Integrable coupled Linard-type systems with balanced loss and gain
arXiv:1804.02366 · doi:10.1016/j.aop.2018.11.013
Abstract
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a suitable choice of co-ordinates, the Hamiltonian can always be reformulated as a many-particle system in the background of a pseudo-Euclidean metric and subjected to an analogous inhomogeneous magnetic field with a functional form that is identical with space-dependent loss/gain co-efficient.The resulting equations of motion from the Hamiltonian are a system of coupled Linard-type differential equations. Partially integrable systems are obtained for two distinct cases, namely, systems with (i) translational symmetry or (ii) rotational invariance in a pseudo-Euclidean space. A total number of integrals of motion are constructed for a system of particles, which are in involution, implying that two-particle systems are completely integrable. A few exact solutions for both the cases are presented for specific choices of the potential and space-dependent gain/loss co-efficients, which include periodic stable solutions. Quantization of the system is discussed with the construction of the integrals of motion for specific choices of the potential and gain-loss coefficients. A few quasi-exactly solvable models admitting bound states in appropriate Stoke wedges are presented.
arXiv commentLatex, 24 pages, 1 figure, Added Discussions and References, Version to appear in Annals of Physics
References in corpus (28)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Pseudo-Hermitian Representation of Quantum Mechanics
- Introduction to PT-Symmetric Quantum Theory
- Exchange Operator Formalism for Integrable Systems of Particles
- No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
- Quantum synchronization of quantum van der Pol oscillators with trapped ions
- Observation of Asymmetric Transport in Structures with Active Nonlinearities
- Twofold Transition in PT-Symmetric Coupled Oscillators
- One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
- Inequivalent Quantizations of the Rational Calogero Model
- Novel Quantum States of the Rational Calogero Models Without the Confining Interaction
- Systems of coupled PT-symmetric oscillators
- Quantum damped oscillator I: dissipation and resonances
- A Canonical Approach to the Quantization of the Damped Harmonic Oscillator
- Multicomponent Calogero Model of -Type Confined in Harmonic Potential
- Bound States in One-Dimensional Quantum N-Body Systems with Inverse Square Interaction
- A class of exact solutions of the Liénard type ordinary non-linear differential equation
- Conservative perturbation theory for nonconservative systems
- Imaginary-Scaling versus Indefinite-Metric Quantization of the Pais-Uhlenbeck Oscillator
- Universal correlations in random matrices: quantum chaos, the integrable model, and quantum gravity
- PT -symmetric rational Calogero model with balanced loss and gain
- Explicit solutions of the classical Calogero & Sutherland systems for any root system
- Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
- Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
- Near-Horizon States of Black Holes and Calogero Models
- Waves and Solitons in the Calogero Model - Revisited
- Fluctuations around Periodic BPS-Density Waves in the Calogero Model
Cited by in corpus (5)
- On regular and chaotic dynamics of a non--symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
- Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction : General results and a case study with Landau Hamiltonian
- Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain
- Classical Hamiltonian Systems with Balanced loss and gain
- Complex dynamical properties of coupled Van der Pol-Duffing oscillators with balanced loss and gain