scholarly journals Complexity from the reduced density matrix: a new diagnostic for chaos

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Arpan Bhattacharyya ◽  
S. Shajidul Haque ◽  
Eugene H. Kim
Keyword(s):  
Density Matrix ◽  
Quantum Chaos ◽  
Open Quantum Systems ◽  
Circuit Complexity ◽  
Quantum Systems ◽  
Harmonic Oscillators ◽  
Quantum Circuits ◽  
Reduced Density Matrix ◽  
Evolution Of Complexity ◽  
Reduced Density

Abstract We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity based on the reduced density matrix by exploring different types of quantum circuits. Through explicit calculations on a toy model of two coupled harmonic oscillators, where one or both of the oscillators are inverted, we demonstrate that the evolution of complexity is a possible diagnostic of chaos.

scholarly journals Quantum chaos: Reduced density matrix fluctuations in coupled systems

2005 ◽  
Vol 204 (1-2) ◽  
pp. 110-121 ◽  
Author(s):  
Sankhasubhra Nag ◽  
Gautam Ghosh ◽  
Avijit Lahiri
Keyword(s):  
Density Matrix ◽  
Quantum Chaos ◽  
Coupled Systems ◽  
Reduced Density Matrix ◽  
Reduced Density

scholarly journals Application of the theory of open quantum systems in nuclear physics

2019 ◽  
Vol 49 ◽  
pp. 1960008
Author(s):  
V. V. Sargsyan ◽  
Z. Kanokov ◽  
G. G. Adamian ◽  
N. V. Antonenko
Keyword(s):  
Nuclear Physics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Reduced Density Matrix ◽  
Quantum Model ◽  
Matrix Formalism ◽  
Capture Process ◽  
Projectile Nucleus ◽  
Density Matrix Formalism ◽  
Reduced Density

Projectile-nucleus capture by a target nucleus at bombarding energies in the vicinity of the Coulomb barrier is treated with the reduced-density-matrix formalism. The effects of dissipation and fluctuations on the capture process are taken self-consistently into account within the quantum model suggested. The excitation functions for the capture in the reactions [Formula: see text]O, [Formula: see text]F, [Formula: see text]Mg, [Formula: see text]Si, [Formula: see text]S, [Formula: see text]Ca, [Formula: see text]Ti, [Formula: see text]Cr [Formula: see text] [Formula: see text]Pb are calculated and compared with the experimental data.

scholarly journals Many-Body Systems and Quantum Chaos: The Multiparticle Quantum Arnol’d Cat

2019 ◽  
Vol 4 (3) ◽  
pp. 72
Author(s):  
Giorgio Mantica
Keyword(s):  
Hamiltonian System ◽  
Density Matrix ◽  
Quantum Chaos ◽  
Reduced Density Matrix ◽  
Von Neumann Entropy ◽  
Physical Parameters ◽  
Many Body ◽  
Von Neumann ◽  
Many Body Systems ◽  
Reduced Density

A multi-particle extension of the Arnol’d cat Hamiltonian system is presented, which can serve as a fully dynamical model of decoherence. The behavior of the von Neumann entropy of the reduced density matrix is studied, in time and as a function of the physical parameters, with special regard to increasing the mass of the cat particle.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

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