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.

Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics

2021 ◽  
Vol 23 (9) ◽  
pp. 5113-5124
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Path Integral ◽  
Von Neumann Entropy ◽  
Level System ◽  
Von Neumann ◽  
Bacteriochlorophyll Dimer ◽  
Two Level Systems ◽  
Tunneling Dynamics ◽  
Reduced Density ◽  
Harmonic Bath

The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer.

scholarly journals High Order Coherence Functions and Spectral Distributions as Given by the Scully-Lamb Quantum Theory of the Laser

2021 ◽  
Vol 9 ◽  
Author(s):  
Tao Peng ◽  
Xingchen Zhao ◽  
Yanhua Shih ◽  
Marlan O. Scully
Keyword(s):  
Quantum Theory ◽  
Matrix Element ◽  
Density Matrix ◽  
Time Evolution ◽  
Decay Rates ◽  
Reduced Density Matrix ◽  
Diagonal Matrix Element ◽  
Spectral Distributions ◽  
Reduced Density ◽  
First Time

We propose and demonstrate a method for measuring the time evolution of the off-diagonal elements ρn,n+k(t) of the reduced density matrix obtained from the quantum theory of the laser. The decay rates of the off-diagonal matrix element ρn,n+k(t) (k = 2,3) are measured for the first time and compared with that of ρn,n+1(t), which corresponds to the linewidth of the laser. The experimental results agree with the Scully-Lamb quantum theory of the laser.

scholarly journals Entanglement Dynamics of Random GUE Hamiltonians

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Daniel Chernowitz ◽  
Vladimir Gritsev
Keyword(s):  
Density Matrix ◽  
Spin Glass ◽  
Time Evolution ◽  
Random Matrices ◽  
Correlation Functions ◽  
Transverse Field ◽  
Reduced Density Matrix ◽  
Entanglement Dynamics ◽  
Point Correlation ◽  
Reduced Density

In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential n-point correlation functions in the gas of GUE eigenvalues.

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