quspin.tools.Floquet.Floquet_t_vec

class quspin.tools.Floquet.Floquet_t_vec(Omega, N_const, len_T=100, N_up=0, N_down=0)[source]

Bases: object

Creates a Floquet time vector with fixed number of points per period.

This time vector hits all stroboscopic times, and has many useful attributes. The time vector can be divided in three parts corresponding to three regimes of periodic evolution: ramp-up, constant and ramp-down.

Particularly useful for studying periodically-driven systems.

Examples

The following code shows how to use the Floquet_t_vec class.

 1import numpy as np  # generic math functions
 2
 3#
 4Omega = 4.5  # drive frequency
 5# define time vector with three stages of evolution, labelled by "up", "const" and "down"
 6t = Floquet_t_vec(Omega, 10, len_T=10, N_up=3, N_down=2)
 7print(t)
 8##### attibutes referring to total time vector
 9# time points values
10print(t.vals)
11# total number of periods
12print(t.N)
13# driving period
14print(t.T)
15# step size
16print(t.dt)
17# initial, final time and total time duration
18print(t.i, t.f, t.tot)
19# length of time vector and length within a period
20print(t.len, t.len_T)
21##### attributes referring to stroboscopic times only
22# indices of stroboscopic times
23print(t.strobo.inds)
24# values of stroboscopic times
25print(t.strobo.vals)
26##### attributes relating to the "up" stage of the evolution
27# time values for the "up"-stage
28print(t.up.vals)
29# initial, final time and total time of "up" duration (similar for "const" and "down")
30print(t.up.i, t.up.f, t.up.tot)

__init__(Omega, N_const, len_T=100, N_up=0, N_down=0)[source]

Parameters:

Omegafloat

Drive frequency.

N_constint

Number of time periods in the constant part (period) of the time vector.

len_Tint

Number of time points within a single period. N.B. the last period interval is assumed open on the right, i.e. [0,T) and the point T is NOT counted towards ‘len_T’.

N_upint, optional

Number of time periods in the up-part (period) of time vector.

N_downint, optional

Number of time periods in the down-part (period) of time vector.

Methods

__init__(Omega, N_const[, len_T, N_up, N_down])
get_coordinates(index)	Returns (period number, index within period) of the Floquet_t_vec value stored at index.

Attributes

N	total number of periods.
T	drive period.
const	refers to time vector of const-part (regime).
down	refers to time vector of down-part (regime).
dt	time vector step size.
f	final time value.
i	initial time value.
len	length of time vector.
len_T	number of time points within one period, assumed half-open; [0,T).
shape	shape of array.
strobo	calculates stroboscopic times in time vector with period length len_T and assigns them as attributes:
tot	total time duration; _.f - _.i .
up	refers to time vector of up-part (regime).
vals	time vector values.

property N

total number of periods.

Type:

int

property T

drive period.

Type:

float

property const

refers to time vector of const-part (regime).

Inherits all attributes (e.g. _.const.strobo.inds) except _.T, _.dt, and _.lenT.

Type:

obj

property down

refers to time vector of down-part (regime).

Inherits all attributes (e.g. _.down.strobo.inds) except _.T, _.dt, and _.lenT.

Requires optional __init___ parameter N_down to be specified.

Type:

obj

property dt

time vector step size.

Type:

float

property f

final time value.

Type:

foat

get_coordinates(index)[source]

Returns (period number, index within period) of the Floquet_t_vec value stored at index.

Parameters:

indexint

Index, to compute the Floquet_t_vec coordinates of.

Returns:

tuple

(i,j) such that t_evolve[t_evolve.strobo.inds[i] + j] = t_evolve[index].

Notes

• This function finds the indegers (i,j), such that t_evolve[t_evolve.strobo.inds[i-1] + j] = t_evolve[index].

• The function may return wrong results if the spacing between two consecutive (i.e. nonstroboscopic) Floquet_t_vec values is smaller than 1E-15.

Examples

>>> t = Floquet_t_vec(10.0,10) # define a Floquet vector
>>> index = 145 # pick a random index
>>> print(t[index]) # check element
>>> (i,j) = t.get_coordinates(index) # decompose index into stroboscopic coordinates
>>> print( t[t.strobo.inds[i] + j] ) # we obtain back original element

property i

initial time value.

Type:

float

property len

length of time vector.

Type:

int

property len_T

number of time points within one period, assumed half-open; [0,T).

Type:

int

property shape

shape of array.

Type:

tuple

property strobo

calculates stroboscopic times in time vector with period length len_T and assigns them as attributes:

_.strobo.indsnumpy.ndarray(int)

indices of stroboscopic times (full periods).

_.strobo.valsnumpy.ndarray(float)

values of stroboscopic times (full periods).

Type:

obj

property tot

total time duration; _.f - _.i .

Type:

float

property up

refers to time vector of up-part (regime).

Inherits all attributes (e.g. _.up.strobo.inds) except _.T, _.dt, and _.lenT.

Requires optional __init___ parameter N_up to be specified.

Type:

obj

property vals

time vector values.

Type:

np.ndarray(float)