Abstract Recent economic research has focused on applying quantum mechanical models to understand complex markets. Real markets are usually complex with nonlinear inverse demand functions and dynamic participants. Furthermore, when these market games are quantized, players interact via quantum channels that are prone to decoherence. In this work, owing to the complexity of real markets, we introduce noise and memory in a dynamic quantum Stackelberg duopoly game for the first time. We shed light on the significance of two-qubit entangling operators, particularly special perfect entanglers (SPEs), in controlling chaos. The following noteworthy observations are made: First, although entangling operators cannot prevent monopolies in the market, they can shift leader dominance to follower dominance. Second, numerical analysis highlights the significance of the B-gate in a correlated noisy channel as a chaos control. We also highlight the significance of the controlled-NOT (CNOT), and double-CNOT (DCNOT) gates in controlling chaos in noisy, memoryless channel 2. Finally, we show that the CNOT and DCNOT gates are more sensitive than the B-gate. These novel features of two-qubit entangling operators in correlated, noisy and dynamic market games shed new light on the role of SPEs in quantum dynamic game settings.Abstract Recent economic research has focused on applying quantum mechanical models to understand complex markets. Real markets are usually complex with nonlinear inverse demand functions and dynamic participants. Furthermore, when these market games are quantized, players interact via quantum channels that are prone to decoherence. In this work, owing to the complexity of real markets, we introduce noise and memory in a dynamic quantum Stackelberg duopoly game for the first time. We shed light on the significance of two-qubit entangling operators, particularly special perfect entanglers (SPEs), in controlling chaos. The following noteworthy observations are made: First, although entangling operators cannot prevent monopolies in the market, they can shift leader dominance to follower dominance. Second, numerical analysis highlights the significance of the B-gate in a correlated noisy channel as a chaos control. We also highlight the significance of the controlled-NOT (CNOT), and double-CNOT (DCNOT) gates in controlling chaos in noisy, memoryless channel 2. Finally, we show that the CNOT and DCNOT gates are more sensitive than the B-gate. These novel features of two-qubit entangling operators in correlated, noisy and dynamic market games shed new light on the role of SPEs in quantum dynamic game settings.

Physica ScriptaMay 7, 20254 citations

Chaos and Order in the Shell Model Eigenvectors

Vladimir Zelevinsky, Mihai Horoi, B. ALEX BROWN

The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the $J-T$ scheme for 12 particles in the $sd$ -shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the $J-T$ scheme for 12 particles in the $sd$-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.

arXiv:nucl-th/9405028May 30, 19940 citations

Magic moment

John Newton

The New ScientistFeb 1, 20090 citations

The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the

J-T

scheme for 12 particles in the

sd

-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.