Related papers: An inversion formula for the 2-body interaction gi…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
We renormalize the two-body contact interaction based on the exact solution of two interacting particles in a harmonic trap. This renormalization extends the validity of the contact interaction to large scattering lengths. We apply this…
Quantum correlations can be used as a resource for quantum computing, eg for quantum state manipulation, and for quantum sensing, eg for creating non-classical states which allow to achieve the quantum advantage regime. This review collects…
The realization of ultracold polar molecules in laboratories has pushed both physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the…
The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings \beta = 1,2 and 4. It has been known for some time that there is an…
Weak-strong coupling duality relations are shown to be present in the quantum-mechanical many-body system with the interacting potential proportional to the pair-wise inverse-squared distance in addition to the harmonic potential. Using…
We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length…
We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant…
We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us…
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit…
We study the ground state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small ($\sim 3$) to very large ($\sim 10^7$) particle numbers. We use the correlated two-body basis functions and the…
Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous, (not necessarily isotropic)…
We investigate the resonance quadrupole-quadrupole interaction between two entangled gravitationally polarizable objects induced by a bath of fluctuating quantum gravitational fields in vacuum in the framework of linearized quantum gravity.…
Quantum states of a two-component Fermi trapped gas are described by introducing an effective trap frequency, determined via variational techniques. Closed expressions for the contribution of a contact interaction potential to the total…
Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few- and many-body systems. We are extending for this purpose the quantum inversion approach for systems…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
The concept of inverse statistics in turbulence has attracted much attention in the recent years. It is argued that the scaling exponents of the direct structure functions and the inverse structure functions satisfy an inversion formula.…
We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our…
We consider a binary system of small and large objects in the continuous space interacting via a non-negative potential. By integrating over the small objects, the effective interaction between the large ones becomes multi-body. We prove…