Abstract
A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed. The infinite hierarchy of quantum conservation laws and many-particle Bethe eigenstates that model quantum solitonic impulse structures are constructed. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related to the thermodynamical equilibrity of the model, are discussed.
Highlights
We shall describe the quantum superradiance properties [1,2,3,4,5,6,7,8,9] of a model of a one-dimensional many particle charged fermionic medium interacting with an external electromagnetic field
As we are interested in describing the so-called super-resonance processes in our fermionic medium induced by an external electromagnetic field, in particular, a possibility of generating strong localized photonic impulses, it is first necessary to investigate the bound photonic medium states and their spectral energy characteristics
The localization manifests itself in the fact that the energy of a many-particle cluster appears to be less [10, 14, 30] than that of the corresponding system of free particles, giving rise to the formation of the so-called quantum solitonic states localized in the space
Summary
We shall describe the quantum superradiance properties [1,2,3,4,5,6,7,8,9] of a model of a one-dimensional many particle charged fermionic medium interacting with an external electromagnetic field. As we are interested in describing the so-called super-resonance processes in our fermionic medium induced by an external electromagnetic field, in particular, a possibility of generating strong localized photonic impulses, it is first necessary to investigate the bound photonic medium states and their spectral energy characteristics Toward this aim, we make an important note that it has been observed that the spectral properties of the Hamiltonian operator (1.4) can be analyzed in great detail owing to the fact that the related Heisenberg nonlinear dynamical system ψ1,t = i[H,ψ1] = ψ1,x + iαε+ψ2, ψ2,t = i[H,ψ2] = −ψ2,x + iαεψ, εt = i[H,ε] = −βεx + iαψ+1 ψ2. The quantum stability, solitonic formation aspects and construction of the physical ground state [10, 14, 17] related to the unbounded a priori from below Hamiltonian operator (1.4) will be the main focus of the succeeding sections
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