Search results for "Bogoliubov transformation"
showing 6 items of 6 documents
Understanding Hawking Radiation from Simple Models of Atomic Bose-Einstein Condensates
2013
This chapter is an introduction to the Bogoliubov theory of dilute Bose condensates as applied to the study of the spontaneous emission of phonons in a stationary condensate flowing at supersonic speeds. This emission process is a condensed-matter analog of Hawking radiation from astrophysical black holes but is derived here from a microscopic quantum theory of the condensate without any use of the analogy with gravitational systems. To facilitate physical understanding of the basic concepts, a simple one-dimensional geometry with a stepwise homogenous flow is considered which allows for a fully analytical treatment.
Hartree-Fock-Bogoliubov solution of the pairing Hamiltonian in finite nuclei
2013
We present an overview of the Hartree-Fock-Bogoliubov (HFB) theory of nucleonic superfluidity for finite nuclei. After introducing basic concepts related to pairing correlations, we show how the correlated pairs are incorporated into the HFB wave function. Thereafter, we present derivation and structure of the HFB equations within the superfluid nuclear density functional formalism and discuss several aspects of the theory, including the unitarity of the Bogoliubov transformation in truncated single-particle and quasiparticle spaces, form of the pairing functional, structure of the HFB continuum, regularization and renormalization of pairing fields, and treatment of pairing in systems with …
Exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: The far-zone Casimir-Polder …
2005
We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expressi…
N-quantum approach to quantum field theory at finite T and mu: the NJL model
1999
We extend the N-quantum approach to quantum field theory to finite temperature ($T$) and chemical potential ($\mu$) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2)$_{rm f}$ $otimes$ SU(3)$_{\rm c}$ version of the …
Multiparticle correlations in the Schwinger mechanism
2009
We discuss the Schwinger mechanism in scalar QED and derive the multiplicity distribution of particles created under an external electric field using the LSZ reduction formula. Assuming that the electric field is spatially homogeneous, we find that the particles of different momenta are produced independently, and that the multiplicity distribution in one mode follows a Bose-Einstein distribution. We confirm the consistency of our results with an intuitive derivation by means of the Bogoliubov transformation on creation and annihilation operators. Finally we revisit a known solvable example of time-dependent electric fields to present exact and explicit expressions for demonstration.
From pseudo-bosons to pseudo-Hermiticity via multiple generalized Bogoliubov transformations
2016
We consider the special type of pseudo-bosonic systems that can be mapped to standard bosons by means of generalized Bogoliubov transformation and demonstrate that a pseudo-Hermitian systems can be obtained from them by means of a second subsequent Bogoliubov transformation. We employ these operators in a simple model and study three different types of scenarios for the constraints on the model parameters giving rise to a Hermitian system, a pseudo-Hermitian system in which the second the Bogoliubov transformations is equivalent to the associated Dyson map and one in which we obtain D-quasi bases.