Metropolitan Kallistos Ware is one of the world's preeminent Eastern Orthodox spiritual writers.  He often deals with the place of the Jesus Prayer in spiritual practice.  In his essay "Silence in Prayer:  the Meaning of Hesychia" he addresses the cultivation of interior stillness--that's basically what hesychia means--and how frequent recitation of the Jesus Prayer can contribute to achieving this stillness.  The essay is included in The Inner Kingdom:  Volume I of the Collected Works (2000, St Vladimir's Seminary Press), pp 99-102.

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Prayer, it was said, is a "laying aside of thoughts," a return from multiplicity to unity.  Now when we first make a serious effort to pray inwardly, standing before God with the mind in the heart, immediately we become conscious of our inward disintegration--of our powerlessness to concentrate ourselves in the present moment, in the kairos.  Thoughts move restlessly through our head, like the buzzing of flies (St Theophan)or the capricious leaping of monkeys from branch to branch (Ramakrishna).  This lack of concentration, this inability to be here and now with the whole of our being, is one of the most tragic consequences of the Fall.

What is to be done?  The Orthodox ascetic tradition distinguishes two main methods of overcoming "thoughts".  The first is direct, to "contradict" our logismoi [errant thoughts], to meet them face to face, attempting to expel them by an effort of will...It is safer to employ the second method...we can seek to direct our attention away from them and to look elsewhere...our immediate objective is not to empty our mind of what is evil but rather to fill it with what is good.

...Although we cannot make the never-idle mind desist altogether from its restlessness, what we can do is to simplify and unify its activity by continually repeating a short formula of prayer.  The flow of images and thoughts will persist, but we shall be enabled gradually to detach ourselves from it...

...This, then, is the ascetic strategy presupposed in the use of the Jesus Prayer.  It assists us in applying the second or oblique method of combating  thoughts:  instead of trying to obliterate our corrupt or trivial imaginings by a direct confrontation, we turn aside and look at the Lord Jesus; instead of relying on our own power, we take refuge in the power and grace that act through the Divine Name.  The repeated invocation helps us to detach ourselves from the ceaseless chattering of our logismoi.

...First, to achieve its purpose the invocation should be rhythmical and regular...

In the second place, during the recitation of the Jesus Prayer the mind should be so far as possible empty of mental pictures.