### Abstract

Original language | English |
---|---|

Pages (from-to) | 355-373 |

Number of pages | 19 |

Journal | PHYSICA. A |

Volume | 505 |

Publication status | Published - 2018 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

### Cite this

*PHYSICA. A*,

*505*, 355-373.

**(H,ρ)-induced dynamics and large time behaviors.** / Bagarello, Fabio; Gargano, Francesco; Bagarello; Di Salvo; Oliveri, Francesco.

Research output: Contribution to journal › Article

*PHYSICA. A*, vol. 505, pp. 355-373.

}

TY - JOUR

T1 - (H,ρ)-induced dynamics and large time behaviors

AU - Bagarello, Fabio

AU - Gargano, Francesco

AU - Bagarello, null

AU - Di Salvo, null

AU - Oliveri, Francesco

PY - 2018

Y1 - 2018

N2 - In some recent papers, the so called (H,ρ)-induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, H is the Hamiltonian for S, while ρ is a certain rule applied periodically (or not) on S. The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the (H,ρ)-induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of S may converge, for large t, to certain asymptotic values. This cannot be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any Heisenberg dynamics implemented by a suitable hermitian operator H can only give an oscillating behavior. We prove our claims both analytically and numerically for a simple system with two degrees of freedom, and then we apply our general scheme to a model describing a biological system of bacteria living in a two-dimensional lattice, where two different choices of the rule are considered.

AB - In some recent papers, the so called (H,ρ)-induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, H is the Hamiltonian for S, while ρ is a certain rule applied periodically (or not) on S. The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the (H,ρ)-induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of S may converge, for large t, to certain asymptotic values. This cannot be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any Heisenberg dynamics implemented by a suitable hermitian operator H can only give an oscillating behavior. We prove our claims both analytically and numerically for a simple system with two degrees of freedom, and then we apply our general scheme to a model describing a biological system of bacteria living in a two-dimensional lattice, where two different choices of the rule are considered.

UR - http://hdl.handle.net/10447/287550

UR - https://www.sciencedirect.com/science/article/pii/S0378437118304047

M3 - Article

VL - 505

SP - 355

EP - 373

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -