In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.

arXiv:1503.01747Journal of Physics A Mathematical and TheoreticalOct 10, 201115 citations

Ladder approximation in quantum optics

Daniel F. Walls

Physics Letters AJun 1, 19716 citations

Coherent State Path Integral Reveals Unexpected Vacuum Structure in Thermal Field Theory

Rens Roosenstein, Maximilian Attems, William Alexander Horowitz

We construct the path integral formulation of the partition function for a free scalar thermal field theory using coherent states, first in the ladder operator basis and then in the field operator basis. In so doing, we provide for the first time a mapping in quantum field theory between the field-basis coherent states and ladder-basis coherent states. Using either basis, one finds terms missed in the usual path integral derivation, which we identify as the vacuum energy contribution to the partition function. We then extend the field-basis coherent state method to the interacting $ϕ^4$ theory. In addition to the vacuum energy contribution, one finds a coupling of a vacuum expectation value to the mass term that is absent in the existing literature.We construct the path integral formulation of the partition function for a free scalar thermal field theory using coherent states, first in the ladder operator basis and then in the field operator basis. In so doing, we provide for the first time a mapping in quantum field theory between the field-basis coherent states and ladder-basis coherent states. Using either basis, one finds terms missed in the usual path integral derivation, which we identify as the vacuum energy contribution to the partition function. We then extend the field-basis coherent state method to the interacting $ϕ^4$ theory. In addition to the vacuum energy contribution, one finds a coupling of a vacuum expectation value to the mass term that is absent in the existing literature.

arXiv:2507.11608Jul 15, 20250 citations

Quantum Complexity in Graphene

G. Baskaran

WORLD SCIENTIFIC eBooksMar 1, 20110 citations

ϕ^4

theory. In addition to the vacuum energy contribution, one finds a coupling of a vacuum expectation value to the mass term that is absent in the existing literature.