Related papers: Superexponential Self-Interacting Oscillator
We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator…
A magnetic dipole-dipole interaction is proposed as a scintillation quenching mechanism. The interaction rate follows $R^{-6}$ as the electric dipole-dipole interaction in F$\mathrm{\ddot{o}}$ster resonance energy transfer theory. The…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
We consider discrete one-dimensional Schroedinger operators whose potentials decay asymptotically like an inverse square. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of…
Super-oscillation is a counter-intuitive phenomenon describing localized fast variations of functions and fields that happen at frequencies higher than the highest Fourier component of their spectra. The physical implications of the effect…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
Spectrum tomography for the energy ($E$) of a ring-shaped Bose-Hubbard circuit is illustrated. There is an inter-particle interaction $U$ that controls superfluidity (SF) and the transition to the Mott Insulator (MI) regime. The circuit is…
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…
Superradiant phase transition represents an important quantum phenomenon that shows the collective excitations based on the coupling between atoms and cavity modes. The spin-orbit coupling is another quantum effect which induced from the…
Systems of disordered interacting bosons with particle-hole symmetry can undergo a quantum phase transition between the superfluid phase and the Mott glass phase which is a gapless incompressible insulator. We employ large-scale Monte Carlo…
Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which…
We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly two orders of magnitude. The full crossover…
We chart out the phase diagram of ultracold `spin-half' bosons in a one-dimensional optical lattice in the presence of Aubry-Andr\'e (AA) potential and with spin-orbit (SO) and Raman couplings investigating the transition from superfluid…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
The Josephson effect characterizes superfluids and superconductors separated by a weak link, the so-called Josephson junction. A recent experiment has shown that Josephson oscillations can be observed also in a supersolid, where the weak…
We consider an autonomous system of two coupled single-mode cavities, one of which interacts with a multimode resonator. We demonstrate that for small coupling strengths between single-mode cavities, the Loschmidt echo oscillates…
We study the superconductor-insulator transition (SIT) in the ground state of the attractive honeycomb Hubbard model in the presence of a staggered potential (a mass term), using a combination of unbiased computational methods, namely,…
Controlling spin-orbit interaction and its effect on superconductivity has been a long-standing problem in two-dimensional inversion symmetry broken superconductors. An open challenge is to understand the role of various energy scales in…
The crossover between ideal Josephson behavior and uniform superconducting flow is studied by solving exactly the Ginzburg-Landau equation for a one-dimensional superconductor in the presence of an effective delta function potential of…
Spin-orbital coupling (SOC) and parity-time ($\mathcal{PT}$) symmetry both have attracted paramount research interest in condensed matter physics, cold atom physics, optics and acoustics to develop spintronics, quantum computation, precise…