Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAn elementary exposition of the Efimov Effect
182
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Two particles that are just shy of binding may develop an infinite number of shallow bound states when a third particle is added. This counter intuitive quantum mechanical result was first predicted by V. Efimov for identical bosons interacting with a short-range pair-wise potential. The so-called Efimov effect persists even for non-identical particles, provided at least two of the three bonds are almost bound. The Efimov effect has recently been verified experimentally using ultra-cold atoms. In this article, we explain the origin of this effect using only elementary quantum mechanics, and summarize the experimental evidence for the Efimov effect. A new, simple derivation for the number of Efimov states is given in the Appendix.
rate research
Read More
We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.
We study a three-body system, formed by two identical heavy bosons and a light particle, in the Born-Oppenheimer approximation for an arbitrary dimension $D$. We restrict $D$ to the interval $2,<,D,<,4$, and derive the heavy-heavy $D$-dimensional effective potential proportional to $1/R^2$ ($R$ is the relative distance between the heavy particles), which is responsible for the Efimov effect. We found that the Efimov states disappear once the critical strength of the heavy-heavy effective potential $1/R^2$ approaches the limit $-(D-2)^2/4$. We obtained the scaling function for the $^{133}$Cs-$^{133}$Cs-$^6$Li system as the limit cycle of the correlation between the energies of two consecutive Efimov states as a function of $D$ and the heavy-light binding energy $E^{D}_2$. In addition, we found that the energy of the $(N+1)^{rm th}$ excited state reaches the two-body continuum independently of the dimension $D$ when $sqrt{E^{D}_2/E_3^{(N)}}=0.89$, where $E_3^{(N)}$ is the $N^{rm th}$ excited three-body binding energy.
The existence of the Efimov effect is drastically affected by the dimensionality of the space in which the system is embedded. The effective spatial dimension containing an atomic cloud can be continuously modified by compressing it in one or two directions. In the present article we determine for a general $AAB$ system formed by two identical bosons $A$ and a third particle $B$ in the two-body unitary limit, the dimensionsality $D$ for which the Efimov effect can exist for different values of the mass ratio $mathpzc{A}=m_B/m_A$. In addition, we provide a prediction for the Efimov discrete scaling factor, ${rm exp},(pi/s)$, as a function of a wide range of values of $mathpzc{A}$ and $D$, which can be tested in experiments that can be realized with currently available technology.
Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.
If the boundary conditions of the quantum vacuum are changed in time, quantum field theory predicts that real, observable particles can be created in the initially empty modes. Here, we realize this effect by changing the boundary conditions of a spinor Bose-Einstein condensate, which yields a population of initially unoccupied spatial and spin excitations. We prove that the excitations are created as entangled excitation pairs by certifying continuous-variable entanglement within the many-particle output state.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
