Related papers: Resonance Cascades and Number Theory
We consider primordial spectra with simple power behaviours and show that in the Navier-Stokes and magnetohydrodynamics equations without forcing, there exists systems in three dimensions with a subsequent inverse cascade, transferring…
Quantum resonance, i.e., amplification in transition probability available under certain conditions, offers a powerful means for determining fundamental quantities in physics, including the time duration of the second adopted in the SI…
In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman…
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the phenomenon of resonance may appear. We give a sufficient condition on the…
We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are…
This article presents a theoretical study of the scaling properties of the kinetic energy spectrum in compressible turbulence. From the fundamental symmetries and linear transformations of the microscopic action, we derive exact relations…
In this work the generalized Collatz problem $qn+1$ ($q$ odd) is studied. As a natural generalization of the original $3n+1$ problem, it consists of a discrete dynamical system of an arithmetical kind. Using standard methods of number…
We propose an implementation scheme for the continuous-time quantum walk using a diatomic molecule and an optical frequency comb. We show an analogy between the quantum walk and the cascade rotational transitions induced by the optical…
We simulate stellar convection at high Reynolds number (Re$\lesssim$7000) with causal time stepping but no explicit viscosity. We use the 3D Euler equations with shock capturing (Colella & Woodward 1984). Anomalous dissipation of turbulent…
The resonant tunneling phenomenon is well understood in quantum mechanics. We argue why a similar phenomenon must be present in quantum field theory. We then use the functional Schr\"odinger method to show how resonant tunneling through…
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some…
We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances,…
In turbulent flows kinetic energy is spread by nonlinear interactions over a broad range of scales. Energy transfer may proceed either toward small scales or in the reverse direction. The latter case is peculiar of two-dimensional (2D)…
Generalised two-dimensional (2D) fluid dynamics is characterised by a relationship between a scalar field $q$, called generalised vorticity, and the stream function $\psi$, namely $q = (-\nabla^2)^\frac{\alpha}{2} \psi$. We study the…
Quantum amplifier is an essential device in quantum information processing. As in the classical (non-quantum) case, its characteristic uncertainty needs to be suppressed by feedback, and in fact such a control theory for a single quantum…
Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have found that such measurements can induce state transitions in the…
We investigate properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence, by means of two direct numerical simulations of decaying turbulence with initial Mach…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
We investigate the cosmological consequences of particle physics theories that admit stable loops of superconducting cosmic string - {\it vortons}. General symmetry breaking schemes are considered, in which strings are formed at one energy…
We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission…