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Dynamics of SU(1,1) coherent states for the time-dependent quadratic Hamiltonian system

Jeong Ryeol Choi

Optics CommunicationsJun 26, 200910 citations

Classical dynamics and ground-state phase transitions of a model SU(1,1) Hamiltonian

Christopher C. Gerry, Jerry Kiefer

We discuss the classical dynamics of a model SU(1,1) Hamiltonian system that may have some application in many-boson systems. A ground-state phase transition is shown to exist in this model, and the energy surface is shown to undergo a qualitative change at this transition.

Physical Review AJan 1, 199018 citations

Symmetries of Liouvillians of squeeze-driven parametric oscillators

FRANCESCO IACHELLO, Colin Coane, Jayameenakshi Venkatraman

Abstract We study the symmetries of the Liouville superoperator of one dimensional parametric oscillators, especially the so-called squeeze-driven Kerr oscillator, and discover a remarkable quasi-spin symmetry su(2) at integer values of the ratio η = ω / K of the detuning parameter ω to the Kerr coefficient K, which reflects the symmetry previously found for the Hamiltonian operator. We find that the Liouvillian of an su(2) representation | j , m j ⟩ has a characteristic double-ellipsoidal structure, and calculate the relaxation time T X for this structure. We then study the phase transitions of the Liouvillian which occur as a function of the parameters ξ = ε 2 / K and η = ω / K . Finally, we study the temperature dependence of the spectrum of eigenvalues of the Liouvillian. Our findings may have applications in the generation and stabilization of states of interest in quantum computing.Abstract We study the symmetries of the Liouville superoperator of one dimensional parametric oscillators, especially the so-called squeeze-driven Kerr oscillator, and discover a remarkable quasi-spin symmetry su(2) at integer values of the ratio η = ω / K of the detuning parameter ω to the Kerr coefficient K, which reflects the symmetry previously found for the Hamiltonian operator. We find that the Liouvillian of an su(2) representation | j , m j ⟩ has a characteristic double-ellipsoidal structure, and calculate the relaxation time T X for this structure. We then study the phase transitions of the Liouvillian which occur as a function of the parameters ξ = ε 2 / K and η = ω / K . Finally, we study the temperature dependence of the spectrum of eigenvalues of the Liouvillian. Our findings may have applications in the generation and stabilization of states of interest in quantum computing.

arXiv:2409.10744Journal of Physics A Mathematical and TheoreticalSep 13, 20245 citations

Time-dependent oscillators with asymptotically increasing mass: classical and coherent state dynamics

Serhat Fevzi Özeren

The European Physical Journal DNov 1, 20250 citations

Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model

Tomoki Nosaka, Tokiro Numasawa

Abstract We study various aspects of the mass deformation of the SYK model which makes the black hole microstates escapable. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of the mass deformed ground state under the SYK Hamiltonian. We give a gravity interpretation of the mass deformed ground state and its time evolutions. In gravity side, mass deformation gives a way to prepare black hole microstates that are similar to pure boundary state black holes. Escaping protocol on these ground states simply gives a global AdS2 with an IR end of the world brane. We also study the thermodynamics and quantum chaotic properties of this mass deformed SYK model. Interestingly, we do not observe the Hawking Page like phase transition in this model in spite of similarity of the Hamiltonian with eternal traversable wormhole model where we have the phase transition.Abstract We study various aspects of the mass deformation of the SYK model which makes the black hole microstates escapable. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of the mass deformed ground state under the SYK Hamiltonian. We give a gravity interpretation of the mass deformed ground state and its time evolutions. In gravity side, mass deformation gives a way to prepare black hole microstates that are similar to pure boundary state black holes. Escaping protocol on these ground states simply gives a global AdS2 with an IR end of the world brane. We also study the thermodynamics and quantum chaotic properties of this mass deformed SYK model. Interestingly, we do not observe the Hawking Page like phase transition in this model in spite of similarity of the Hamiltonian with eternal traversable wormhole model where we have the phase transition.

arXiv:1912.12302Journal of High Energy PhysicsAug 1, 202021 citations

Dynamic phase transition in the Heisenberg model under a time-dependent oscillating field

Zhigao Huang, Zhigao Chen, Fengming Zhang +1 more

Physics Letters AMar 16, 200511 citations

Ground-state phase transitions of a model SU(1,1) Hamiltonian driven by a time-dependent mass oscillator

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