Exploring Chaos and Entanglement in the Hénon–Heiles System Using Squeezed Coherent States

2016 ◽  
Vol 26 (03) ◽  
pp. 1650052
Author(s):  
Sijo K. Joseph ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Quantum Entanglement ◽  
Local Structure ◽  
Coherent States ◽  
Quantum Systems ◽  
Initial Condition ◽  
Chaotic Orbit ◽  
Chaotic Orbits ◽  
Classical Correspondence ◽  
Squeezed Coherent State ◽  
Classical Phase Space

Quantum entanglement in the Hénon–Heiles system is analyzed using the squeezed coherent state. Enhancement of quantum entanglement via squeezing is explored in connection with chaotic and regular dynamics of the system. It is found that the entanglement enhancement via squeezing is implicitly linked to the local structure of the classical phase-space and it shows a clear quantum-classical correspondence. In particular, the entanglement enhancement via squeezing is found to be negligible for a highly chaotic orbit compared to the regular and weakly chaotic orbits, and shows a clear correspondence to the degree of chaos present in the classical initial condition. We believe that these results might be useful to develop efficient strategies to enhance entanglement in quantum systems.

scholarly journals Signatures of Quantum Mechanics in Chaotic Systems

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 618 ◽  
Author(s):  
Kevin M. Short ◽  
Matthew A. Morena
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Chaotic Systems ◽  
Measurement Problem ◽  
Quantum Systems ◽  
Analytical Tool ◽  
Quantum Mechanical ◽  
Unstable Periodic Orbits ◽  
Classical Correspondence ◽  
Quantum Mechanical Systems

We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.

scholarly journals Classical correspondence of quantum entanglement in mesoscopic circuit

2022 ◽  
Vol 71 (1) ◽  
pp. 1-7
Author(s):  
Fan Hong-yi ◽  
◽  
Wu Ze ◽  
Keyword(s):  
Quantum Entanglement ◽  
Classical Correspondence

scholarly journals Residual Entropy and Critical Behavior of Two Interacting Boson Species in a Double Well

2017 ◽  
Author(s):  
Fabio Lingua ◽  
Andrea Richaud ◽  
Vittorio Penna
Keyword(s):  
Coherent States ◽  
Variational Approach ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Residual Entropy ◽  
Zero Temperature ◽  
Temperature Scenario ◽  
Physical Insight ◽  
Insight Into ◽  
Specific Quantum

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerbly good approximation of the entanglement entropy. Finally, we show that the effectiveness of residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.

Correlated coherent states and emission by quantum systems

1993 ◽  
Vol 14 (3) ◽  
pp. 223-236
Author(s):  
V. V. Dodonov ◽  
V. I. Man'ko ◽  
O. V. Man'ko
Keyword(s):  
Coherent States ◽  
Quantum Systems

Control and Applications of Chaos

1997 ◽  
Vol 07 (10) ◽  
pp. 2175-2197 ◽  
Author(s):  
Celso Grebogi ◽  
Ying–Cheng Lai ◽  
Scott Hayes
Keyword(s):  
Feedback Control ◽  
Power Systems ◽  
System Performance ◽  
Chaotic Systems ◽  
Electrical Power ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Chaotic Orbit ◽  
Electrical Power Systems ◽  
Dissipative Dynamical Systems

This review describes a procedure for stabilizing a desirable chaotic orbit embedded in a chaotic attractor of dissipative dynamical systems by using small feedback control. The key observation is that certain chaotic orbits may correspond to a desirable system performance. By carefully selecting such an orbit, and then applying small feedback control to stabilize a trajectory from a random initial condition around the target chaotic orbit, desirable system performance can be achieved. As applications, three examples are considered: (1) synchronization of chaotic systems; (2) conversion of transient chaos into sustained chaos; and (3) controlling symbolic dynamics for communication. The first and third problems are potentially relevant to communication in engineering, and the solution of the second problem can be applied to electrical power systems to avoid catastrophic events such as the voltage collapse.

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