what is logic behind rebirth

As per my understanding of Buddhism & Science all things that exist in the universe is made up of matter & energy. The energy that is found in any animal is generally referred to as the soul. The body we carry is made up of matter. According to the teachings of lord Buddha which is what now discovered by scientists as quantum mechanics is, that every thought & action we do releases a positive or negative energy to the universe. It then creates a set of possible futures that can happen. This will be following us till we reach enlightment. The process that happens to us at death is similar to what happens when we change clothes. The body we possess is similar to a cloth. As soon as we (the soul) leaves this body, it'll get hold of another body. This body that we get hold of is determined by the possitive & negative forces that we have released to the universe in our previous life.

It is Kamma, rooted in ignorance and craving, that conditions rebirth. This life-stream flows ad infinitum, as long as it is fed by the muddy waters of ignorance and craving. When these two are completely cut off, then only, if one so wishes, does the stream cease to flow, rebirth ends as in the case of the Buddhas and Arahats. The most valuable evidence Buddhists cite in favor of rebirth is the Buddha, for He developed a knowledge which enabled Him to read past and future lives.

The Right View on Rebirth is explained in the famous Buddhist book “Milindaparsna” which contains a long dialogue between the Greek king Minander I and Arhat Nagasena.

Miln III.5.5: Transmigration and Rebirth (Miln 71)
The king asked: "Venerable Nagasena, is it so that one does not transmigrate and one is reborn?"
"Yes, your majesty, one does not transmigrate and one is reborn."
"How, venerable Nagasena, is it that one does not transmigrate and one is reborn? Give me an analogy."
"Just as, your majesty, if someone kindled one lamp from another, is it indeed so, your majesty, that the lamp would transmigrate from the other lamp?"
"Certainly not, venerable sir."
"Indeed just so, your majesty, one does not transmigrate and one is reborn."

As per the scriptures, a being is a stream of Mind connected ‘ Nama-Rupa’. When a person dies, no soul departs. The stream of consciousness ( viññana) upon death, becomes one of the contributing causes for the arising of a new set of five aggregates of clinging (Panca Upadana Khandas) elsewhere. In the Attakara sutta, you will find that you do exist. But there is no permanent self in you and the five clinging aggregates (panca upadanakkanda) which constitutes you is beyond your control, and therefore Anatta (non-self). (read Anatta Lakkana Sutta).

A Stream Entrant is incapable of actions of craving and hatred that will definitively lead to rebirth in the four states of misery (Hell, Asura, Hungry Ghost and Animal realms), but the remaining gross craving and hatred is only eradicated when one becomes a Once-Returner; subtle craving and hatred are eliminated for the Non-Returner.

You won't find one single answer which covers all traditions. Different Buddhist traditions have different interpretations of the mechanism of rebirth.

I think you are looking for something material which facilitates a movement of something from one life to the next. However, Buddhism doesn't require that the world governed by materialism. We can consider a world which is entirely driven by mental ideas or "the mind" as we call it.

Buddhists are not in agreement about how the world exists, some would say that the world doesn't exist. If you consider one of these traditions then you have to ask if it even makes sense for something to move from one body to the next life's body. Bodies can also be considered as being entirely constructed by the mind. Yogachara is an example of a Buddhist tradition which is "mind-only".