How to publish sim time at desired frequency

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Hi, I want to run the simulated time at frequency of 1Hz by publishing to the /clock topic and set rosparam /use_sim_time to be true/1.

However my following code produce simulated clock at a frequency of few kHz.

If use the commented part, the simulated clock will start at 0 and stops there.

If rosparam /use_sim_time is not set or set to false, the commented part will work fine. I am guessing that this clock topic is treated as a usual topic published and the rospy.Rate refers back and use the wall time to time the Rate object?

rospy.init_node('tmp')
pub = rospy.Publisher('/clock', Clock, queue_size=1)
epoch = rospy.Time(1546300800, 0)
rate = rospy.Rate(1)
clock = rospy.Time()
clock.set(1546300800,0)
rate = rospy.Rate(1)


while not rospy.is_shutdown():
    rospy.loginfo('')
    epoch += rospy.Duration(1)
    pub.publish(epoch)
    # rate.sleep()
    # rospy.sleep(1)