In a country so unequivocally committed to "scientific socialism," the old Russian beliefs in supernatural and other mystical powers linger on with unusual persistence.

A visitor is frequently struck by the popular belief in magical powers. This phenomenon creates a sharp contrast between the social and economic advances that have occurred and the traditional patterns of life here.

A recent sensation here has been a "real" miracle healer from "Tbilisi, in Soviet Georgia, who is said to have cured hundreds of people with the "biological force" in her hands.

Her name is Dzhuna Davitishvili and she is about 30. Although married to a Georgian, she is an Assyrian, a fact that for many people reinforces belief in her "bionic" powers. According to folk legends, Assyrians are a people endowed with magic powers. An ancient people of the Middle East, a few of them survive in the southern Soviet Union along the Black Sea Coast.

All this may sound like the beginning of a story about a Soviet bionic woman, Except that the exploits of Dzhuna, as she is widely known here, have been sanctioned by the Kremlin. She is holding her seances at a government clinic and many prominent Soviet figures are said to be among her patients.

There are rumors that even President Leonid Brezhnev has sought her help. In fact, her ministrations are said to be responsible for the noticeable improvement in his physical appearance earlier this year when, after years of decline, he approved to be the picture of health and vigor.

Davitishvili's reputation for magical healing powers is not new. There have been numerous magic health healers in Russian history. One notable figure was Rasputin, the "mad monk" in the court of Czar Nicholas II. The imperial couple believed Rasputin could cure their only son who suffered from hemophilia. With this entre to court, Rasputin subsequently acquired great political power.

The Communists, with their insistence on scientific approach, have traditionally fought all sorts of quackery and supernatural powers. This time, it seems; Dzhuna's healing methods have won her powerful supporters not only in the political establishment but among some important and widely respected members of the Soviet Acaemy of Sciences.

Last week, academician Yuri Kobzaryev, who pioneered the development of radar for the Soviet Union, publicly endorsed Dzhuna's exploits as genuine -- not a response to any mysticism that may be deeply rooted among her paitients.

Kobzaryev said that some healers are known to emanate electomagnetic waves and that they have a physical rather than psychological effect on the patients.

The endorsement appeared in Komsomolsakya Pravda. A reporter for that paper claimed to have witnessed a number of miracles. These included Dzhuna's reviving a bouquet of dried roses by passing her hand over them.

He also reported that the woman placed her fingers on a box of cigarettes, raised her hand "and the box rose with it."

Earlier this summer, another academy member, Alexander Spirkin, wrote an article in which he described an experiment performed by Dzhuna. He said that "biological field force" from her hands dried out a trophic ulcer in 15 minutes after the bandages were removed. But Spirkin is a philosopher and his article was interpreted as a signal of political approval of the miracle healer who otherwise would be in conflict with Moscow's official medical establishment.

Most Soviet doctors are said to oppose Dzhuna's methods as unscientific. But the endorsement by Kobzaryey, a man of genuine scientific accomplishment who enjoys a great reputation here, suggests a division on the issue within the scientific elite.

Meanwhile -- despite her fee of $340 a session -- there is a long waiting list of people seeking Dzhuna's help.