Utilities

Physical Constants

SimOS provides a series of physical constants that are commonly required in spin dynamics simulations.

c = 299792458

Speed of light (CODATA 2018)

elementary_charge = 1.602176634e-19

Elementary charge (CODATA 2018)

ge = 2.00231930436256

g factor electron (CODATA 2018)

hbar = 1.054571817e-34

Planck’s constant (CODATA 2018)

kB = 1.380649e-23

Boltzman constant (CODATA 2018)

magic_angle = np.float64(0.9553166181245092)

Magic angle in radians

me = 9.1093837015e-31

electron mass (CODATA 2018)

mub = 9.2740100783e-24

Bohr magneton (CODATA 2018)

munuc = 5.0507837461e-27

Nuclear magneton (CODATA 2018)

u = 1.6605390666e-27

Atomic mass u (CODATA 2018)

yH1_H20 = 267515315.1

Gyromagn. ratio 1H in H20 (CODATA 2018)

ye = -176085963023.0

Electron gyromagn. ratio (CODATA 2018)

Gyromagnetic Ratios

We offer a complete list of gyromagnetic ratios (any nucleus that is reasonably stable is included). Our list can also be accessed on a separate webpage.

Trivial Conversion Functions

SimOS further provides a series of trivial conversion functions that can help in making your code more readable.

cart2spher(*args, rad=True)

Transforms cartesian into spherical coordinates.

Parameters:

*args –

A single or multiple sets of cartesian x, y, z coordinates. Coordinates can be provided as a single argument, i.e. [x, y, z] or [[x1,y1,z1], [x2,y2,z2]] or as three separate arguments, i.e. x, y, z or [x1, x2], [y1, y2], [z1, z2]

Returns:

The corresponding spherical coordinates.

deg2rad(angle)

Takes an angle in degrees and returns it in radians.

Parameters:

angle – A single angle or a list, tuple or numpy array of angles in degrees.

Returns:

The angle in radians.

efield(*args, eps_rel=1, mode='cart')

Calculates the electric field of individual charges as well as total electric field in [V/m] Vectorized.

f2w(freq)

Takes a frequency and returns the corresponding angular frequency.

Parameters:

freq – A single frequency or a list, tuple or a numpy array of frequencies.

Returns:

The corresponding angular frequency.

flatten(S)

Flattens a nested list of lists, i.e. makes a single list out of it.

Parameters:

S (list) – A nested list of lists.

Returns:

The flattened list.

fuse_dictionaries(*args)

Fuses dictionaries into a single dictionary.

Parameters:

*args –

A list of dictionaries or a series of dictionary arguments:

Returns:

A single, fused dictionary.

mafm(T_in, f)

Takes a given time and rounds the value to the multiples of the period of a given frequency

:param T_in : Time, scalar or array :param f: Frequency (cycles) to take for the rounding

parse_state_string(s)

Parse a string which desribes a state of a given system into a dictionary of spin name (key) and projected spin value (value). :param str s: A string which describes the state. :returns: The parsed dictionary.

rad2deg(angle)

Takes an angle in radians and returns it in degrees.

Parameters:

angle – A single angle or a list, tuple or numpy array of angles in radians.

Returns:

The angle in degrees.

rotate_matrix(mat, *args, inverse=False, **kwargs)

Rotates a matrix by applying a “sandwich product” with a rotation matrix. The rotation matrix can be specified using a scipy Rotation object, a sympy Quaternion object or three euler angles.

Do not use this routine for quantum objects. Use .transform() or rotate_operator() instead.

Parameters:

• mat – Input matrix.

• *args –

  Rotation descripton: * Scipy Rotation object (scipy.spatial.transform.Rotation) * 3 euler angles. If euler angles are provided, the keyword argument convention=… must be given (e.g. convention=”zyx”). * sympy Quaternion object (sympy.quaternion.Quaternion)

Keyword Arguments:

• inverse (‘’bool’’) – If True, rotation is inverted.

  • convention (‘’bool’’) – e.g. “zyz” or “zxy”, only required if euler angles are provided, axes convention.

Example:

>>> rotate_matrix([[0,0,0],[1,0,0],[0,0,0]], np.pi/2, 0, 0, convention = "zxy")
>>> R = Rotation.from_euler("zxy", [np.pi/2, 0, 0])
>>> rotate_matrix([[0,0,0],[1,0,0],[0,0,0]], R)

Returns:

The rotated matrix.

spher2cart(*args, rad=True)

Transforms spherical into cartesian coordinates.

Parameters:

*args –

A single or multiple sets of spherical coordinates r, theta, phi. Coordinates can be provided as a single argument, i.e. [r, theta, phi] or [[r1,theta1,phi1], [r2,theta2,phi2]] or as three separate arguments, i.e. r, theta, phi or [r1, r2], [theta1, theta2], [phi1 , phi2].

Returns:

The corresponding cartesian coordinates.

t2p(total_time, f)

Takes a time and returns the corresponding phase at a given frequency

totalflatten(S)

Flattens nestest lists and tuples into a single, flat list.

Parameters:

S (list) – A nested list or tuples of lists and/or tuples.

Returns:

The flattened list.

w2f(freq)

Takes an angular frequency and returns the corresponding frequency.

Parameters:

freq – A single angular frequency or a list, tuple or numpy array of angular frequencies.

Returns:

The corresponding frequency.

write_state_string(d)

Writes a string which desribes a state of a given system from a dictionary of spin name (key) and projected spin value (value). :param dict d: A dictionary which describes the state. :returns: The state string.