Related papers: On exact discretization of the cubic-quintic Duffi…
Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by…
A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multi-stability emerges associated with…
We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical…
Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's…
We consider a general discretization strategy for Hamiltonian field theories generated by Lie-Poisson brackets which we call dual PIC (DPIC). This method involves prescribing two different discrete representations of the dynamical variable…
We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Weyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator…
We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well…
Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep…
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable…
Quantum chaos---the study of quantized nonintegrable Hamiltonian systems---is an extremely well-developed and sophisticated field. By contrast, very little work has been done in looking at quantum versions of systems which classically…
We describe a method for computing Casimir invariants that is applicable to both finite and infinite-dimensional Poisson brackets. We apply the method to various finite and infinite-dimensional examples, including a Poisson bracket…
High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…
The limits of direct unitary transformation of many-fermion Hamiltonians are explored. Practical application of such transformations requires that effective many-body interactions be discarded over the course of a calculation. The…
In a previous work we showcased the factorization method to find the symmetries of superintegrable systems with spherical separability in flat spaces. Here we analyze the same problem, but in constant curvature spaces along the examples of…
The exact solutions of both the cubic Duffing equation and cubic-quintic Duffing equation are presented by using only leaf functions. In previous studies, exact solutions of the cubic Duffing equation have been proposed using functions that…
We investigate the quantum dissipative dynamics near the stable states (attractors) of a driven Duffing oscillator. A refined perturbation theory that can treat two perturbative parameters with different orders is developed to calculate the…
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…