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.

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.

Study of the time evolution of correlation functions of the transverse Ising chain with ring frustration by perturbative theory

2018 ◽  
Vol 32 (10) ◽  
pp. 1850121
Author(s):  
Zhen-Yu Zheng ◽  
Peng Li
Keyword(s):  
Correlation Function ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Correlation Functions ◽  
Schrodinger Equation ◽  
Transverse Field ◽  
Time Dependent ◽  
Ising Chain ◽  
Point Correlation ◽  
Point Correlation Function

We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.

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 Reexamining the variational two-particle reduced density matrix for nuclear systems

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
J. G. Li ◽  
N. Michel ◽  
W. Zuo ◽  
F. R. Xu
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Nuclear Systems ◽  
Reduced Density

scholarly journals Entanglement spectrum of geometric states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Wu-zhong Guo
Keyword(s):  
Entanglement Entropy ◽  
Vacuum State ◽  
Reduced Density Matrix ◽  
Microcanonical Ensemble ◽  
Equality Case ◽  
Entanglement Spectrum ◽  
The Matrix ◽  
Point Correlation ◽  
Single Interval ◽  
Reduced Density

Abstract The reduced density matrix of a given subsystem, denoted by ρA, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρA,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ0 which can be seen as an approximate state of ρA. The parameter λ0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.

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