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Anti- PT -Symmetric Harmonic Oscillator and its Relation to the Inverted Harmonic Oscillator

Nadjat Amaouche, Ishak Bouguerche, Rahma Zerimeche +1 more

Reports on Mathematical PhysicsNov 30, 20223 citations

Algebraic treatment of a double ring-shaped oscillator

M. Victoria Carpio-Bernido, Christopher Casenas Bernido

Physics Letters AMay 1, 198936 citations

Complexity and operator growth for quantum systems in dynamic equilibrium

Cameron Beetar, Nitin Gupta, S. Shajidul Haque +2 more

A bstract Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a PT-symmetric system of oscillators, which exhibits two phase transitions that separate a dissipative state, a Rabi-oscillation state, and an ultra-strongly coupled regime. We use a generalization of the su (1) algebra associated to the Bateman oscillator to describe the Hamiltonian of the coupled system, and construct a set of coherent states associated with this algebra. We compute the Krylov (spread) complexity using these coherent states, and find that it can distinguish between the PT-symmetric and PT symmetry-broken phases. We also show that the Krylov complexity reveals the ill-defined nature of the vacuum of the Bateman oscillator, which is a special case of our system. Our results demonstrate the utility of Krylov complexity as a tool to probe the properties and transitions of PT-symmetric systems.A bstract Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a PT-symmetric system of oscillators, which exhibits two phase transitions that separate a dissipative state, a Rabi-oscillation state, and an ultra-strongly coupled regime. We use a generalization of the su (1) algebra associated to the Bateman oscillator to describe the Hamiltonian of the coupled system, and construct a set of coherent states associated with this algebra. We compute the Krylov (spread) complexity using these coherent states, and find that it can distinguish between the PT-symmetric and PT symmetry-broken phases. We also show that the Krylov complexity reveals the ill-defined nature of the vacuum of the Bateman oscillator, which is a special case of our system. Our results demonstrate the utility of Krylov complexity as a tool to probe the properties and transitions of PT-symmetric systems.

arXiv:2312.15790Journal of High Energy PhysicsAug 20, 20248 citations

Algebraic and scattering aspects of a 𝒫𝒯-symmetric solvable potential

GÉZA LÉVAI, F. Cannata, Alberto Ventura

We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.

Journal of Physics A Mathematical and GeneralJan 18, 200182 citations

Algebraic approach to the forced anharmonic oscillator

Iris Benjamin

Chemical Physics LettersDec 1, 198410 citations

Algebraic treatment of a simple model for the electromagnetic self-force

Francisco Marcelo Fernández

The problem of the electromagnetic self-force can be studied in terms of a quadratic PT-symmetric Hamiltonian. Here, we apply a straightforward algebraic method to determine the regions of model-parameter space where the quantum-mechanical operator exhibits real spectrum. An alternative point of view consists of finding the values of the model parameters so that a symmetric operator supports bound states.

arXiv:1509.00002Aug 31, 20153 citations

Algebraic Treatment of 𝓟𝓣-Symmetric Coupled Oscillators

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