Related papers: Variational approach to anharmonic collective moti…
The fractional operators together with exponential quantum in coordinate and momentum space corresponding to the power of observables are introduced. Based on an exponential relation between energy and momentum, the fractional Schr\"odinger…
It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…
We have perfomed Time Dependant Hartree-Fock (TDHF) calculations on the non linear response of nuclei. We have shown that quadrupole (and dipole) motion produces monopole (and quadrupole) oscillations in all atomic nuclei. We have shown…
For many physical quantities, theory supplies weak- and strong-coupling expansions of the types $\sum a_n \alpha ^n$ and $ \alpha ^p\sum b_n (\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero radius of convergence. We…
An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We study the wave form emitted by a particle moving along an arbitrary (in general open) geodesic of the Schwarzschild geometry. The mathematical problem can be phrased in terms of quantities in ${\cal N}=2$ supersymmetric gauge theories…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
The effective dynamics of solitons for the generalized nonlinear Schr\"odinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton,…
As a step towards a more realistic modeling of vibrations in single-molecule devices, we investigate the effects of charge-dependent vibrational frequencies and anharmonic potentials on electronic transport. For weak phonon relaxation, we…
We derive a general effective many-body theory for bosonic polar molecules in strong interaction regime, which cannot be correctly described by previous theories within the first Born approximation. The effective Hamiltonian has additional…
A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the…
In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting pont is propagated separately using the Time-Dependent Hartree-Fock equation of…
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with…
It is shown that variation of the one-particle dispersion in a universal many-body system enables us to obtain Tan's adiabatic sweep theorem and its generalization. The derivation is based on the Hellmann-Feynman theorem and the variational…
The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is…
We consider the classical response in a chaotic system. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in a chaotic system vanishes at long times. The response also reveals certain…
We present a review of recent works devoted to the variation of the fine structure constant alpha, strong interaction and fundamental masses. There are some hints for the variation in quasar absorption spectra, Big Bang nucleosynthesis, and…
A theoretical and numerical analysis of the transition from chaotic to nonchaotic behavior in an ensemble of particles with different initial conditions which move according to Newton's equations in a bounding potential and are driven by an…
We show that the field equations for cosmological perturbations in Newtonian gauge always have an adiabatic solution, for which a quantity ${\cal R}$ is non-zero and constant in all eras in the limit of large wavelength, so that it can be…