

v()

const std::vector< double > & eonc::tunneling::Profile::v ( ) const

inline

Definition at line 59 of file Tunneling.h.

{ return v_; }

Member Data Documentation

m_

std::vector<double> eonc::tunneling::Profile::m_

private

Definition at line 62 of file Tunneling.h.

s_

std::vector<double> eonc::tunneling::Profile::s_

private

Definition at line 62 of file Tunneling.h.

v_

std::vector<double> eonc::tunneling::Profile::v_

private

Definition at line 62 of file Tunneling.h.

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The documentation for this class was generated from the following files:

• /home/runner/work/eOn/eOn/include/eon/Tunneling.h
• /home/runner/work/eOn/eOn/client/Tunneling.cpp