spin_m Module

This module defines the data type 'spin', which represents 2×2 complex matrices in spin space. The module overloads common arithmetic operators to work with the new data type, and defines and exports the Pauli matrices as constants. To make it easier to interact with common differential equation solvers, which often operate on real state vectors, the assignment operator is overloaded in such a way that 'spin' can be easily imported/exported to a real vector(8).

Contents

Variables

pauli0 pauli1 pauli2 pauli3 pauli

Interfaces

inverse trace sum conjg norm2

Derived Types

spin

Variables

Type	Visibility	Attributes		Name		Initial
type(spin),	public,	parameter	::	pauli0	=	spin(reshape([(1, 0), (0, 0), (0, 0), (1, 0)], [2, 2], order=[2, 1]))
type(spin),	public,	parameter	::	pauli1	=	spin(reshape([(0, 0), (1, 0), (1, 0), (0, 0)], [2, 2], order=[2, 1]))
type(spin),	public,	parameter	::	pauli2	=	spin(reshape([(0, 0), (0, -1), (0, 1), (0, 0)], [2, 2], order=[2, 1]))
type(spin),	public,	parameter	::	pauli3	=	spin(reshape([(1, 0), (0, 0), (0, 0), (-1, 0)], [2, 2], order=[2, 1]))
type(spin),	public,	parameter, dimension(0:3)	::	pauli	=	[pauli0, pauli1, pauli2, pauli3]

Interfaces

public interface inverse

Matrix inverse

• private pure function spin_inv(this) result(r)

  Calculate the inverse of the spin matrix.

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(spin),	intent(in)			::	this

  Return Value type(spin)

public interface trace

Matrix trace

• private pure elemental function spin_trace(this) result(r)

  Calculate the trace of the spin matrix.

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(spin),	intent(in)			::	this

  Return Value complex(kind=wp)

public interface sum

Matrix sum

• private pure function spin_sum(this) result(r)

  Calculate the sum of an array of spin matrices.

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(spin),	intent(in)			::	this(:)

  Return Value type(spin)

public interface conjg

Complex conjugation

• private pure elemental function spin_conjg(this) result(r)

  Calculate the complex conjugate of the spin matrix.

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(spin),	intent(in)			::	this

  Return Value type(spin)

public interface norm2

Matrix norm

• private pure elemental function spin_norm(this) result(r)

  Calculate the Frobenius norm of the spin matrix.

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(spin),	intent(in)			::	this

  Return Value real(kind=wp)

Derived Types

type, public :: spin

Components

Type	Visibility	Attributes		Name		Initial
complex(kind=wp),	public		::	matrix(2,2)	=	0.0_wp	Encapsulate a spin matrix

Type-Bound Procedures

generic, public :: spin => cons_rscalar, cons_cscalar, cons_cmatrix, cons_rvector, cons_spin
generic, public :: assignment(=) => assr_rscalar, assr_cscalar, assr_cmatrix, assr_rvector, assl_cmatrix, assl_rvector
generic, public :: operator(+) => addl_rscalar, addr_rscalar, addl_cscalar, addr_cscalar, addl_cmatrix, addr_cmatrix, add_spin
generic, public :: operator(-) => subl_rscalar, subr_rscalar, subl_cscalar, subr_cscalar, subl_cmatrix, subr_cmatrix, sub_spin
generic, public :: operator(*) => mull_rscalar, mulr_rscalar, mull_cscalar, mulr_cscalar, mull_cmatrix, mulr_cmatrix, mul_spin
generic, public :: operator(/) => divr_rscalar, divr_cscalar
generic, public :: operator(**) => expr_iscalar