arXiv subjects

Giovanni Jona-Lasinio

Publications and source records attributed to Giovanni Jona-Lasinio.

24 records · Page 2Linked to original sources

arXiv1999

On the Pairing Structure of the Vacuum induced by a Magnetic Field in 2+1-dimensional Dirac Field Theory

Using a sequence of Bogoliubov transformations, we obtain an exact expression for the vacuum state of a Dirac field in 2+1 dimensions in presence of a constant magnetic field. This expression reveals a peculiar two level pairing structure for any value of the mass m greater than zero. This calculation clarifies the nature of the condensate in the lowest Landau level whose existence has been emphasized recently by a several authors.

hep-th↗

arXiv1999

An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo method in the limit when the latter becomes exact.

cond-mat↗

arXiv1997

Nonlinear feedback oscillations in resonant tunneling through double barriers

We analyze the dynamical evolution of the resonant tunneling of an ensemble of electrons through a double barrier in the presence of the self-consistent potential created by the charge accumulation in the well. The intrinsic nonlinearity of the transmission process is shown to lead to oscillations of the stored charge and of the transmitted and reflected fluxes. The dependence on the electrostatic feedback induced by the self-consistent potential and on the energy width of the incident distribution is discussed.

cond-mat.mes-hall↗

arXiv1996

Chaotic properties of quantum many-body systems in the thermodynamic limit

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.

cond-mat↗

arXiv1996

Spectral properties of quantum $N$-body systems versus chaotic properties of their mean field approximations

We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean field evolution. This correspondence, analogous to the usual quantum-classical correspondence, is related to the formal parallel between the second quantization of the mean field, which generates the exact dynamics of the quantum $N$-body system, and the first quantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed.

cond-mat↗

arXiv1995

On Schroedinger Equations with Concentrated Nonlinearities

Schrödinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to separate the relevant degrees of freedom by noticing that in the regions where the nonlinearities are effective all states are suppressed but the metastable ones (resonances). In this way the description of the nonlinear regions is reduced to ordinary differential equations weakly coupled to standard Schrödinger equations valid in the linear regions. The idea is illustrated through the study of a prototype equation recently proposed for resonant tunneling of electrons through a double barrier heterostructure and for which nonlinear oscillations have been numerically predicted.

cond-mat↗