Particle number fluctuations in the quasiparticle random-phase approximation (QRPA) and the renormalized quasiparticle random-phase approximation are investigated. A closed expression for the ground state wave function is used, which allows an exact evaluation of the ground state phonon number and correlation function, being valid to any order in the backward amplitudes. In realistic calculations a sudden increase in the particle number fluctuations is found in both approximations when the particle-particle interaction approaches the value at which the QRPA collapses. This behavior is strongly correlated with the ground state quasiparticle content and can be understood as a signature of the phase transition previously found in simpler exactly solvable models.Particle number fluctuations in the quasiparticle random-phase approximation (QRPA) and the renormalized quasiparticle random-phase approximation are investigated. A closed expression for the ground state wave function is used, which allows an exact evaluation of the ground state phonon number and correlation function, being valid to any order in the backward amplitudes. In realistic calculations a sudden increase in the particle number fluctuations is found in both approximations when the particle-particle interaction approaches the value at which the QRPA collapses. This behavior is strongly correlated with the ground state quasiparticle content and can be understood as a signature of the phase transition previously found in simpler exactly solvable models.

Physical Review CJun 1, 19986 citations

Comparison of a quasiparticle model with some exact calculations

Pál, K.F., N. Rowley, M.A. Nagarajan

Jan 1, 19900 citations

Quantum kinetics and thermalization in an exactly solvable model

S. M. Alamoudi, D. Boyanovsky, Hector J. de Vega +1 more

We study the dynamics of relaxation and thermalization in an exactly solvable model of a quantum particle interacting with a thermal bath of oscillators with the goal of understanding the effects of off-shell processes. The focus is to compare the exact evolution of the distribution function with different approximations to the relaxational dynamics: Boltzmann, non-Markovian and Markovian quantum kinetics. The time evolution of the distribution function is evaluated exactly using different approaches where each method provides different insights. There are two different cases that are studied in detail: (i) no stable particle states below threshold of the bath and a quasiparticle resonance above it and (ii) a stable discrete exact ``particle'' state below threshold. The exact solution for the evolution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of particles and quasiparticles. For the case of quasiparticles in the continuum (resonances) the exact quasiparticle distribution asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes such as the strength of the quasiparticle poles, the width of the unstable particle and proximity to thresholds. In case (ii), the distribution of particles does not thermalize with the bath. We study the kinetics of thermalization and relaxation by deriving a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation are obtained from the quantum kinetic equation in the limit of a wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian and Boltzmann approximations are compared to the exact result of the model. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important. Implications for thermalization in field theory models are discussed.We study the dynamics of relaxation and thermalization in an exactly solvable model of a quantum particle interacting with a thermal bath of oscillators with the goal of understanding the effects of off-shell processes. The focus is to compare the exact evolution of the distribution function with different approximations to the relaxational dynamics: Boltzmann, non-Markovian and Markovian quantum kinetics. The time evolution of the distribution function is evaluated exactly using different approaches where each method provides different insights. There are two different cases that are studied in detail: (i) no stable particle states below threshold of the bath and a quasiparticle resonance above it and (ii) a stable discrete exact ``particle'' state below threshold. The exact solution for the evolution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of particles and quasiparticles. For the case of quasiparticles in the continuum (resonances) the exact quasiparticle distribution asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes such as the strength of the quasiparticle poles, the width of the unstable particle and proximity to thresholds. In case (ii), the distribution of particles does not thermalize with the bath. We study the kinetics of thermalization and relaxation by deriving a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation are obtained from the quantum kinetic equation in the limit of a wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian and Boltzmann approximations are compared to the exact result of the model. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important. Implications for thermalization in field theory models are discussed.

arXiv:hep-ph/9806235Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsDec 7, 199820 citations

On the quasiparticle transformation theory

Paul Mandel

PhysicaAug 1, 197015 citations

Self-consistent quasiparticle random-phase approximation for a multilevel pairing model

Nguyễn Quang Hưng, Nguyen Dinh Dang

Particle-number projection within the Lipkin-Nogami (LN) method is applied to the self-consistent quasiparticle random-phase approximation (SCQRPA), which is tested in an exactly solvable multilevel pairing model. The SCQRPA equations are numerically solved to find the energies of the ground and excited states at various numbers \ensuremath{\Omega} of doubly degenerate equidistant levels. The use of the LN method allows one to avoid the collapse of the BCS (QRPA) to obtain the energies of the ground and excited states as smooth functions of the interaction parameter $G$ . The comparison between results given by different approximations such as the SCRPA, QRPA, LNQRPA, SCQRPA, and LNSCQRPA is carried out. Although the use of the LN method significantly improves the agreement with the exact results in the intermediate coupling region, we found that in the strong coupling region the SCQRPA results are closest to the exact ones.Particle-number projection within the Lipkin-Nogami (LN) method is applied to the self-consistent quasiparticle random-phase approximation (SCQRPA), which is tested in an exactly solvable multilevel pairing model. The SCQRPA equations are numerically solved to find the energies of the ground and excited states at various numbers \ensuremath{\Omega} of doubly degenerate equidistant levels. The use of the LN method allows one to avoid the collapse of the BCS (QRPA) to obtain the energies of the ground and excited states as smooth functions of the interaction parameter $G$. The comparison between results given by different approximations such as the SCRPA, QRPA, LNQRPA, SCQRPA, and LNSCQRPA is carried out. Although the use of the LN method significantly improves the agreement with the exact results in the intermediate coupling region, we found that in the strong coupling region the SCQRPA results are closest to the exact ones.

arXiv:0710.0935Physical Review CNov 2, 200715 citations

Interacting Systems and Quasiparticles

John C. Inkson

Springer eBooksJan 1, 19841 citation

G

. The comparison between results given by different approximations such as the SCRPA, QRPA, LNQRPA, SCQRPA, and LNSCQRPA is carried out. Although the use of the LN method significantly improves the agreement with the exact results in the intermediate coupling region, we found that in the strong coupling region the SCQRPA results are closest to the exact ones.